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Mathematics Complete(All books Categorized)

2007-10-07T21:30:00.000-07:00

Mathematics Complete(All books Categorized)

Algebra :

A Computational Introduction To Number Theory And Algebra - Victor Shoups
A course in computational algebraic number theory - Cohen
A Course in Homological Algebra - P. Hilton, U. Stammbach
A Course In Universal Algebra - S. Burris and H.P. Sankappanavar
A First Course In Linear Algebra - Robert A. Beezer
A First Course in Noncommutative Rings - T. Lam
A Primer of Algebraic D-modules - S. Coutinho
Abel's Theorem in Problems and Solutions - V.B. Alekseev
Abstract Algebra - the Basic Graduate Year - R. Ash
Advanced Modern Algebra - Joseph J. Rotman
Algebra & Trigonometry Graphs & Models 3rd ed - Marvin L. Bittinger
Algebra Abstract - Robert B. Ash
Algebra Demystified - Rhonda Huettenmueller
Algebra I Basic Notions Of Algebra - Kostrikin A I , Shafarevich I R
Algebra Sucsess In 20 Minutes a Day - LearningExpress
Algebraic D-modules - A. Borel et. al
Algebraic Groups and Discontinuous Subgroups - A. Borel, G. Mostow
Algebraic Surfaces and Holomorphic Vector Bundles - R. Friedman
Algorithmic Algebra - B. Mishra
Algorithms for Computer Algebra - K. Geddes, S. Czapor, G. Labahn
An Elementary Approach to Homological Algebra - L. Vermani
An Introduction To Linear Algebra - Kenneth Kuttler
Applications of Abstract Algebra with MAPLE - R. Klima, N. Sigmon, E. Stitzinger
Applied Linear Algebra And Matrix Analysis - Thomas S. Shores
Applied Numerical Linear Algebra - James W. Demmel
Bialgebraic Structures - W. Kandasamy
Calculus approach to matrix eigenvalue algorithms - Hueper
Commutative Algebra 2nd ed. - H. Matsumura
Commutative Ring Theory - H. Matsumura
Compact Numerical Methods for Computers Linear Algebra and Function Minimisation 2Ed - Adam Hilger
Computational Commutative Algebra - Kreuzer and Robbiano
Computer Algebra and Differential Equations - E. Tournier
Determinants and Their Applications in Mathematical Physics - R. Vein, P. Dale
Differential Galois Theory - M. van der Put, M. Singer
Elementary Linear Algebra - K. R. MATTHEWS
Elements of Abstract and Linear Algebra - E. H. Connell
Fileds and Galois Theory [jnl article] - J. Milne
fundamental problems in algorithmic algebra - chee keng yap
Galois Theory 2nd ed. - E. Artin
Group Characters, Symmetric Functions and the Hecke Algebras - D. Goldschmidt
Handbook of Algebra Vol 1 - M. Hazewinkel
Handbook of Algebra Vol 2 - M. Hazewinkel
Hankel and Toeplitz Matrices and Forms - I. Iohvidov
Homotopical Algebra - D. Quillen
Intro Abstract Algera - P.Garret
Introduction to Commutative Algebra - M. Atiyah, I. Macdonald
Invitation to Higher Local Feilds - I. Fesenko, M. Kurihara
Lectures on Matrices - wedderburn
Linear Algebra - Jim Hefferon
Linear algebra 3ed - Greub, W.H
Linear Algebra And Its Applications - David C Lay
Linear Algebra and Its Applications 3e - Gilbert Strang
Linear Algebra and Multidimensional Geometry - R. Sharipov
LINEAR ALGEBRA and SMARANDACHE LINEAR ALGEBRA - w. b. vasantha kandasamy
Linear Algebra Done Right, 2nd Ed - Sheldon Axler
Linear Algebra Gateway to Mathematics - Robert Messer
Linear Algebra with Applications 3rd Edition - Nicholson, W. Keith
Linear Algebra, 2Nd Edition - Kenneth Hoffmann And Ray Kunze
Linear algebraic groups 2ed - Borel A
Logic and Boolean Algebra - Kathleen and Hilbert Levitz
Matrices Over Commutative Rings - W. Brown
Matrices theory and applications - Serre D.
Matrix Analysis & Applied Linear Algebra - Carl D Meyer
Matrix Theory - [jnl article] - T. Banks
Methods of Homological Algebra - S. Gelfand, Y. Manin
Modern Algebra With Applications 2Ed - Gilbert, Nicholson
Modern Computer Algebra - Von Zur Gathen, Gerhard
Operator Algebras and Quantum Statistical Mechanics V1 2nd ed. - O. Bratelli.djv
Operator Algebras and Quantum Statistical Mechanics V2 2nd ed. - O. Bratelli.djv
Polynomials and Polynomial Inequalities
Quadratic Forms and their Applications
Ring of Quotients - Introduction to Methods of Ring Theory - Bo Stenstrom
SCHAUM'S OUTLINE OF THEORY AND PROBLEMS OF LINEAR ALGEBRA Second Edition - SEYMOUR LIPSCHUTZ
Schemes - D. Eisenbud, J. Harris
SMARANDACHE FUZZY ALGEBRA - W. B. Vasantha Kandasamy
Smarandache Loops - W. Kandasamy
Smarandache Near-Rings - W. Kandasamy
Smarandache Rings - W. Kandasamy
Smarandache Semirings, Semifields,Semi Vector Spaces - W. Kandasamy
Structure and Representation of Jordan Algebras - N. Jacobson
The Algebraic Theory of Spinors and Clifford Algebras - C. Chevalley
The Theory Of Algebraic Numbers 2nd ed. - H. Pollard, H. Diamond
Toposes, Triples and Theories - M. Barr, W. Wells
Treatise on Quantum Clifford Algebras - Fauser
Vector Math for 3D Computer Graphics - Interactive Tutorial
Workbook in Higher Algebra - David Surowski

Code:

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http://www.rapidsafe.net/rc-QzMzgDOxcTM/Algebra.part2.rar
http://www.rapidsafe.net/rc-UjZzgDOxcTM/Algebra.part3.rar
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http://www.rapidsafe.net/rc-gDN2gDOxcTM/Algebra.part6.rar

Algebraic geometry :

Abelian Varieties - D. Mumford
Algebraic Curves and Riemann Surfaces - R. Miranda
Algebraic Geometry - D. Bump
Algebraic Geometry - Js Mine
Algebraic Geometry - R. Hartshorne
Algebraic geometry I-V - Shafarevich I.R
Algebraic Geometry I. From Algebraic Varieties to Schemes - K. Ueno
Combinatorial Convexity and Algebraic Geometry - G. Ewald
Commutative Algebra, with a View Toward Algebraic Geometry - D. Eisenbud
Computational Algebraic Geometry - F. Eyssette, A. Galligo
Current Trends in Arithmetical Algebraic Geometry - K. Ribet
Geometric Algebra - E. Artin.djv
Geometric Algebra and its Application to Mathematical Physics - C. Doran
Geometry of Algebraic Curves (vol 1) - E. Arabello, M. Cornalba, P. Griffiths, J. Harris
Introduction to Algebraic Geometry - Dolgachev
Mirror Symmetry and Algebraic Geometry - D. Cox, S. Katz
Moduli of Curves - J. Harris, I. Morrison
Positivity In Algebraic Geometry - R. Lazarsfeld
Real Algebraic Geometry - J. Bochnak, M. Coste, M. Roy
Zeta Functions, Introduction to Algebraic Geometry - Thomas

Code:

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http://www.rapidsafe.net/rc-cjNxgDOxcTM/Algebraic_geometry.part2.rar

Analysis :

A Course of Higher Mathematics vol 1 - V. Smirnov.djv
A Course of Higher Mathematics vol 2 - V. Smirnov.djv
A Course of Modern Analysis 4th ed. - E. Whittaker, G. Watson.djv
A Quick Introduction to Tensor Analysis - R. Sharipov
Acourse of pure mathematics - Hardy
Algebraic Numbers and Fourier Analysis - Salem
An Introduction to Complex Analysis for Engineers - M. Adler
An Introduction To Functional Analysis - Vitali Milman
An Introduction to Numerical Analysis for Electrical and Computer Engineers - Wiley
Analysis - Hyland
Analysis and Simulation of Chaotic Systems 2nd ed. - F. Hoppensteadt
Applied and Computational Complex Analysis Vol 1 - P. Henrici
Applied and Computational Complex Analysis Vol 2 - P. Henrici
Applied Nonlinear Analysis - A. Sequeira, H. da Vega, J. Videman.djv
Automorphic Forms on GL(2) - H. Jacquet, R. Langlands
Automorphic Forms, Representations and L-Functions Part 1 - A. Borel, W. Casselman
Automorphic Forms, Representations and L-Functions Part 2 - A. Borel, W. Casselman
Basic Analysis - K. Kuttler
Basic Elements of Real Analysis - M. Protter
Basic Math Conecpts - E. Zakon
Complex Analysis - Ahlfors
Complex Analysis - cain
Complex Analysis - K. Houston
Complex Analysis 2nd ed. - L. Alhford
Computer Analysis of Number Sequences - H. Ibstedt
Convex Analysis and Non Linear Optimization Theory and Examples - Borwein,Lewis
Differential Inequalities - J. Szarski.djv
Elementary Numerical Analysis An Algorithmic Approach, 3rd Ed - de Boor
Finite Element Analysis Theory and Application with ANSYS - S. Moaveni
Foundations of Algebra and Analysis - C. Dodge
Foundations of modern analysis - Friedman
Foundations of Real and Abstract Analysis - Axler , Gehring , Ribet
Fourier analysis on groups - Rudin, Walter
Fourier Theory - B. Clarke
Functional Analysis - K Yoshida
Functional Analysis - W. Rudin
Functional Analysis and Semi-Groups - E. Hille, R. Phillips
Functional Equations in a Single Variable - M. Kuczma.djv
Functional Operators, Vol.1 - Measures and Integrals - J. von Neumann
Functions of One Complex Variable 2nd ed. - J. Conway
Fundamental Numerical Methods and Data Analysis - G. W. Collins
Harmonic Analysis And Partial Differential Equations - B. Dahlberg, C. Kenig
Harmonic Analysis on Semisimple Lie Groups - V. Varadarajan.djv
Harmonic Analysis, Real Variable Methods Orthogonality & Oscillatory Integrals - Stein
Homeomorphisms in Analysis - C. Goffman, T. Nishiura, D. Waterman.djv
Integral Equations - A Practical Treatment - D. Porter, D. Stirling.djv
Integral Equations - H. Hochstadt.djv
Introduction to Complex Analysis - R. Nevanlinna, V. Paatero
Introduction to Complex Analysis Lecture notes - W. Chen
Introduction to Numerical Analysis 2 ed - J.Stoer,R.Bulirsch
Introduction To p-adic Numbers and p-adic Analysis - A. Baker
Introduction to the theory of Fourier's series and integrals 2ed- Carslaw H.S.
Introductory Real Analysis - A. Kolmogorov, S. Fomin
Manifolds, Tensor Analysis and Applications 3rd ed. - Marsden, Ratiu and Abraham
Mathematical analysis - Apostol T.M.
Mathematical Analysis - E. Zakon
Mathematical Methods of Engineering Analysis - E. Cinlar, R. Vanderbei
Mathematics of the Discrete Fourier Transform
Means of Hilbert Space Operators - F. Hiai, H. Kosaki
Measure And Integral an introduction to Real analysis - Wheeden and Zygmund,
Mixed Motives - M. Levine
Monotone Operators in Banach Space and Nonlinear partial differential equation - P. Showalter
Nonlinear System Theory - W. Rugh
Notions of Convexity - L. Hoermander
p-adic numbers, p-adic analysis, and zeta-functions 2nd ed. - N. Koblitz
Partial Differantial Equations and Fourier Analysis an Introduction - K. Tung
Principles and Applications of Tensor Analysis - M. Smith
Principles of Mathematical Analysis 3ed - Rudin W
Real And Complex Analysis International Student edn - W. Rudin
Real and complex analysis third edition - Rudin
Real Mathematical Analysis- Charles Chapman
Summation of Series 2nd rev. ed. - L. B. W. Jolley
The Elements of Real Analysis - R. Bartle
The Theory Of The Riemann Zeta-Function -Titshmarch
theory and Problems Of Fourier Analysis with Applications to Boundary value problems - Spiegel
Theory of Functions of a Real Variable - S. Sternberg
Vector and Tensor Analysis with Applications - A. Borisenko and I.Tarapov.djv

Code:

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http://www.rapidsafe.net/rc-Y2M4gDOxcTM/Analysis.part2.rar
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Applied mathematics :

A First Course On Wavelets - E. Hernandez, G. Weiss
Applied Mathematics - P. Oliver, C. Shakiban
Chaos Theory Tamed - G. Williams
Classification of Nuclear C-algebras - Entropy in Operator Algebras
Explaining Chaos - P. Smith
Fundamentals of Wavelets - Theory, Algorithms, and Applications - J. Goswami, A. Chan
Information Theory - R. Ash
Intro to the Math. and Stat. Foundations of Econometrics - H. Bierens
Introduction To Finite Mathematics, 3Rd Edition
Inverse Problem Theory and Methods for Model Parameter Estimation - A. Tarantola
Linear Programming - Foundation and Extensions 2nd ed. - R. vanderbei
Mathematics of Quantum Computation - Chen and Brylinski
Probabilistic Inference Using Markov Chain Monte Carlo Methods - R. Neal
Renormalization Groups - G. Benfatto, G. Gallavotti
The Mathematical Theory Of Cosmic Strings - M. Anderson
Theory and Problems of Finite Mathematics (Schaums Outlines) - S. Lipschutz

Code:

 http://www.rapidsafe.net/rc-QGMihDOxcTM/Applied_mathematics.part1.rar
http://www.rapidsafe.net/rc-kjMihDOxcTM/Applied_mathematics.part2.rar

calculus :

A Treatise On The Differential Calculus with numerous examples - Todd Hunter
Advanced Calculus - a Differential Forms Approach - H. Edwards
Advanced Calculus - Widder D.V.
Advanced Calculus 2Ed , 1990 - Loomis L H , Sternberg S
Advanced Calculus 2Nd Ed - wrede & Spiegel
Advanced Calculus 3rd Edition - Taylor Angus & Wiley.Fayez
Advanced Calculus and Analysis - Ian craw
Advanced Calculus fifth edition - Wilfred Kaplan
Advanced Calculus of real valued functions of real variable and vectored valued functions of a vector variable - Sagan
Advanced Calculus With Applications In Statistics - A Khuri
An introduction to the fractional calculus and fractional differential equations - Miller K.S., Ross B.
Calculus 5th Edition - James Stewart solution
Calculus 5th Edition - James Stewart
Calculus Bible
Calculus Concepts and Contexts 2nd Ed - James Stewart
Calculus Demystified - Krantz
Calculus for the Clueless - Calc.I - Bob Miller's
Calculus for the Clueless, Calc II - Bob Millers
Calculus For The Utterly Confused - Oman
CALCULUS OF FINITE DIFFERENCES - jordan
Calculus of Variations & Optimal Control - Sasane
Calculus of Variations & Solution Manual - Russak
Calculus Of Variations, With Applications To Physics And Engineering - Weinstock R
Calculus on manifolds - Spivak, M.
Calculus With Complex Numbers - Read
Calculus Workbook For Dummies - Mark Ryan
Calculus, applications and theory - K Kuttler
Derivatives and Integrals Chart (basic)
Dictionary of analysis, calculus, and differential equations - Gibilisco
Differential Forms, a Complement to Vector Calculus - S. Weintraub
Elementary calculus an infinitesimal approach 2ed - Keisler H.J.
Elementary Textbook on the Calculus - Snyder
Foundations Of Differential Calculus - Euler
Foundations Of Infinitesimal Calculus 2nd ed. - K. Stroyan
From Calculus to Chaos - D. Acheson
Functional Calculus of Pseudo-Differential Boundary Problems - Birkhauser
Geometric Approach to Differential Forms - D. Bachman
Handbook Of Integral Equations - A. Polyanin, A. Manzhirov
How To Solve Word Problems In Calculus - Don
INTRODUCTION TO THE CALCULUS OF VARIATIONS - Bernard Dacorogna
Introduction To The Calculus Of Variations - Byerly 1917
Master Math Pre-Calculus And Geometry - Debra Ross
Mathematical Background Foundations of Infinitesimal Calculus 2nd Ed - K. D. Stroyan
Mlulti Variable Calculus and Linear Algebra, with Applications to DifFeren tial Equations and Probability SECOND EDITION - Apostol
Multivariate Calculus - Alder
On the Shoulders of Giants A Course in Single Variable Calculus - Smith & Mcleland
One-Variable Calculus, with an Introduction to Linear Algebra SECOND EDITION vol I - Apostol
Quantum calculus - Kac V. & Cheung P.
Rings of Differential Operators - J. Bjoerk.djv
Ryerson Calculus & Advanced Functions - McGraw-Hill
Selected Chapters In The Calculus Of Variations - Moser J
The Fractional Calculus Theory And Applications Of Differentiation And Integration To Arbitrary Order - Oldham K B , Spanier J
Theory and Problems of ADVANCED CALCULUS Second Edition - WREDE & SPIEGE
Theory and Problems of Beginning Calculus Second Edition - Elliott Mendelson
THEORY AND PROBLEMS OF DIFFERENTIAL AND INTEGRAL CALCULUS Third Edition - AYRES & MENDELSON
Vector Calculus - Theodore Voronov

Code:

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http://www.rapidsafe.net/rc-YDZjhDOxcTM/calculus.part2.rar
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CRC Concise Encyclopedia of Mathematics :

CRC Concise Encyclopedia of Mathematics [part 1 of 4] - E. Weisstein
CRC Concise Encyclopedia of Mathematics [part 2 of 4] - E. Weisstein
CRC Concise Encyclopedia of Mathematics [part 3 of 4] - E. Weisstein
CRC Concise Encyclopedia of Mathematics [part 4 of 4] - E. Weisstein

Code:

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http://www.rapidsafe.net/rc-kzYxkDOxcTM/CRC_Concise_Encyclopedia_of_Mathematics.part2.rar
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http://www.rapidsafe.net/rc-UmYykDOxcTM/CRC_Concise_Encyclopedia_of_Mathematics.part4.rar

Cryptography :

Applied Cryptography 2nd ed. - B. Schneier
Cryptography Theory And Practice - Douglas Stinson.chm
Guide to Elliptic Curve Cryptography - D. Hankerson, A. Menezes, S. Vanstone
Handbook of Applied Cryptography - A. Menezes, P. VanOorschot, S. Vanstone
Modern Cryptography Theory And Practice - Wenbo Mao

Code:

http://rapidshare.com/files/44900223/Cryptography.rar

Differential Algebra :

Differential Algebra - Joseph Ritt
Differential Algebra and Algebraic Groups - E. Kolchin
Differential Algebra and Diophantine Geometry - A. Buium
Differential Algebraic Groups - E. Kolchin
Differential Algebraic Groups of Finite Dimension - A. Buium
Differential Function Fields and Moduli of Algebraic Varieties - A. Buium

Code:

http://rapidshare.com/files/44900294/Differential_Algebra.rar

Differential Geometry :

An Introduction To Differential Geometry With Use Of Tensor Calculus - Eisenhart L P.djv
Classical differential geometry of curves and surfaces - Varliron G.
Complex Analytic and Differential Geometry - J. Demailly
Complex Analytic Differential Geometry - Demailly
Course of Differential Geometry - R. Sharipov
Differential and Physical Geometry - J. Lee
Differential Geometry in Physics - G. Lugo (
Foundations Differential Geometry - Michor
Foundations of Differential Geometry - P. Michor
Foundations of Differential Geometry vol 1 - Kobayashi, Nomizu
Intro to Differential Geometry and General Relativity - S. Warner
Introduction to Differential Geometry & General Relativity - waner
Lectures on Differential Geometry - S. Chen, W. Chen, K. Lam
Minkowski Geometry - A. Thompson
Modern Differential Geometry for Physicists 2nd ed. - C. Isham
Natural Operations in Differential Geometry - Ivan ,Peter, Jan

Code:

http://rapidshare.com/files/44900475/Differential_Geometry.rar

differentials equations :

A First Course in Partial Differential Equations with complex variables and transform methods - H. Weinberger
A Treatise on Differential Equations 2nd ed. - A. Forsyth.djv
An Introduction to MultiGrid Methods - P. Wesseling
Difference Equations and Inequalities - Theory, Methods, and Applications 2nd ed. - P. Agarwal.djv
Differential Equations Crash Course - R. Bronson
Differential Equations From the Group Standpoint - L. Dickson.djv
Differential Equations with Mathematica - M. Abell, J. Braselton
Differential Equations, Dynamical Systems and Linear Algebra - M. Hirsch, S. Smale.djv
Differential Subordinations, Theory and Applications - S. Miller, P. Mocanu.djv
Elementary Differential Equations and boundry value problems 7th ed. - W. Boyce, R. Diprima
Exterior Diff Systems And Euler-Lagrange Partial Diff Eqns - Bryant, Griffiths and Grossman
Galois Theory of Linear Differential Equations - M. van der Put, M. Singer
Generalized Difference Methods for Differential Equations - R. Li, Z. Chen, W. Wu
Hilbert Space Methods For Partial Differential Equations - R. Showalter
Introduction to Partial Differential Equations - A Computational Approach - A. Tveito, R. Winther
Introduction to Stochastic Differential Equations v1.2 (Berkeley lecture notes) - L. Evans
Introduction To Tensor Calculus & Continuum Mechanics - J. Heinbockel
Linear Diff Eqns in the Complex Domain - Problems of Analytic Continuation Y. Sibuya.djv
Mesh-free Methods - Moving Beyond Finite Element Methods - G. Liu
Nonlinear Analysis & Differential Equations, An Introduction - Schmitt & Thompson
Nonlinear Partial Differential Equations - G. Chen, E. DiBenedetto.djv
Numerical Methods for Ordinary Differential Equations - J.C. Butcher
Numerical Methods for Partial Differential Equations 2nd ed. - W. Ames
Ordinary Differential Equations - P. Hartman.djv
Ordinary Differential Equations - V. Arnold.djv
Ordinary Differential Equations and Dynamical Systems - G. Teschl
Ordinary Differential Equations, with Intro to Lie Theory - J. Page
Partial Differential Equations - L. Evans
Partial Differential Equations and Mathematica - P. Kythe
Partial differential equations and the finite element method - Pave1 Solin
Partial Differential Equations Vol 1 - Basic Theory - M. Taylor.djv
Partial Differential Equations Vol 2 - Qualitative Studies of Linear Equations - M. Taylor.djv
Partial Differential Equations Vol 3 - Nonlinear Equations - M. Taylor.djv
Partial Differential Equations, (MA3132 lecture notes) - B. Neta (
Singular Perturbation Theory - Math and Analyt Technique w. appl to Engineering - R. Johnson
Stochastic Differential Equations 5th ed. - B. Oksendal
The Qualitative Theory of Ordinary Diff. Equations - F. Brauer, H. Nohel

Code:

http://rapidshare.com/files/44900857/differentials_equations.part1.rar
http://rapidshare.com/files/44901173/differentials_equations.part2.rar

Discrete Mathematics :

A First Course in Discrete Mathematics 2nd ed - ANdersonn
Advanced Combinatorics (revised) - L. Comtet
Algorithm theory - Penttonen,Meineche
Algorithms - R. Sedgewick
Algorithms and Complexity - wilf
Combinatorics - Topics, Techniques and Algorithms - P. Cameron
Combinatorics 2nd ed. - R. Merris
Concrete Mathematics - R. Graham, D. Knuth, O. Patashnik
Discrete Math in Computer Science - Bogart , Stein
Discrete Mathematics - Chen
Discrete Mathematics - Yale
Discrete Mathematics And Its Applications 4Th Ed - Rosen
Discrete Mathematics for New Technology Second Edition - Garnier , Taylor
Generatingfunctionology - H. Wilf
Handbook of Combinatorics Vol 2 - R. Graham, M. Grotschel, L. Lovasz
Handbook of discrete and combinatorial mathematics - Crc Press
Introduction to Algorithms 2nd ed. - MIT Faculty
Introduction to Genetic Algorithms for Scientists and Engineers - D. Coley
Monte Carlo Concepts, Algorithms and Applications - G. Fishman
Probabilistic methods in algorithmic discrete mathematics - Springer
Representations for Genetic and Evolutionary Algorithms 2nd ed. - F. Rothlauf

Code:

http://rapidshare.com/files/44901497/Discrete_Mathematics.part1.rar
http://rapidshare.com/files/44901568/Discrete_Mathematics.part2.rar

Dynamical Systems :

Dynamical Systems - G. Birkhoff
Dynamical Systems and Fractals - Computer Graphics Exper. in Pascal - K. Becker, M. Dorfler
Elementary Catastrophe Theory - P. Michor

Code:

http://rapidshare.com/files/44901608/Dynamical_Systems.rar

Encyclopedia of Mathematics - Gale Group :

Encyclopedia of Mathematics - Gale Group (Vol.1 Ab-Cy)
Encyclopedia of Mathematics - Gale Group (Vol.2 Da-Lo)
Encyclopedia of Mathematics - Gale Group (Vol.3 Ma-Ro)
Encyclopedia of Mathematics - Gale Group (Vol.4 Sc-Ze)

Code:

http://rapidshare.com/files/44901643/Encyclopedia_of_Mathematics_-_Gale_Group.rar

Fun :

Abel's Proof - Essay on the Sources and Meaning of Mathematical Unsolvability - P. Pesic
Breakthroughs in Mathematics - P. Wolff
Math Wonders to Inspire Teachers and Students
Prime Numbers - The Most Mysterious Figures in Math
The Art of the Infinite - The Pleasures of Math
The Riemann Hypothesis The Greatest Unsolved Problem in Mathematics . - J. Derbyshire.djv
Wiley Mathematical Journeys

Code:

http://rapidshare.com/files/44902052/Fun.rar

Geometry :

Euclid's Elements
Algebraic geometry a first course - Harris.J
Computational Geometry algorithms and applications 2d ed - De berg
Computational Geometry in C - J o'orourk
Computational Geometry Methods And Applications - chen
Conceptual Spaces The Geometry Of Thought - Gardenfors.chm
Exploring Analytic Geometry with Mathematica - D. Vossler
Exploring analytic geometry with Mathematica - Vossler
Fractal Geometry Mathematical Foundations & Applications - Falconer
Fundamentals of College Geometry 2nd ed. - E. M. Hemmerling
Fundamentals of Mathematics Vol.2, Geometry - Behnke, Bachmann
Geometric Models for Noncummutative Algebras - A.da Silva, A. Weinstein
Geometry Asymptotics - Guillemin,Sternberg
Glimpses of Algebra and Geometry, 2nd Edition - Verlag
Handbook of discrete and computational geometry and its applications - Rosen
Introduction to geometry 2ed - coxeter
Introduction to Lie groups and symplectic geometry - Bryant R.L.
Mirrors and Reflections- The Geometry of Finite Reflection Groups - A. Borovik, A. Borovik
Non-Euclidean Geometry 6th ed. - H.S.M. Coxeter
Plane Analytic Geometry With Differential Calculus - Maxime Bocher
Sphere Packings - C. Zong
The Geometry & Topology of 3-Manifold - Thurston
The Geometry of Hamilton and Lagrange Spaces - Miron, Hrimiuc, Shimara, Sabau.
The Geometry of Schemes - Eisenbud D., J.Harris.
Treatise of plane geometry through geometric algebra - Calvet R.G. -

Code:

http://rapidshare.com/files/44902383/Geometry.part1.rar
http://rapidshare.com/files/44902692/Geometry.part2.rar
http://rapidshare.com/files/44903074/Geometry.part3.rar
http://rapidshare.com/files/44903102/Geometry.part4.rar

Graph Theory :

Graph Theory - R. Diestel
Graph Theory With Applications - J. Bondy, U. Murty

Code:

http://rapidshare.com/files/44903232/Graph_Theory.rar

Group Theory :

Planar Graph Drawing - T. Nishizeki, M. Rahman
Abstract Theory of Groups - O. Schmidt
An Elementary Introduction to Groups and Representations - B. Hall
Buildings and Classical Groups - P. Garrett
Cohomological Topics in Group Theory - K. Gruenberg
Galois Theory 2nd ed. - E. Artin
Group Theory (Lie's, Tracks and Exceptional Groups) - P. Cvitanovic
Group Theory Exceptional Lie Groups As Invariance Groups - P. Cvitanovic
Group Theory [jnl article] - J. Milne
Groupoids. and Smarandache Groupoids - W. Kandasamy
Introduction To Groups, Invariants and Particles
Introduction to the Theory of Groups - G. Polites
Isometric Actions of Lie Groups and Invariants [jnl article] - P. Michor
Lectures on Lie Groups - D. Milicic
Lie Algebras - S. Sternberg
Linear Algebraic Groups - A. Borel
Problems in Group Theory - J. Dixon
Quantum Groups and Knot Algebra - T. Dieck
Representation Theory - A First Course - W. Fulton, J. Harris
Representation Theory of Lie groups - M. Atiyah et al.
Smarandache Semigroups - W. Kandasamy
The Classification of the Finite Simple Groups - D. Greenstein, R. Lyons, R. Solomon
The Theory of Groups - H. Bechtell
the Theory of Groups 2nd ed. Vol.1 - A. Kurosh
Theory Of Groups of Finite Order - W. Burnside

Code:

http://rapidshare.com/files/44903594/Group_Theory.rar

Math For Engineers :

Advanced Mathematical Methods for Scientists and Engineers - C. Bender, S. Orszag.djv
CRC Press - Dictionary of Applied Math for Engineers and Scientists - D. Clark
CRC Press - Elem. Math. and Comp. Tools for Engineers using MATLAB - J. Manassah
Engineering Mathematics 4th ed. - J. Bird
Essential Math Skills for Engineering, Science and Appl Math - S. Barry, S. Davis.djv
Intro to Methods of Appl. Math - Adv Math Methods for Scientists and Engineers - S. Mauch
Math - Functional and Structural Tensor Analysis for Engineers - Brannon
Math methods in physics and engineering with Mathematica - F. Cap
Math. and Phys. Data - Equations and Rules of Thumb - S. Gibilisco
Mathematical Methods of Classical Mechanics, 2nd ed., - V. I. Arnold
Mathematics for Electrical Engineering and Computing - M. Attenborough
Mathematics of Quantum Computation - G. Chen, R. Brylinski (eds)
Methods of Mathematical Physics Vol 3 - Scattering Theory - M. Reed

Code:

http://rapidshare.com/files/44904063/Math_For_Engineers.rar

Number theory :
A Computational Introduction to Number Theory and Algebra - Victor Shoup
A Concise Introduction to the Theory of Numbers- Baker A.
A Course in Arithmetic (graduate level) - J. Serre
A course in computational algebraic number theory - Cohen H.
A Course in Number Theory and Cryptography 2 ed - Neal Koblitz
A Course In Number Theory And Cryptography 2Ed - Koblitz N
Advanced Number Theory - Cohn
Algebra and number theory - Baker A.
Algebraic Groups and Number Theory - Platonov & Rapinchuk
Algebraic Number Theory - IYANAGA
ALGEBRAIC NUMBER THEORY - MILNE
Algorithmic Methods In Algebra And Number Theory - Pohst M
Algorithmic number theory - Cohen H.
Algorithmic number theory, vol. 1 Efficient algorithms - Bach E., Shallit J.
An Explicit Approach To Elementary Number Theory - stein
An Introduction to Conformal Field Theory [jnl article] - M. Gaberdiel
AN INTRODUCTION TO THE THEORY OF NUMBERS - hardy & wright
An Introduction to the Theory of Numbers - Leo Moser
An introduction to the theory of numbers 5ed - Niven I., Zuckerman H.S., Montgomery H.L.
Analytic number theory - Iwaniec H.,Kowalski E.
Analytic Number Theory - Newman D.J.
Analytic Number Theory- Jia & Matsumoto
Arithmetic Theory of Elliptic Curves - J. Coates
Computational Algebraic Number Theory - Pohst M E
Computational excursions in analysis and number theory - Borwein P.
Contributions to the Founding of the Theory of Transfinite Numbers - Georg Cantor
Definitions, Solved And Unsolved Problems, Conjectures and Theorems, In Number Theory And Geometry - Smarandache F
Elementary Methods in Number Theory - Nathanson M.B
Elementary Number Theory - Clark
Elementary Number Theory - David M. Burton
Elementary Number Theory And Primality Tests
Elementary Number Theory Notes - santos
Elementary theory of numbers - Sierpinski W.
Elliptic Curves - Notes for Math 679 - J. Milne, U. Michigan
Elliptic Curves 2nd ed. - D. Husemoeller
Geometric Theorems, Diophantine Equations and Arithmetic Functions - J. Sandor
History of the theory of numbers Vol.2. - Dickson L.E.
Introduction To Analytic Number Theory - Apostol
Introduction to Modern Number Theory Fundamental Problems, Ideas and Theories 2nd Edition - Manin I., Panchishkin A
Introduction to p-adic numbers and valuation theory- Bachman G.
Introduction to the Theory of Numbers 4th ed. - G. Hardy, E. Wright
Lectures on topics in algebraic number theory - Ghorpade
Mainly Natural Numbers - Studies on Sequences - H. Ibstedt
Math. problems and proofs combinatorics, number theory and geometry - B. Kisacanin
Mathematical Problems And Proofs Combinatorics, Number Theory, and Geometry - Kluwer Academic
My Numbers, My Friends - Popular Lectures on Number Theory
My Numbers,My Friends Popular Lectures On Number Theory - Ribenboim
Number Theory - Z.Borevitch, I. Shafarevich
Number theory for beginners - Weil A.
Number theory for computing - Yan S Y.
Numerical Mathematics - A. Quarteroni, A. Sacco, F. Saleri
Numerical Methods for Engineers and Scientists 2nd ed. - J. Hoffman
Numerical Optimization - J. Nocedal, S. Wright
Numerical Recipes in C - The Art Of Scientific Computing 2nd ed.
Numerical Recipes in Fortran 77 2nd ed. Vol 1
Old And New Problems And Results In Combinatorial Number Theory - Erdos, P.&Graham, R.L
Only Problems Not Solutions - F. Smarandache
Prime Numbers The Most Mysterious Figures in Math - D. Wells
Problems In Algebraic Number Theory 2Ed - Murty M , Esmonde J
SOlved and unsolved problems in Number Theory - Daniel Shanks
Surfing on the Ocean of Numbers - H. Ibstedt
Survey Of Diophantine Geometry - Serge Lang
The elements of the theory of algebraic numbers - Hilbert.djv
The Foundations of Arithmetic 2nd ed. revised - G. Frege
The New Book Of Prime Number Records 3rd ed. - P. Ribenboim
The Theory of algebraic numbers sec ed - Pollard H., Diamond H.G.
the theory of functions and sets of natural numbers - Odifreddi, P
Three Pearls of Number Theory - Khinchin
Transcendental number theory - Baker A.
Unsolved Problems In Number Theory 2 Ed - R K Guy.djv

Code:

http://rapidshare.com/files/44904459/Number_theory.part1.rar
http://rapidshare.com/files/44904770/Number_theory.part2.rar
http://rapidshare.com/files/44905184/Number_theory.part3.rar
http://rapidshare.com/files/44905529/Number_theory.part4.rar

Probability and statistics :

A Course In Probability Theory - Chung K L
An Introduction to Probability Theory - Geiss
An Introduction to Probability Theory and its Applications Vol I - Feller W.
Applied Bayesian Modelling - P. Congdon
Applied Probability - Lange K.
Applied Probability and Stochastic Processes - Bryc
Applied Statistics And Probability For Engineers - Montgomery && Runger
Applied Statistics And Probability For Engineers solution - Montgomery && Runger
CRC - standard probability and Statistics tables and formulae - DANIEL ZWILLINGER
Foundations of Modern Probability - Olav Kallenberg
Foundations of the Theory of Probability - A.N. KOLMOGOROV
Fundamentals of Probability and Statistics for Engineers - T T Soong
Introduction to Mathematical Statistics 6th ed. - P. Hoel
Introduction To Probability - Dimitri Bertsekas And John N Tsitsiklis
Introduction to Probability - Grinstead & Snell
Introduction to Probability 2nd Ed - C M Grinstead & J L Snell
Introduction To Probability Models Sixth Ed -Sheldon M ross
Introduction to Statistical Pattern Recognition 2nd ed. - K. Fukunaga
Lectures on Probability Theory and Statistics - Jean Picard
Markov Random Fields And Their Applications - kinderman & snell
Mathematics, Pre-Calculus and Introduction to Probability
Measure Integral & Probability - Capinski & Kopp
Multivariable Bayesian Statistics - D. Rowe.djv
Probability and Finance It's only a game
Probability and its applications - Ollav Kallenberg
Probability and measurements - Tarantola A.
Probability And Statistical Inference - NITIS MUKHOPADHYAY
Probability Demystified - bluman
Probability Theory and Examples second edition - Durrett R
Probability Theory The Logic Of Science - E. T. Jaynes
Probability, random processes and ergodic properties - Gray
Probability, Random Processes, and Ergodic Properties - R. Gray
Probability, Random Variables and Random Signal Principles 2nd ed. - P. Peebles
Probability, Random Variables and Stochastic Processes 3rd ed- Papoulis
Radically Elementary Probability Theory - edward Nelson
Recent Advances in Applied Probability - Springer
Schaum's Outlines - Theory and Problems of Statistics 3rd ed. - M. Spiegel, L. Stephens
Six Sigma and Beyond Statistics and Probability, Volume III - satamtis.chm
Statistics and Probability for Engineering Applications With Microsoft® Excel - W.J. DeCoursey
Statistics for Dummies - D. Rumsey.chm
Statistics Hacks - B. Frey.chm
The Basic Practice of Statistics 3rd ed. - D. S. Moore
Theory and problems of probability - Lipschutz, Seymour
Theory and Problems of Probability, Random Variables, and Random Processes - Hwei P. Hsu
Tutorials in Probability

Code:

http://rapidshare.com/files/44905747/Probability_and_statistics.part1.rar
http://rapidshare.com/files/44906021/Probability_and_statistics.part2.rar
http://rapidshare.com/files/44906356/Probability_and_statistics.part3.rar
http://rapidshare.com/files/44906501/Probability_and_statistics.part4.rar

Ramanujan's Notebooks :

Ramanujan's Notebooks vol 1 - B. Berndt.djv
Ramanujan's Notebooks vol 2 - B. Berndt.djv
Ramanujan's Notebooks vol 3 - B. Berndt.djv
Ramanujan's Notebooks vol 4 - B. Berndt.djv
Ramanujan's Notebooks vol 5 - B. Berndt.djv

Code:

http://rapidshare.com/files/44906638/Ramanujan_s_Notebooks.rar

Topology :

A concise course in algebraic topology - May J.P.
A Panoramic View of Riemannian Geometry - M. Berger
Algebraic Topology A Computational Approach - Kaczynski , Mischaikow , Mrozek
Algebraic Topology - A. Hatcher
Algebraic Topology - S. Lefschetz
Algebraic Topology an Intuitive Approach - H. Sato
Algebraic Topology From A Homotopical Viewpoint - SPringer
Cohomology of Arithmetic Groups, L-Functions and Automorphic - T. Venkatamarana
Counterexamples In Topology - Steen , Seebach
Curvature and Homology, Revised Ed. - S. Goldberg
differential topology - Dundas
Differential Topology - Morris
Elementary Concepts In Topology - P. Alexandroff
Elementary topology a first course - Viro, Ivanov
general topology - muller
Geometry and Topology of 3-Manifolds - W. Thurston
Index Theory, Coarse Geometry, and Topology of Manifolds - J. Roe
Intorduction to Topology and Modern Analysis - G. Simmons
Introduction to Algebraic Topology and Algebraic Geometry - U. Bruzzo
Introduction to Differential Topology - Brin
Introduction to Smooth Manifolds - J. Lee
K-theory for Operator Algebras 2nd ed. - B. Blackadar
Lecture Notes On Elementary Topology And Geometry - Singer,Thorpe
Lectures on Algebraic Topology 2nd ed. - A. Dold
Notes on basic 3-manifold topology - Hatcher, Allen
Notes On The Topology Of Complex Singularities - Nicolaescu
Open Problems In Topology-Jan Van Hill, George Reed
Operator algebras and topology - Schick
Riemannian Geometry - M. doCarmo
Riemannian Geometry, a Beginners Guide - F. Morgan
Theory and problems of general topology - Lipschutz, Seymour
Topics In Topology And Homotopy Theory - Warner
topology 2Ed - James Munkres
Topology & Sobolev Spaces - Brezis
topology - Yan
Topology and functional analysis - Driver
Topology Course lecture notes - A. McCluskey, B. McMaster
Topology for Computing - ZOMORODIAN
Topology Lecture Notes - Ward, Thomas
Topology Without Tears - SIDNEY A. MORRIS
Vector Bundles and K-Theory - A. hatcher

Code:

http://rapidshare.com/files/44907028/Topology.part1.rar
http://rapidshare.com/files/44908748/Topology.part2.rar
http://rapidshare.com/files/44908814/Topology.part3.rar

useful :

Daves Math Tables
Dictionary of Algebra, Arithmetic and Trigonometry - S. Krantz
Dictionary of Classical and Theoretical Mathematics
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables - M. Abramowitz, I. Stegun
McGraw Hill Mastering Technical Mathematics 2Ed
Real Analysis, Quantitative Topology, and Geometric Complexity - S. Semmes
Schaum's Mathematical Handbook of Formulas and Tables - Murray R Spiegel
Standard Mathematical Tables and Formulae 31st Edition - Zwillinger
Tables of Integrals and Other Math. Data 3rd ed. - H. Dwight
The Seven Famous Unsolved Math Puzzles
Well-Posed Linear Systems - O. Staffans

Code:

http://rapidshare.com/files/44909216/useful.rar

Ready to return~

2007-08-13T08:30:00.001-07:00

QT fucking Hell

2007-05-13T02:40:00.000-07:00

Qt4 with Visual Studio

From qtnode

Contrary to popular belief, you can use Qt4 with Visual Studio to create Open Source software. These instructions are for Qt 4.2.3

[NEW] unable to compile any Qt4 app ? see how to fix the bug that appears after installing service pack1 or .NET Framwork 3.0 click here ( trolltech post http://lists.trolltech.com/qt-intere...ad00584-0.html )

[hide]

[edit]

Building Qt

[edit]

Obtain and install the Qt source

To start, download the source package: Download Qt (Be sure to download the source package, not the package that installs MinGW. The source package is a .zip file, whereas the binary package for use with MinGW is an executable.)
Unzip your Qt source to a logical location.
Here are some suggestions:
C:\Qt\4.2\
C:\Qt\4.2-msvc2005\ (<-- if for instance you plan on using Visual Studio 2005)

[edit]

Download and install the patch allowing Qt to be compiled with Visual Studio compilers

Download acs-4.2.3-patch1.zip from sourceforge.net.
Unzip the contents of acs-4.2.3-patch1.zip into the directory that you have unzipped the Qt sources.

[edit]

Open a command prompt in the Qt source directory

Run cmd.exe however you prefer, but you must make sure that the Visual Studio compiler files are in your path.

If you want to build Qt as a 64-bit library under Windows, all you need to do is use the 64-bit Command Prompt supplied with the Visual Studio Tools.
If you are using Microsoft Visual Studio 6.0, try running vcvars32.bat from the command-line.
If you are using Microsoft Visual Studio .NET or 2005, go into the program group called 'Visual Studio Tools' and run the command prompt shortcut.
- Note for Visual C++ 2005 Express users (this may also apply to the non-express version) : make sure you installed the Platform SDK. Step 3 of the Platform SDK installation describes how to add paths to Visual C++. However, you also have to manually add those paths in your environment in order to compile Qt. Here is what you can do before launching the command prompt:
  - Add the three paths (LIB, INCLUDE and PATH) to your vsvars32.bat file, normally found under C:\Program Files\Microsoft Visual Studio 8\Common7\Tools. For example:

@set INCLUDE=C:\Program Files\Microsoft Visual Studio 8\VC\INCLUDE;%INCLUDE%

would become

@set INCLUDE=C:\Program Files\Microsoft Platform SDK for Windows Server 2003 R2\Include;

C:\Program Files\Microsoft Visual Studio 8\VC\INCLUDE;%INCLUDE%

A simple way to ensure your environment is setup properly is to see if nmake.exe is in your path:

C:\Qt\4.2> nmake /?

Microsoft (R) Program Maintenance Utility Version 8.00.50727.42
Copyright (C) Microsoft Corporation.  All rights reserved.

Usage:  NMAKE @commandfile
       NMAKE [options] [/f makefile] [/x stderrfile] [macrodefs] [targets]

Options:

....

Once you are sure that you have the Visual Studio compiler in your path and you're at the command prompt in the Qt source directory, you are ready to proceed.

[edit]

Patching the Qt sources

If you have installed the patch files from acs-4.2.2-patch1.zip correctly, then you should be able to patch the Qt sources by running:

C:\Qt\4.2> installpatch42.bat

You should see a lot of action, which is normal, which shows all of the files that are being patched:

C:\Qt\4.2> installpatch42.bat
patching file qconfigure.bat
patching file examples/threads/waitconditions/waitconditions.pro
patching file misc/bcc32pch/Makefile.win32-borland
patching file misc/bcc32pch/bcc32pch.cpp
patching file misc/bcc32pch/bcc32pch.pri
patching file misc/bcc32pch/bcc32pch.pro
patching file mkspecs/win32-bccx/qmake.conf

   [snip]

patching file tools/porting/src/rpptreeevaluator.cpp
patching file tools/porting/src/rpptreewalker.cpp
patching file tools/porting/src/src.pro
Press any key to continue . . .
Now run qconfigure.bat

You are now ready for the next step: configuring your Qt install.

[edit]

Configuring your Qt install (and building `qmake`)

We will not use the standard configure.exe that ships with Qt. We will use qconfigure.bat, included with the acs-4.2.2-patch1.zip file.

But, if you are not sure about which options you want, run configure.exe with the --help option:

configure.exe  --help

A list of options will be displayed. Take note of any options that you are interested in. Note that by default, static and debug versions of the library are built - this is usually the appropriate choice for most developers.

Once you have written down (or mentally noted) which options you will use, we will run qconfigure.bat. It will in turn call configure.exe with your chosen options.

qconfigure.bat requires as the first parameter, one of the following compiler choices:

msvc <- if you are using Visual Studio 6.0
msvc.net <- if you are using Visual Studio .NET (2003)
msvc2005 <- if you are using Visual Studio 2005

After the first option, you can pass qconfigure.bat any of the configure.exe you had previously noted. For instance you might type:

C:\Qt\4.2> qconfigure.bat msvc.net -release -no-stl

(This command would produce only the release libraries and would exclude STL support in Qt.)

(Note that if you want to build static libraries instead of shared, see Building static)

You will be prompted 3 times while running qconfigure.bat:

You will be asked to accept the GPL license. Type 'y' followed by to continue.
You will then be informed that qmake is about to be built. Type 'y' followed by to continue. This will take a few moments.
You will then be informed that the Makefiles will be generated. Type 'y' followed by to continue. This will be a short operation.

Once qconfigure.bat has finished, you will be presented with the following message:

====================================================

You are now ready to build Qt (msvc2005)

If you specified -static, type 'nmake sub-src'
              otherwise, type 'nmake'

To start over, type 'nmake distclean'
and then re-run qconfigure.bat

====================================================

You may run into this bug if you're using Visual Studio 2005 SP1.

[edit]

Building the Qt library

Once configuration and building qmake are completed, you are now ready to build the library. Simply run nmake:

C:\Qt\4.2> nmake

Qt takes a long time to compile. Now is a good time to brew a pot of coffee.

(If you have specified -static as one of your configuration options, see Building static)

[edit]

Setting up your environment

There are multiple approaches to this, but this is a foolproof way to ensure that your newly create Qt libs are usable.

Prepend the Qt bin directory to your PATH. Depending on where you installed your Qt sources, the full path may be similar to:

C:\Qt\4.2\bin
C:\Qt\4.2-msvc2005\bin
C:\Qt\4.2-visual-studio\bin

Ensure that the QMAKESPEC environment variable is set to the appropriate value.

If you use Visual Studio 6.0, then win32-msvc is the correct value.
If you use Visual Studio .NET (2003), then win32-msvc.net is the correct value.
If you use Visual Studio 2005, then win32-msvc2005 is the correct value.

(Note: this is the recommended practice from qtnode. You can use Qt in other ways with different settings, but this way is foolproof.)

To set your environment variables in Windows, please see http://www.cs.usask.ca/grads/wew036/latex/env.html

Note that you may have to re-open a command window before your settings are changed.

To check that your PATH is set correctly:

C:\> qmake -v
QMake version: 2.01a
Using Qt version 4.2 in C:\Qt\4.2\lib

To see if QMAKESPEC is set correctly:

C:\> echo %QMAKESPEC%
win32-msvc2005

[edit]

Testing your install

Please test your install from the command-line first. Follow the Hello World instructions.

[edit]

Creating Visual Studio projects

{Note: The following works with MS Visual Studio 2005 and 2003, and has not been tested on other versions - look for an expanded section of this section later}

To create a project, use the -t and -o options.

Normally, (as in the Hello World example), you would simply type:

prompt> qmake -project
prompt> qmake

To create a .vcproj which will be used by Visual Studio, we will type:

prompt> qmake -project -t vcapp -o projectname.pro

In this command, projectname.pro is the desired name of your project file. Be sure to include the extension .pro with your project file name.

From here, you can modify the projectname.pro file if needed. For example, in order to compile an OpenGL project, you should open the file and add QT += opengl at the beginning of the file. You can then continue with:

prompt> qmake

If the above command is executed as written in a directory that includes source files (either in that directory or in a subdirectory of that directory), a new Visual Studio project file is created:

projectname.vcproj

You can double-click on this vcproj file, or simply type its name in the command window and Visual Studio will create an associated .sln file.

The -t option was used to specify the templates used by qmake. By default, the template is app. The app template creates Makefiles which can be used on the command-line when running nmake. But since we are interest in using the Visual Studio IDE, we want a vcapp which will give us a .vcproj instead of a regular Makefile.

Note that you can also use the -tp vc option instead of -t vcapp. This will prepend vc to the default template (which is normally app).

[edit]

Notes on Creating Visual Studio projects

{Note: This may only apply to static builds. If so move this to Qt4_with_Visual_Studio_and_static_C_runtime, or else remove this note}

You can create the Visual Studio project file with your standard .pro file, using: "qmake -t vcapp".

With Qt 4.2.2 "qmake -t vcapp" forgets about the standard libraries like gdi32.lib comdlg32.lib... The best way to fix this is: you generate the Makefiles using "qmake". You look for the LIBS line in Makefile.* and add the lacking libs with "win32:LIBS +=" to the .pro file. This also applies to the method described above.

[edit]

Maintaining Visual Studio Projects

To add files to your project, you can edit your .pro file and re-run qmake. The only problem is that any customizations to your .vcproj will be lost. However, changes made to the .sln are kept and you can simply reopen the solution file after updating the .vcproj.

Can someone see if there is a better way to deal with both .pros and .slns?

[edit]

Another way for creating and maintaining Visual Studio Projects

This should be a little better way to deal with Qt and Visual Studio: You only have to maintain a .pro File, and you can use the normal build buttons in Visual Studio, and you get errors and so on shown in VS. This is written for Visual Studio.Net 2003, but should also work with Visual Studio 2005 (may somebody try please? - yes it does)

First you create a new Makefile Project in a empty solution. Then go to the project Property Pages (right click project->Properties). Make sure that Debug is the current Configuration and choose "NMake" in the left menu. Then open the Window for "Build command Line" by clicking the "..." Button. Here you enter:

%QTDIR%\bin\qmake
nmake debug

In "Rebuild Command Line" you enter:

%QTDIR%\bin\qmake
nmake debug-clean
nmake debug

And in "Clean Command Line":

%QTDIR%\bin\qmake
nmake debug-clean

Now the last change, in "Output" enter:

debug\[you app Name].exe

Now do the same thing for release Configuration, but substitute "debug" with "release" ( also in Output Path!)

Now confirm this dialog with OK and create a new File. To do so right click your project and choose Add->Add new Files. Here choose "Text File (.txt)" and as name enter "src.pro", or something similar. In this file enter:

TEMPLATE = app
CONFIG  += qt [do you config here, mine would be: "qt warn_on"]
QT  += [do you qt-config here]
SOURCES  = main.cpp
HEADERS  =
TARGET  = [your App Name]

win32:debug:CONFIG += console [->if you want to receive qDebug() messages on Windows...]

Save this file and add another file to your project: main.cpp, do it as you did it with the pro File, but choose "C++ File (.cpp)" as file type.

If you want to add another source file to your project, just add it with the add menu, and don't forget to add the files to the right section in your pro-File. This pro file can be used like any normal pro-File, without any problems.

To give you a better start-off here is a little example solution: Image:Visual studio example project 1.zip

[edit]

Buildproblems with Visual Studio 2005 and service pack 1

After installing service pack 1 for Visual Studio 2005 you will get compiler errors like this one:

c:\qt\4.1.4\include\qtcore\../../src/corelib/tools/qhash.h(805) : error C2244: 'QMultiHash::replace' : unable to match function definition to an existing declaration
       c:\qt\4.1.4\include\qtcore\../../src/corelib/tools/qhash.h(790) : see declaration of 'QMultiHash::replace'
       definition
       'QHash::iterator QMultiHash::replace(const Key &,const T &)'
       existing declarations
       'QHash::iterator QMultiHash::replace(const Key &,const T &)'

This is because of a regression in the compiler and can not be solved by Trolltech.

There are two ways to solve the problem:

(NEW) you can download the fix by going to [1] and then English>Visual Studio 2005>VS80sp1-KB930859-X86-ENU.exe for more information you can look at the post on the Qt forum [2] (This fix work perfectly !)
(Not recommended) you can patch the Qt libray

The patch for the QMap sourcecode:

==== //depot/qt/4.2/src/corelib/tools/qmap.h#3 - f:\depot_vs2005\qt-4.2\src\corelib\tools\qmap.h ====
302a303,304
>    
>     typedef typename QMap::iterator DummyMapIterator;
883,884c885,886
<>::iterator replace(const Key &key, const T &value);
<>::iterator insert(const Key &key, const T &value);
---
>     inline typename DummyMapIterator replace(const Key &key, const T &value);
>     inline typename DummyMapIterator insert(const Key &key, const T &value);

And the patch for the QHash sourcecode:

==== //depot/qt/4.2/src/corelib/tools/qhash.h#2 - f:\depot_vs2005\qt-4.2\src\corelib\tools\qhash.h ====
386a387,388
>     typedef typename QHash::iterator DummyHashIterator;
>    
841,842c843,844
<>::iterator replace(const Key &key, const T &value);
<>::iterator insert(const Key &key, const T &value);
---
>     inline typename DummyHashIterator replace(const Key &key, const T &value);
>     inline typename DummyHashIterator insert(const Key &key, const T &value);

This patch works for Qt 4.2.2 but you'll need these for Qt 4.2.3:

==== //depot/qt/4.2.3/src/corelib/tools/qmap.h#3 - f:\depot_vs2005\qt-4.2.3\src\corelib\tools\qmap.h ====
244a245,246
>     typedef typename QMap::iterator DummyMapIterator;
>
893,894c896,897
<>::iterator replace(const Key &key, const T &value);
<>::iterator insert(const Key &key, const T &value);
---
>     inline typename DummyMapIterator replace(const Key &key, const T &value);
>     inline typename DummyMapIterator insert(const Key &key, const T &value);

and

=== //depot/qt/4.2.3/src/corelib/tools/qhash.h#2 - f:\depot_vs2005\qt-4.2.3\src\corelib\tools\qhash.h ====
329a330,331
>     typedef typename QHash::iterator DummyHashIterator;
>
851,852c853,854
<>::iterator replace(const Key &key, const T &value);
<>::iterator insert(const Key &key, const T &value);
---
>     inline typename DummyHashIterator replace(const Key &key, const T &value);
>     inline typename DummyHashIterator insert(const Key &key, const T &value);

If you're trying to apply this manually, the trick is to put the typedef for the dummy iterator right after the friend declaration for the iterator in QMap or QHash.

Retrieved from "http://qtnode.net/wiki/Qt4_with_Visual_Studio"

Categories: Qt Setup

Relationships Among MFC Objects

2007-05-09T02:17:00.000-07:00

To help put the document/view creation process in perspective, consider a running program: a document, the frame window used to contain the view, and the view associated with the document.

A document keeps a list of the views of that document and a pointer to the document template that created the document.
A view keeps a pointer to its document and is a child of its parent frame window.
A document frame window keeps a pointer to its current active view.
A document template keeps a list of its open documents.
The application keeps a list of its document templates.
Windows keeps track of all open windows so it can send messages to them.

These relationships are established during document/view creation. The following table shows how objects in a running program can access other objects. Any object can obtain a pointer to the application object by calling the global function AfxGetApp.

Gaining Access to Other Objects in Your Application

From object	How to access other objects
Document	Use GetFirstViewPosition and GetNextView to access the document's view list. Call GetDocTemplate to get the document template.
View	Call GetDocument to get the document. Call GetParentFrame to get the frame window.
Document frame window	Call GetActiveView to get the current view. Call GetActiveDocument to get the document attached to the current view.
MDI frame window	Call MDIGetActive to get the currently active CMDIChildWnd.

Typically, a frame window has one view, but sometimes, as in splitter windows, the same frame window contains multiple views. The frame window keeps a pointer to the currently active view; the pointer is updated any time another view is activated.

Note
A pointer to the main frame window is stored in the m_pMainWnd member variable of the application object. A call to OnFileNew in your override of the InitInstance member function of CWinApp sets m_pMainWnd for you. If you do not call OnFileNew, you must set the variable's value in InitInstance yourself. (SDI COM component (server) applications may not set the variable if /Embedding is on the command line.) Note that m_pMainWnd is now a member of class CWinThread rather than CWinApp.

Note

A pointer to the main frame window is stored in the m_pMainWnd member variable of the application object. A call to OnFileNew in your override of the InitInstance member function of CWinApp sets m_pMainWnd for you. If you do not call OnFileNew, you must set the variable's value in InitInstance yourself. (SDI COM component (server) applications may not set the variable if /Embedding is on the command line.) Note that m_pMainWnd is now a member of class CWinThread rather than CWinApp.

How to: Convert Between Various String Types

2007-05-07T19:37:00.000-07:00

Converting from char *

Example

This example demonstrates how to convert from a char * to the other string types listed above.

// convert_from_char.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"

using namespace std;
using namespace System;

int main()
{
   char *orig = "Hello, World!";
   cout << orig << " (char *)" << endl;

   // Convert to a wchar_t*
   size_t origsize = strlen(orig) + 1;
   const size_t newsize = 100;
   size_t convertedChars = 0;
   wchar_t wcstring[newsize];
   mbstowcs_s(&convertedChars, wcstring, origsize, orig, _TRUNCATE);
   wcscat_s(wcstring, L" (wchar_t *)");
   wcout << wcstring << endl;

   // Convert to a _bstr_t
   _bstr_t bstrt(orig);
   bstrt += " (_bstr_t)";
   cout << bstrt << endl;

   // Convert to a CComBSTR
   CComBSTR ccombstr(orig);
   if (ccombstr.Append(L" (CComBSTR)") == S_OK)
   {
       CW2A printstr(ccombstr);
       cout << printstr << endl;
   }

   // Convert to a CString
   CString cstring(orig);
   cstring += " (CString)";
   cout << cstring << endl;

   // Convert to a basic_string
   string basicstring(orig);
   basicstring += " (basic_string)";
   cout << basicstring << endl;

   // Convert to a System::String
   String ^systemstring = gcnew String(orig);
   systemstring += " (System::String)";
   Console::WriteLine("{0}", systemstring);
   delete systemstring;
}

Output

Hello, World! (char *)
Hello, World! (wchar_t *)
Hello, World! (_bstr_t)
Hello, World! (CComBSTR)
Hello, World! (CString)
Hello, World! (basic_string)
Hello, World! (System::String)

Converting from wchar_t *

Example

This example demonstrates how to convert from a wchar_t * to the other string types listed above.

// convert_from_wchar_t.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"

using namespace std;
using namespace System;

int main()
{
   wchar_t *orig = L"Hello, World!";
   wcout << orig << L" (wchar_t *)" << endl;

   // Convert to a char*
   size_t origsize = wcslen(orig) + 1;
   const size_t newsize = 100;
   size_t convertedChars = 0;
   char nstring[newsize];
   wcstombs_s(&convertedChars, nstring, origsize, orig, _TRUNCATE);
   strcat_s(nstring, " (char *)");
   cout << nstring << endl;

   // Convert to a _bstr_t
   _bstr_t bstrt(orig);
   bstrt += " (_bstr_t)";
   cout << bstrt << endl;

   // Convert to a CComBSTR
   CComBSTR ccombstr(orig);
   if (ccombstr.Append(L" (CComBSTR)") == S_OK)
   {
       CW2A printstr(ccombstr);
       cout << printstr << endl;
   }

   // Convert to a CString
   CString cstring(orig);
   cstring += " (CString)";
   cout << cstring << endl;

   // Convert to a basic_string
   wstring basicstring(orig);
   basicstring += L" (basic_string)";
   wcout << basicstring << endl;

   // Convert to a System::String
   String ^systemstring = gcnew String(orig);
   systemstring += " (System::String)";
   Console::WriteLine("{0}", systemstring);
   delete systemstring;
}

Output

Hello, World! (wchar_t *)
Hello, World! (char *)
Hello, World! (_bstr_t)
Hello, World! (CComBSTR)
Hello, World! (CString)
Hello, World! (basic_string)
Hello, World! (System::String)

Converting from _bstr_t

Example

This example demonstrates how to convert from a _bstr_t to the other string types listed above.

// convert_from_bstr_t.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"

using namespace std;
using namespace System;

int main()
{
   _bstr_t orig("Hello, World!");
   wcout << orig << " (_bstr_t)" << endl;

   // Convert to a char*
   const size_t newsize = 100;
   char nstring[newsize];
   strcpy_s(nstring, (char *)orig);
   strcat_s(nstring, " (char *)");
   cout << nstring << endl;

   // Convert to a wchar_t*
   wchar_t wcstring[newsize];
   wcscpy_s(wcstring, (wchar_t *)orig);
   wcscat_s(wcstring, L" (wchar_t *)");
   wcout << wcstring << endl;

   // Convert to a CComBSTR
   CComBSTR ccombstr((char *)orig);
   if (ccombstr.Append(L" (CComBSTR)") == S_OK)
   {
       CW2A printstr(ccombstr);
       cout << printstr << endl;
   }

   // Convert to a CString
   CString cstring((char *)orig);
   cstring += " (CString)";
   cout << cstring << endl;

   // Convert to a basic_string
   string basicstring((char *)orig);
   basicstring += " (basic_string)";
   cout << basicstring << endl;

   // Convert to a System::String
   String ^systemstring = gcnew String((char *)orig);
   systemstring += " (System::String)";
   Console::WriteLine("{0}", systemstring);
   delete systemstring;
}

Output

Hello, World! (_bstr_t)
Hello, World! (char *)
Hello, World! (wchar_t *)
Hello, World! (CComBSTR)
Hello, World! (CString)
Hello, World! (basic_string)
Hello, World! (System::String)

Converting from CComBSTR

Example

This example demonstrates how to convert from a CComBSTR to the other string types listed above.

// convert_from_ccombstr.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"
#include "vcclr.h"

using namespace std;
using namespace System;
using namespace System::Runtime::InteropServices;

int main()
{
   CComBSTR orig("Hello, World!");
   CW2A printstr(orig);
   cout << printstr << " (CComBSTR)" << endl;

   // Convert to a char*
   const size_t newsize = 100;
   char nstring[newsize];
   CW2A tmpstr1(orig);
   strcpy_s(nstring, tmpstr1);
   strcat_s(nstring, " (char *)");
   cout << nstring << endl;

   // Convert to a wchar_t*
   wchar_t wcstring[newsize];
   wcscpy_s(wcstring, orig);
   wcscat_s(wcstring, L" (wchar_t *)");
   wcout << wcstring << endl;

   // Convert to a _bstr_t
   _bstr_t bstrt(orig);
   bstrt += " (_bstr_t)";
   cout << bstrt << endl;

   // Convert to a CString
   CString cstring(orig);
   cstring += " (CString)";
   cout << cstring << endl;

   // Convert to a basic_string
   wstring basicstring(orig);
   basicstring += L" (basic_string)";
   wcout << basicstring << endl;

   // Convert to a System::String
   String ^systemstring = gcnew String(orig);
   systemstring += " (System::String)";
   Console::WriteLine("{0}", systemstring);
   delete systemstring;
}

Output

Hello, World! (CComBSTR)
Hello, World! (char *)
Hello, World! (wchar_t *)
Hello, World! (_bstr_t)
Hello, World! (CString)
Hello, World! (basic_string)
Hello, World! (System::String)

Converting from CString

Example

This example demonstrates how to convert from a CString to the other string types listed above.

// convert_from_cstring.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"

using namespace std;
using namespace System;

int main()
{
   CString orig("Hello, World!");
   wcout << orig << " (CString)" << endl;

   // Convert to a char*
   const size_t newsize = 100;
   char nstring[newsize];
   strcpy_s(nstring, orig);
   strcat_s(nstring, " (char *)");
   cout << nstring << endl;

   // Convert to a wchar_t*
   // You must first convert to a char * for this to work.
   size_t origsize = strlen(orig) + 1;
   size_t convertedChars = 0;
   wchar_t wcstring[newsize];
   mbstowcs_s(&convertedChars, wcstring, origsize, orig, _TRUNCATE);
   wcscat_s(wcstring, L" (wchar_t *)");
   wcout << wcstring << endl;

   // Convert to a _bstr_t
   _bstr_t bstrt(orig);
   bstrt += " (_bstr_t)";
   cout << bstrt << endl;

   // Convert to a CComBSTR
   CComBSTR ccombstr(orig);
   if (ccombstr.Append(L" (CComBSTR)") == S_OK)
   {
       CW2A printstr(ccombstr);
       cout << printstr << endl;
   }

   // Convert to a basic_string
   string basicstring(orig);
   basicstring += " (basic_string)";
   cout << basicstring << endl;

   // Convert to a System::String
   String ^systemstring = gcnew String(orig);
   systemstring += " (System::String)";
   Console::WriteLine("{0}", systemstring);
   delete systemstring;
}

Output

Hello, World! (CString)
Hello, World! (char *)
Hello, World! (wchar_t *)
Hello, World! (_bstr_t)
Hello, World! (CComBSTR)
Hello, World! (basic_string)
Hello, World! (System::String)

Converting from basic_string

Example

This example demonstrates how to convert from a basic_string to the other string types listed above.

// convert_from_basic_string.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"

using namespace std;
using namespace System;

int main()
{
   string orig("Hello, World!");
   cout << orig << " (basic_string)" << endl;

   // Convert to a char*
   const size_t newsize = 100;
   char nstring[newsize];
   strcpy_s(nstring, orig.c_str());
   strcat_s(nstring, " (char *)");
   cout << nstring << endl;

   // Convert to a wchar_t*
   // You must first convert to a char * for this to work.
   size_t origsize = strlen(orig.c_str()) + 1;
   size_t convertedChars = 0;
   wchar_t wcstring[newsize];
   mbstowcs_s(&convertedChars, wcstring, origsize, orig.c_str(), _TRUNCATE);
   wcscat_s(wcstring, L" (wchar_t *)");
   wcout << wcstring << endl;

   // Convert to a _bstr_t
   _bstr_t bstrt(orig.c_str());
   bstrt += " (_bstr_t)";
   cout << bstrt << endl;

   // Convert to a CComBSTR
   CComBSTR ccombstr(orig.c_str());
   if (ccombstr.Append(L" (CComBSTR)") == S_OK)
   {
       CW2A printstr(ccombstr);
       cout << printstr << endl;
   }

   // Convert to a CString
   CString cstring(orig.c_str());
   cstring += " (CString)";
   cout << cstring << endl;

   // Convert to a System::String
   String ^systemstring = gcnew String(orig.c_str());
   systemstring += " (System::String)";
   Console::WriteLine("{0}", systemstring);
   delete systemstring;
}

Output

Hello, World! (basic_string)
Hello, World! (char *)
Hello, World! (wchar_t *)
Hello, World! (_bstr_t)
Hello, World! (CComBSTR)
Hello, World! (CString)
Hello, World! (System::String)

Converting from System::String

Example

This example demonstrates how to convert from a System.String to the other string types listed above.

// convert_from_system_string.cpp
// compile with: /clr /link comsuppw.lib

#include 
#include 
#include 

#include "atlbase.h"
#include "atlstr.h"
#include "comutil.h"
#include "vcclr.h"

using namespace std;
using namespace System;
using namespace System::Runtime::InteropServices;

int main()
{
   String ^orig = gcnew String("Hello, World!");
   Console::WriteLine("{0} (System::String)", orig);

   pin_ptr wch = PtrToStringChars(orig);

   // Convert to a char*
   size_t origsize = wcslen(wch) + 1;
   const size_t newsize = 100;
   size_t convertedChars = 0;
   char nstring[newsize];
   wcstombs_s(&convertedChars, nstring, origsize, wch, _TRUNCATE);
   strcat_s(nstring, " (char *)");
   cout << nstring << endl;

   // Convert to a wchar_t*
   wchar_t wcstring[newsize];
   wcscpy_s(wcstring, wch);
   wcscat_s(wcstring, L" (wchar_t *)");
   wcout << wcstring << endl;

   // Convert to a _bstr_t
   _bstr_t bstrt(wch);
   bstrt += " (_bstr_t)";
   cout << bstrt << endl;

   // Convert to a CComBSTR
   CComBSTR ccombstr(wch);
   if (ccombstr.Append(L" (CComBSTR)") == S_OK)
   {
       CW2A printstr(ccombstr);
       cout << printstr << endl;
   }

   // Convert to a CString
   CString cstring(wch);
   cstring += " (CString)";
   cout << cstring << endl;

   // Convert to a basic_string
   wstring basicstring(wch);
   basicstring += L" (basic_string)";
   wcout << basicstring << endl;

   delete orig;
}

Output

Hello, World! (System::String)
Hello, World! (char *)
Hello, World! (wchar_t *)
Hello, World! (_bstr_t)
Hello, World! (CComBSTR)
Hello, World! (CString)
Hello, World! (basic_string)

Computer Vision Software

2007-05-06T19:15:00.000-07:00

The Software is grouped into the following categories 3D, contours, display tools, features, ocr, mathematical toolkits, pattern recognition, stereo, synthetic data generators, texture, toolkits, tracking, misc.

3D

ZipPack Polygon Mesh Zippering Combines several range images into a polygonal mesh.

Contours

Segmentation of Skin-Cancer Images Implementation of an algorithm for segmenting images of skin cancer and other pigmented lesions (see Image and Vision Computing, January 1999, pp. 65-74).
An automatic method for segmention of images of skin cancer and other pigmented lesions is implemented. This method first reduces a color image into an intensity image and approximately segments the image by intensity thresholding. Then, it refines the segmentation using image edges. Double thresholding is used to focus on an image area where a lesion boundary potentially exists. Image edges are then used to localize the boundary in that area. A closed elastic curve is fitted to the initial boundary and is locally shrunk or expanded to approximate edges in its neighborhood in the area of focus. Segmentation results from twenty randomly selected images show an average error that is about the same as that obtained by four experts manually segmenting the images. (by L. Xu, M. Jackowski, A. Goshtasby, C. Yu, D. Roseman, S. Bines, A. Dhawan, A. Huntley / Intelligent Systems Laboratory / Wright State University)

Display Tools

The FreeImage Library at Sourceforge
3DViewnix - Demo of a commercial package.
FP Image - View/Process Floating Point and integer images in Windows 95/98/NT. Formats include DICOM and user defined formats. Includes a image processing scripting language.
FP Image for Windows - Scientific/Medical imaging software. Formats include floating point, integer and DICOM. Built-in image processing scripting language, batch processing, 3D solid modeling. ( FP Image)
FreeImage - FreeImage is an Open Source project for developers who would like to support popular graphics image formats like BMP, JPEG, TIFF, PNG, RAS, PNM, PCX, TGA in their C++ applications for Windows. (by Floris van den Berg, Hervé Drolon)
GD - a graphics library for GIF creation - provides GIF read/write code in a C library. It also provides minimal image manipulation functions (lines, arcs, text, colors). Includes versions for Unix and Windows systems. (by Thomas Boutell / Boutell.Com)
Ghostscript and ghostview - PostScript previewer and pretty user interface for X11.
MSDOS Ghostscript and supplemental font files are also available.
GNU Image Manipulation Program (GIMP) - Photoshop-style image editor.
ImageMagick - Load, display, process, save, and convert images in many formats. Works on Unix, Linux, Windows, and Mac. Includes a display program, a converter, screen capture, animator, and more.
Imaging Primer - Interactive and comprehensive images analysis and processing software for windows95 (commercial product). (by Pepi Cima / Rio Grande Software)
JPEG - Library source code and simple display tools.
Mesa - OpenGL implementation.
MPEG-1 player and encoder
Also: FAQ and fancy VCR-like interface using Motif.
NIH Image - for Macintosh
TIFF - Library source code and tools
Volumetric Image Display and Analysis (VIDA) - Demo of a commercial package.
XAnim - X11 display tool.
Supports many animation and image formats ("everything" except mpeg). Notes on integrating xanim with Web clients/MIME are also available.
XLI - X11 display tool.
Not as featureful as xv but it understands nearly all the same formats and displays images much more quickly. Source archive is available.
XV - X11 Image Display tool.
Provides an amazing assortment of image operators, reads and writes images in many different formats.
Ygl - Emulation of SGI GL library for X11.

Features

Convex grouping algorithm Robustly locates salient convex collections of line segments in an image.
Edge list approximation code From Nonparametric segmentation of curves into various representations, PAMI 1995 pp 1140-1153. by Paul Rosin and Geoff West.
Gradient Vector Flow Active Contour The purpose of GVF active contour is to extract parameterized contour description from images. Matlab implementation is available for both UNIX and Windows. (by Chenyang Xu and Jerry L. Prince / Image Analysis and Communications Laboratory / Johns Hopkins University)
GSnake Contour modeling, extraction, detection, and classification.
Logical/Linear Operators (by Lee Iverson)
MegaWave Wavelet, Snake and Segmentation source code.
MMach A Mathematical Morphology Toolbox for the Khoros System
Savitzky-Golay Filters for 2D Images - This web page describes the derivation of the Savitzky-Golay filters for 2D images, gives MatLab routines for computing the filters, and gives C files with the filter coefficients. (by John Krumm / Vision Technology Research Group / Microsoft Research)
SUSAN Low-level image processing.
SUSAN is an acronym for Smallest Univalue Segment Assimilating Nucleus. The SUSAN algorithms cover image noise filtering, edge finding and corner finding. (by Steve Smith / Oxford University)

OCR

NIST Handwriting OCR Testbed OCR software and datasets for UNIX systems.
SketchUp (ftp download) A demo package for recognizing hand-drawn sketches through Size Functions. ( Vision Mathematics group / University of Bologna)

Mathematical Toolkits

CGAL - Computational Geometry Algorithms Library - C++ library of geometric primitives and standard data structures and algorithms used in computational geometry.
The CGAL project is a collaborative effort to develop a robust, easy to use, and efficient C++ software library of geometric data structures and algorithms. The CGAL library contains: - Basic geometric primitives such as points, vectors, lines, predicates such as for relative positions of points, and operations such as intersections and distance calculation. - A collection of standard data structures and geometric algorithms, such as convex hull, (Delaunay) triangulation, planar map, polyhedron, smallest enclosing sphere, and multidimensional query structures. - Interfaces to other packages, e.g. for visualisation, and I/O, and other support facilities. For further information and for downloading the library and documentation, please visit the CGAL web page: http://www.cs.uu.nl/CGAL/ Should you have any questions or comments, please send a message to cgal@cs.uu.nl ( CGAL Consortium)
Netlib - Public domain collection of mathematical software, papers, and databases.
Mostly in Fortran, but f2c (included in netlib) converts Fortran to C.
Numerical Recipies - Public Domain code for the famous book (only some of the code is public domain).
Reviver - A Practical Provable Surface Reconstructor - Free software that takes unorganised point clouds as input and produces 3D models automatically in various industry standard formats (runs on Unix and Windows)
StatLib - Statistical software, datasets, and information.

Pattern Recognition

Active Appearance Models - Extensions and Case home site for the the AAM-API which is a free C++ implementation of the Active Appearance Model method. Several results and models are also given. ( Section for Image Analysis / The Technical University of Denmark)
Hidden Markov Model routines Implementation of Forward, Backward, Viterbi and Baum-Welch algorithms. The code follows Rabiner and Juang notation. Written in C. (by Tapas Kanungo / Center for Automation Research / University of Maryland, College Park)
Perceptual Organization Software
ToolDiag Pattern recognition of multivariate numerical data.

Stereo

Camera Calibration Routines for calibrating using Roger Tsai's perspective projection camera model. (by Reg Willson / CMU)
Disparity Analysis of Images This java-based application estimates the disparity between two images. It works by first detecting remarkable points in both images and then finding the best possible match between the two sets of points. (by Lionel Le Briquer)
Maximum-Flow Stereo Algorithm Code for the maximum-flow formulation of the N camera stereo correspondence problem. (by Sebastien Roy / Université de Montréal)
Microsoft Easy Camera Calibration Tool a flexible camera calibration technique, which only requires the camera to observe a planar pattern shown at a few (at least two) different (unknown) orientations. (by Zhengyou Zhang / Vision Technology Group / Microsoft Corp.)
Projective Vision Toolkit PVT is a series of utilities that allows one to take an image sequence and compute the fundamental matrix and trilinear tensor.
This can be used for such problems as camera self-calibration, structure from motion, camera motion annotation, image stabilization, 3D tracking and recognition, etc. (Computational Video Group of NRC)
SRI Stereo Engine Software - fast stereo software for PCs. It performs disparity calculations and filtering in real time on images up to 320x240 in size. ( SRI Artificial Intelligence Center / SRI International)
Uncalibrated Stereo by Singular Value Decomposition This stereo algorithm allows to match features across a pair of stereo images with unparalleled algorithmic simplicity and neatness. Results are comparable to complex relaxation methods. Its simple implementation has made it a good off-the-shelf solution for a number of researchers needing a fast a easy-to-integrate matching module. (by Maurizio Pilu / Hewlett Packard Research Laboratories)

Synthetic Data Generators

MESHBASE Intelligent 3D modeling program for Windows - An intelligent 3D modeling program for Windows platform. It provides true WYSIWYG and WYDSIWYDG easy editing environment. (30 day trial) (by Sean Kung / Modelsoft, Inc.)
Persistence of Vision - Ray Tracer.
Philip Torr's stereo vision code - routines to generate synthetic data for testing and evaluating fundamental matrix estimation algorithms (by Philip Torr / Machine Learning and Perception Group / Microsoft)
Radiance - Ray tracer
Produces floating point photometrically accurate images, with emphasis on good light source modeling.
Random dot stereogram generator - For X11.
Includes support for animations and user-defined objects. More stereograms are also available.
Ray Tracers - A nice summary of free ray tracers. (by Eric Haines)
Rayshade - Ray tracing renderer.
Generates realistic 2D images from a text description of a 3D world. Supports texture mapping, surface ("heightfield") rendering, multiple light sources, defocus, animation and more. Range image output extension and documentation are also available.
Synthetic Fingerprint Generator - SFinGe is a novel method for the generation of synthetic fingerprint images ("sfinge" is the Italian for "sphinx").
Gabor-like space-variant filters are used for iteratively expanding an initially empty image containing just one or a few seeds. A directional image model, whose inputs are the number and location of the fingerprint cores and deltas, is used for tuning the filters. Very-realistic fingerprint images are obtained after the final noising-and-rendering stage. ( Biometric Systems Lab / University of Bologna)

Texture

MeasTex A framework for quantitative measurement of image texture classification algorithms.

Toolkits

Gandalf Gandalf is a computer vision and numerical algorithm library, written in C, which allows you to develop new applications that will be portable and run FAST. Includes many useful vision routines, including camera calibration, homographies, fundamental matrix computation, and feature detectors (includes source code).
Dynamically reconfigurable vector, matrix and image structures in Gandalf allow efficient use of memory. Gandalf has been used to develop the "MoKey" motion editing software, released at IBC'2001 in Amsterdam. MoKey performs automatic inpainting of moving objects over an image sequence, and can also be used to compute an accurate alpha matte or outline of an object. Gandalf currently contains four packages: 1) Common package of simple structures and routines used by the other packages, such as memory allocation, linked lists and error handling; 2) Linear algebra package with a large number of routines for matrix and vector manipulations; 3) Image package defining a general purpose image structure and low-level image manipulation routines; 4) Vision package containing a number of standard image processing, computer vision and numerical routines. The major design features of Gandalf are: (i) Efficient use of memory through dynamically reconfigurable structures; (ii) Emphasis on support of numerical algorithms, especially optimisation; (iii) A very flexible and efficient internal image representation, (iv) A comprehensive set of matrix/vector operations, incorporating implicit matrix transpose & inverse, and in-place computation where appropriate; Exploitation of the computational and compilation speed advantages of C over C++ in reducing the number of layers of abstraction over the raw data, an approach we believe is appropriate for simple objects such as matrices, vectors and images. The documentation for Gandalf comes in two parts. There is a LaTex tutorial with examples available also in HTML (via Latex2html). Reference documentation for Gandalf has also been generated using ObjectOutline, ( by Philip McLauchlan)
Intel Open Source Computer Vision Library Computer vision routines, applications and tutorials. Open Source, FREE for academic AND commercial use. Assembly language optimized on Intel's processor line. Areas covered are Geometric Methods, Recognition, Image Pyramids Camera Calibration, Tracking, and Fitting. (by Vadim Pisarevsky, Dmitry Abrosimov , Jean-Yves Bouguet , Gary R. Bradski , Valery Cherepennikov , Michael Chu , Boris Chudinovich , Prof. Trevor , Bob Davies , Prof. James Davis , Victor Eroukhimov , Prof. Irfan Essa , Radek Grzeszczuk , Mark Holler , Prof. Jitendra Malik , Sergey Molinov , Valery Mosyagin , Ara Nefian , Sergey Oblomov , Prof. Pietro Perona , Vadim Pisarevsky, Alexander Pleskov, Chuck Richards, Prof. Stan Scarloff, Stewart Taylor, Prof. Carlo Tomasi / Visual Interactivity Lab / Intel Corporation)
University of Calgary vision software Includes chain code, Hough transform, and others.
VXL - C++ libraries for Computer Vision The Vision-something-Libraries are a collection of C++ libraries designed for computer vision research. It was created from TargetJr and the Image Understanding Environment (IUE) with the aim of making a lighter, faster and more consistent system. VXL is written in ANSI/ISO C++ and is designed to be portable over many platforms. It is developed and used by a consortium including groups from the Universities of Leuven, Oxford, Manchester, and RPI, GE CRD. ( VXL Consortium)
AcquireNow - A real-time image acquisition and processing product. (Commercial product $$).
The product includes a COM (Component Object Model) component, which allows developers to create powerful imaging applications quickly and easily using COM supported languages such as C++ and Visual Basic. The AcquireNow package include the AcquireNowClient application. AcquireNowClient is a stand-alone application, which can be used to acquire, display, and save images to disk. The AcquireNowClient application also allows the user to perform real time image averaging, scaling and flat fielding. Source code for the AcquireNowClient application is included, and can be used by customers as a base for their own imaging applications. ( Boulder Imaging, Inc.)
AdOculos - PC-based image processing without the need of extensive programming knowledge
The following image processing functions are realized as DLLs. The complete C source code of these DLLs is part of the standard pack. Point, local and global, morphological operations Texture, image sequence Histograms procedures Hough and color transformations Automatic counting and interactive measuring Pattern recognition, graylevel profile General purpose and display functions ( The Imaging Source)
Aphelion - Commercial image processing and understanding package for Windows. Features a rapid prototyping environment, image processing and object recognition libraries, and a vision tutorial.
Aphelion is a commercial software product which can be used to quickly develop vertical imaging applications. It is a comprehensive and powerful development environment and a delivery vehicle for image-based applications, including a Graphical User Interface, Image Processing libraries available as DLLs or ActiveX components, a Visual Basic compatible scripting language, a chart server, etc. Aphelion provides the very latest developments in mathematical morphology and symbolic representation/recognition, as well as effective tools for quantitative analysis, microscopy, pattern recognition, and classification. (by Bruno Lay / Amerinex Applied Imaging Inc.)
AutoTrace - AutoTrace converts bitmap to vector graphics (by Martin Weber)
Bersoft Image Measurement - Measure length, angle, segments, perimeter and area in digital images. Commercial package for windows.
Bersoft Image Measurement runs under Windows 9.x/NT and it is intended to measure length, angle, segments, perimeter and area in digital images. It can be used in multiple scientific disciplines, such as Biology, Ecology, Geography, Agronomy, and Natural Sciences. It also can export matrixes (Exporting RGB values) with the decimal or hexadecimal values of the image pixels. The DEMO version can realize all the functions, but only over images saved in a propietary format: Image Bersoft Bitmap (bim extension). ( Bersoft)
Clemex Vision - Commercial software for analysis of images from microscopes.
Color Reduction and Multithresholding - Free image processing software for color reduction and quantization, multithresholding, Hough Transform etc. (Image and Multimedia Laboratory / Democritus University of Thrace, Greece)
Common Vision Blox - A modular and open software development platform to solve image processing and machine vision applications (Windows, Commercial product) ( Stemmer Imaging GmbH)
Computer Vision Workshop - An image analysis tool based on the Vista software environment
CppIma - C++ image processing library.
CVIPtools - GUI-based computer vision and image processing tools, ANSI-C source code and libraries for Windows95/NT and UNIX, extended computer imaging TCL shell.
Also contains an extended Tcl shell with all the computer imaging functions. ANSI-C source code and libraries for image analysis, image compression, image enhancement, image restoration, and many imaging utilities. Used for both research and education, as well as applications development. (by Scott E Umbaugh, Greg Hance, Arve Kjoelen, Kun Luo, Mark Zuke, Yansheng Wei and others / CVIP Group / Southern Illinois University at Edwardsville)
DTU Image Viewer and Analyser - The DIVA consists of a number of image analysis functions collected in C++ template image classes and a windows interface, which handles a wide variety of different image file formats and pixel types. Everything is available as source code. (Section for Image Analysis / Technical University of Denmark)
eVision - Commercial image processing and analysis toolkit for use in industrial applications on Windows platforms. There is also a rapid prototyping development environment called EasyAccess.
eVision provides all familiar tools in image processing such as image linear and morphological filtering, projections, profiles, geometric transforms, color conversions, blob analysis, pattern matching as well as application libraries such as OCR, matrix code reading, mark inspection. These tools are provided in a form well suited for rapid application development and are extremely fast. ( Euresys)
Exbem: Scientific Image Processing & Analysis - Exbem is a software for scientific image processing & analysis under MacOS. Exbem handles images, QuickTime movies, and live-video. Multiple operators can be assigned to multiple ROIs. ( Pixlock e.K. (company))
Graphics Gems - Generally useful graphics and image processing subroutines from the similarly-named books.
GRASS - Geographic Information System
HALCON - a commercial computer vision tool consisting of an image processing library, C and C++ interfaces, and a rapid prototyping tool called HDevelop.
HALCON is manufactured by MVTec, which is a spin-off of the Technische Universität München and the Bavarian Research Center for Knowledge Based Systems (FORWISS). The company is specialized in software solutions for image processing using standard hardware and framegrabbers. HALCON covers a wide field of applications like factory automation, quality control, medical image analysis, aerial image analyis, surveillance, research, and education. ( MVTec Software GmbH)
HIPS - General Unix-based Image Processing System with C source code (Commercial package $$)
HIPS is a software package for image processing that runs under the UNIX operating system. HIPS is modular and flexible, it provides automatic documentation of its actions, and is almost entirely independents of special equipment. It handles sequences of images (movies) in precisely the same manner as single frames. Over 200 such image transformation programs have been developed. HIPS is written in C, provided as source code, and is both a set of separate programs as well as a callable library. (by Michael S. Landy)
ILIB Imaging Libraries - commercial package of image processing libraries for the Windows environment (C/C++ interface). It also includes neural and genetic imaging capabilities. ( Inventions)
Image Processing Library - The main purpose of Image Processing Library (IPL) is to simplify image processing under Windows environment. ( Medical Imaging Lab)
Image Processing Library 98 - A platform independent image manipulating C/C++ library
The purpose of the library is to be useful, for combining tailor-made image processing and interpretation with standard methods for acquisitions, processing, display and storage of image information. Emphasis is put on interactivity in projects made by students, as well as for advanced research and development. (by Ivar Balslev and René Dencker / The Maersk Mc-Kinney Moller Institute for Production Technology / University of Southern Denmark, Odense University)
Image-Pro Plus - Commercial image analysis software used in biological and industrial microscopy applications.
ImageLib - An Image Processing C++ Class Library (template based)
ImageLib is a C++ class library providing image processing and related facilities. The main set of classes provides a variety of image and vector types, with additional modules supporting scalar and vector quantisation, wavelet transforms, DCT transforms, and simple histogram operations. (by Brendt Wohlberg / University of Cape Town)
IMAQ Vision - Adds machine vision and image processing functionality to LabVIEW and ActiveX containers (National Instruments)
ImgStar Image Processing Tools - Complements Pbmplus with edge detection, high/low/band-pass filters, thresholding, etc. (by Simon Winder)
ImLib3D - ImLib3D is an open source C++ library for 3D (volumetric) image processing. It comes with an optional viewer that features 3D (OpenGL) multiplanar.
Templated: ImLib3D images are STL-like templated containers. This means you can create images of arbitrary types (examples: float, int, complex, 3D vectors for deformation fields, ...) Iterators: ImLib3D provides STL-like iterators for moving around images. This provides a much faster, more efficient and easier to use framework. This also provides a common simple syntax for moving around images in special ways, like in masked images or rectangular sub-zones in an image. Speed: ImLib3D is very fast. Iterators hide all the gory details of making it fast. Command line: All image processing operators can be called from the unix command line. This is, with the viewer, important for easy image processing experimentation. Fast BSpline interpolation (thanks to Unser et all.) Rigid, affine, deformable registration (thanks to O.Musse) Very fast fft (thanks to fftw) Image processing (arithmetic,convolution,morphological operations...) 3D image viewer. (by Marcel Bosc, Torbjorn Vik / LSIIT/IPB ULP Strasbourg France)
Intel Image Processing Library - Optimized assembly MMX code for image processing, pattern recognition, signal processing, and matrix manipulation (no source - but still free) ( Performance Library Suite / Intel Corporation)
Interactive Data Language (IDL) - IDL is a development environment for data visualization, 2D and 3D graphics, and image processing.
IPTool - Freeware image processing toolkit for Windows
Khoros - An integrated software environment for data exploration and visualization, visual programming and simulation, and sofware development.
LEADTOOLS Imaging Development Toolkit - commercial toolkit that supports loading, saving, converting, and processing of color, greyscale, and document images - Windows-based
commercial toolkit that ( LEAD Technologies, Inc.)
LookingGlass Real-time ImageProcessing System - multithreaded PC-based image proccessing environment that supports realtime video processing.
LookingGlass is an Image Processing Environment for developing imaging applications and for research and development of new image system. LookingGlass supports real-time live video processing from VideoForWindow compatible device, and also supports BMP, JPG, GIF89 and AVI or user can write a dll to support other vdo format or image acquisition device. LookingGlass can produce AVI file, sequence of BMP or JPG files, or just display images to screen, or users can write a dll to do what ever output they want. LookingGlass is derived from RobotVision2(http://www.ccs.neu.edu/home/psksvp/rv2.htm), so LookingGlass uses the pipeline idea and support using the same IP-DLL as RobotVision2. (by PongSuvan)
Matlab Pyramid Tools - MatLab tools for multi-scale (pyramid) image decomposition.
This includes Laplacian pyramids, QMFs/wavelets, and steerable pyramids as well as fast convolution routines, histogram tools, and synthetic image generation.
Matrox Imaging - Matrox Imaging Library (MIL) is a development toolkit for machine vision, medical imaging and image analysis. ActiveMIL, a collection of ActiveX controls for managing image capture, transfer, processing, analysis and display is bundled with MIL. Additional software includes Matrox Inspector, an interactive Microsoft® Windows®-based prototyping tool and an intelligent camera interface utility.
Microsoft Vision SDK - Visual C++ library for vision which defines an image object and supports digitizer independent image acquisition.
Multi-Threaded Image Processing - commercial Image Processing Environment with ISO12087 based "drag and drop" modules and a powerful API for C,C++ programming of own modules. ( Dynamic Imaging AS)
NeatVision: An Image Analysis & Software Development Environment - NeatVision is a Java based image analysis and software development environment. It provides high level access to a wide range of machine vision algorithms through a well defined and easy to use graphical interface. NeatVision is distributed as a shareware product.
NeatVision contains over 200 image and general data processing algorithms. Users can extend the core NeatVision library using the developers interface, a plug-in which features, automatic source code generation, compilation with full error feedback and dynamic algorithm updates. The Developers interface supports algorithm development based on Java AWT Imaging, Java 2D Imaging and Java Advanced Imaging. NeatVision is primarily an image processing application and offers an extensive range of image analysis and visualisation tools (these include zoom, pseudo colour, intensity scan, histogram and 3D profile mesh). In addition, the ability to read and write a wide range of image file formats is supported. ( Vision Systems Laboratory / Dublin City University)
NeuroCheck - Commercial Windows-based image processing system for automatic presence verification, bar and DataMatrix code reading, character and pattern recognition, robot guidance and gauging.
NeuroCheck^® is the complete framework for configuring and operating industrial visual quality control systems. Its powerful graphical tools enable the user to easily develop solutions within a familiar Windows - based environment to achieve rapid system integration into production line processes. ( DS GmbH)
Nuages - A 3-D shape from contour package.
Optimas: Analytical Imaging - Complete commercial image-analysis program for Windows used in biological and industrial measurement environments.
Optimas implements hundreds of measurement, image processing, and image management operations, all available from the graphical user interface. Optimas is designed for the imaging professional who needs the ability to prototype and quickly develop custom imaging solutions, and therefore includes an integrated development environment enabling one to record, edit, and debug macros. It is being used the world over to develop cutting-edge solutions to imaging problems. An Automation Server and Client (formerly known as "OLE Automation") Optimas also allows itself to be controlled via VB or any Automation Client, and conversely can control Excel or any Automation Server via an elegant syntax. Help is richly linked and context-sensitive. ( Media Cybernetics)
PBMPlus - Image manipulation toolkit.
This is the standard toolkit for Unix, it converts between dozens of formats. A version with many more features called NetPBM is also available, but may not be as easy to install. Some NetPBM patches are available.
Perl Data Language - An extension to perl that implements fast, compact manipulation of large, N-dimensional data arrays for scientific computing and image processing.
PiXCL and geoPiXCL - A commercial image processing scripting language and Win9x/NT/2000 EXE builder for TWAIN scanner and digital camera image sources. geoPiXCL adds geographic imagery extensions. IP and geo library APIs are available. (by Stewart DIBBS)
RobotVision2 - real-time image processing software that uses any VideoForWindow(VFW) compatible camera as the image source (by Pong Suvan / Northeastern University)
RobotVisionCAD - RobotVisionCAD(RvCAD) is an Image Processing Environment for developing imaging applications and for research and development of new image system.
RobotVisionCAD(RvCAD) is an Image Processing Environment for developing imaging applications and for research and development of new image system. RvCAD supports real-time live video processing from VideoForWindow compatible device, and also supports BMP, JPG, GIF89 and AVI or user can write a dll to support other vdo format or image acquisition device. RvCAD can also produce AVI file, sequence of BMP or JPG files, or just display images to screen, or users can write a dll to output images to whatever device they'd like. RvCAD is similar to an electonic logic gate simulation Program. Users drag and drop RvCadProcessor components from the left tree view then connect them together to build an ImageProcessing pipeline. (by pong suvan)
SDC Morphology Toolbox for Matlab - Matlab add-on: Gray-scale morphological tools for image segmentation, non-linear filtering, pattern recognition and image analysis: watershed, Euclidean distance transform, top-hat, reconstruction. (many real-life demonstrations)
SpikeNet Technology - (Company) Vendor of SpikeNet, a biologically-inspired computer vision system for object detection, recognition, and related applications. (by Simon Thorpe / Centre de Recherche Cerveau & Cognition)
The Delft Scientific Image Processing Library - DIPlib is a scientific image processing library written in C. It contains a large number of functions for processing and analysing multi dimensional image data.
The library provides functions for performing transforms, filter operations, object generation, and statistical analysis of images. (by Michael van Ginkel, Geert van Kempen, Cris Luengo Hendriks, Lucas van Vliet Geert van Kempen Cris Luengo Hendriks Lucas van Vliet / Pattern Recognition Group / Delft University of Technology)
The Image Processing Tool Kit - Comprehensive set of image processing and analysis routines in the form of Photoshop-compatible plug-ins for Mac and PC, with extensive tutorial. (commercial package $$) (by Chris Russ, John Russ)
TINA - A set of vision algorithm development libraries written in C
TINA is the result of over 50 man years of vision research. It is a set of libraries providing many levels of infrastructure for people wishing to develop vision algorithms. It contains a vast array of code from image reading and writing to depth estimation from stereo pairs. TINA is used as an on-going research tool by several vision research groups in the UK. It is written in C and has been compiled on many UNIX platforms including Sun workstations, HP workstations and PCs running Linux flavours. It requires only the basic UNIX system, a current gcc compiler and the X graphics libraries.
USB camera driver toolkit for LabVIEW - USB cameras and video capture devices are now included in the LabVIEW programming world.
INVENTvisionVFW 1.0 gives you the power to view and capture any VFW (Video For Windows) video devices in any programming language that can interface to activex technology. INVENTvisionVFW can be implemented in VB, VC++, G (LabVIEW) programming environments. This mean that USB cameras and video capture devices are now included in the LabVIEW programming world. This product integrates and works with LabVIEW Picture Control and IMAQ. A real-time overlay is display on the activex control placed on the LabVIEW front Panel. Images can be captured to a 2D Array[U32], Visual Basic Picturebox, LabVIEW Picture Control or IMAQ Image. Images can be loaded from and saved to disk in BMP and JPG formats. (by George Miles / INVENTeering)
Utah Raster Toolkit - UNIX commands and C libraries for an 8 bits/pixel, 1-255 channel image format.
Contains a nice display tool for X11; it's fast, supports animation and zooms in on any image. Wes Barris' URT extensions are quite useful too.
UTHSCSA ImageTool - free image processing and analysis program for windows.
VASARI Image Processing Software - An optimised library in C/C++ running on Unix. Its strengths are handling high-resolution images and colour spaces. Automatically parallel on SMP systems. ( Intelligence Agents and Multimedia Research Group (IAM) / University of Southampton, UK)
Video OCX - Windows-based interface for easy integration of video capture into your applications. It supports VFW video devices (USB cameras or framegrabber) AND AVI sequences as image sources. ( vision pearls GbR)
Vista - A flexible library of C-routines, command-line filters, and Motif widgets for image representation and manipulation.
VISU - Tcl/Tk toolkit for visualization and interactive segmentation of 2D gray-scale images
Visus Imaging - Image analysis toolkit and complete systems aimed at researchers and microscopists in Biomedical and Material Sciences. (commercial product $$) (Foresthill Products)
WiT - Visual programming environment for image processing (demo).
XCaliper - Commercial Windows NT software toolkit for machine vision and thermal imaging applications. ( FSI Automation)
XMegaWave, an Image Processing Environment - a freeware graphical windows environment oriented towards image processing, where the user can create his own function in a very easy way.
Some european universities have developed a freeware image processing environment, named XMegaWave (XMW). It runs on Unix workstations or Linux machines, running Motif and X11 windows libraries. XMW includes some classical procedures for image processing (edge detection, segmentation, morphological filters). But the important thing is that XMW is also a programming library, where the user can implement his own image processing algorythm in C in a very very very easy way. The time needed to write the code and debug it is very short, so you can obtain results rapidly. Besides, XMW is a pedagogic tool suitable for using in image processing classes. It can be explained in just one class, and the students can easily implement any kind of image filter. (Image Mathematical Analysys Group (AMI) / University Las Palmas )

Tracking

XVision visual tracking software Application independent, configurable interface to high-speed tools for visual feature tracking. Uses include tracking a person's eyes and mouth, gesture recognition. Contains interfaces to many popular cameras and frame grabbers. (by Greg Hager / Computational Interaction with Physical Systems)

Miscellaneous

Steerable Pyramid
Check Eero's home page for a tar file. (by Eero Simoncelli)
Carina - commercial package for recognizing license plates (Adaptive Recognition Hungary)
Grabbo: vision-based MIDI controller - Grabbo uses orientation histograms for realtime image matching and 3D interpolation. MIDI output. Free demo version for BeOS. (Tebo Software)
IEEE-1394 Digital Camera Windows Driver - Windows device driver and C/C++ software library for IEEE-1394 digital cameras.
The web site also contains a demo program, documentation, example images, links, and other information. IEEE-1394 digital cameras are an ideal solution for acquiring high quality images with a regular laptop computer. (by Iwan Ulrich / Mobile Robot Programming Lab / Carnegie Mellon University)
MeteorCapture - Application to capture video to memory or disk using PC and Matrox Meteor (written using Visual C++). (by Ross Cutler / Computer Vision Lab / UMCP)
Modular Flow Scheduling Middleware - An open source, windows-based framework for developing programs with good software engineering qualities. It has been used for developing real-time vision applications.
Modular Flow Scheduling Middleware is an open source implementation of a generic, modular, extensible software architecture for dataflow processing of datastreams. It provides a framework for the implementation of algorithms and development of applications with desirable software engineering qualities, such as efficiency, scalability, extensibility, reusability, interoperability. (Windows - VC++) (by Alexandre RJ Francois / IMSC / IRIS / University of Southern California)
PicDB - an image database system with query by image content capabilities.
Real-time Head Tracking - automatic real-time head-tracking in video images. ( vision pearls GbR)
Renoir - 3D reconstruction from photos - 3D reconstruction from photos. 3D photomontage. ($$ payware $$ - free demo version available). Mainly useful for computer graphics, but uses some computer vision techniques
Model of an object is created manually from parametric blocks. Corresponding edges are marked on images and model. Camera and model parameters are reconstructed through minimization of distance between projected edges of model and corresponding edges, marked on photos. (by Ildar Valiev / Integra, Inc.)
RRCapture - a video capture program used to capture uncompressed image sequences using a PC configured with a 1 to 3 Bitflow RoadRunner digital frame grabbers. (by Ross Cutler / Computer Vision Lab / University of Maryland)
Verifinger - Fingerprint processing and recognition - SDK for fingerprint processing and recognition ( Neurotechnologija Ltd.)
VisualMouse - Our software translates user's head motion into the motion of the cursor on the screen, by processing the image from a web cam
Zaxel 3D Imaging Systems - Zaxel's 3D Imaging Systems create an infinite number of virtual cameras around the object or moving subject from a limited number of real camera inputs.

Digital Geometry

2007-04-21T09:59:00.000-07:00

Digital_Geometry.rar

Intro to Topology

2007-04-21T09:56:00.000-07:00

Planar Machines' web site. An invitation to Topology.

Limits.h

2007-04-20T06:31:00.000-07:00

#define CHAR_BIT 8 /* number of bits in a char */
#define SCHAR_MIN (-128) /* minimum signed char value */
#define SCHAR_MAX 127 /* maximum signed char value */
#define UCHAR_MAX 0xff /* maximum unsigned char value */

#ifndef _CHAR_UNSIGNED
#define CHAR_MIN SCHAR_MIN /* mimimum char value */
#define CHAR_MAX SCHAR_MAX /* maximum char value */
#else
#define CHAR_MIN 0
#define CHAR_MAX UCHAR_MAX
#endif /* _CHAR_UNSIGNED */

#define MB_LEN_MAX 5 /* max. # bytes in multibyte char */
#define SHRT_MIN (-32768) /* minimum (signed) short value */
#define SHRT_MAX 32767 /* maximum (signed) short value */
#define USHRT_MAX 0xffff /* maximum unsigned short value */
#define INT_MIN (-2147483647 - 1) /* minimum (signed) int value */
#define INT_MAX 2147483647 /* maximum (signed) int value */
#define UINT_MAX 0xffffffff /* maximum unsigned int value */
#define LONG_MIN (-2147483647L - 1) /* minimum (signed) long value */
#define LONG_MAX 2147483647L /* maximum (signed) long value */
#define ULONG_MAX 0xffffffffUL /* maximum unsigned long value */
#define LLONG_MAX 9223372036854775807i64 /* maximum signed long long int value */
#define LLONG_MIN (-9223372036854775807i64 - 1) /* minimum signed long long int value */
#define ULLONG_MAX 0xffffffffffffffffui64 /* maximum unsigned long long int value */

#if _INTEGRAL_MAX_BITS >= 8
#define _I8_MIN (-127i8 - 1) /* minimum signed 8 bit value */
#define _I8_MAX 127i8 /* maximum signed 8 bit value */
#define _UI8_MAX 0xffui8 /* maximum unsigned 8 bit value */
#endif

#if _INTEGRAL_MAX_BITS >= 16
#define _I16_MIN (-32767i16 - 1) /* minimum signed 16 bit value */
#define _I16_MAX 32767i16 /* maximum signed 16 bit value */
#define _UI16_MAX 0xffffui16 /* maximum unsigned 16 bit value */
#endif

#if _INTEGRAL_MAX_BITS >= 32
#define _I32_MIN (-2147483647i32 - 1) /* minimum signed 32 bit value */
#define _I32_MAX 2147483647i32 /* maximum signed 32 bit value */
#define _UI32_MAX 0xffffffffui32 /* maximum unsigned 32 bit value */
#endif

#if _INTEGRAL_MAX_BITS >= 64
/* minimum signed 64 bit value */
#define _I64_MIN (-9223372036854775807i64 - 1)
/* maximum signed 64 bit value */
#define _I64_MAX 9223372036854775807i64
/* maximum unsigned 64 bit value */
#define _UI64_MAX 0xffffffffffffffffui64
#endif

#if _INTEGRAL_MAX_BITS >= 128
/* minimum signed 128 bit value */
#define _I128_MIN (-170141183460469231731687303715884105727i128 - 1)
/* maximum signed 128 bit value */
#define _I128_MAX 170141183460469231731687303715884105727i128
/* maximum unsigned 128 bit value */
#define _UI128_MAX 0xffffffffffffffffffffffffffffffffui128
#endif

#ifndef SIZE_MAX
#ifdef _WIN64
#define SIZE_MAX _UI64_MAX
#else
#define SIZE_MAX UINT_MAX
#endif
#endif

A Useful site to understanding B-Spline Curve

2007-04-20T00:51:00.000-07:00

Spline Curves and Surfaces
Introduction
This tutorial is designed to help students learn about spline curves and surfaces. It is not designed to be a full lesson; it is more suited to those who have already learnt the basics and would like to reinforce their knowledge.
The tutorial consists of a combination of writing, java applets, VRML worlds and links to other pages. These links are there because the descriptions given elsewhere are likely to be a great help to those learning this material from scratch, as I only give a brief account of the mathematics involved here. The java applets are essentially interactive diagrams. They are there for you to learn by experience, so do experiment!
A note about viewing these pages
In order to see diagrams as large as possible, please maximise your browser window. All of the diagrams on these pages are sized in relation to your window size; if this is too small, the diagrams will be too. It should be possible to resize the window during browsing these pages, but I believe some versions of Netscape do not resize the applets correctly, so choose your window size before you move on.
For some basic notes on how to use the Java applets see the introduction to spline curves. For notes on how to use the VRML worlds see the surface introduction.
Table of Contents
1. Introduction to spline curves
2. Explicit curves
3. Parametric curves
4. Bezier curves
5. B-Spline curves
6. Introduction to surfaces
7. Bezier surfaces
8. B-Spline surfaces
This tutorial was written as an individual project, a required part of the MSc Computing Science degree at Imperial College, by Andy Salter.

Error with MSVCR80.DLL !!!!!!!!!!!!

2007-04-19T04:05:00.000-07:00

Encoutered this error, I had to spend 4 hours to fix it. Until now, I have never understand how the "magic codes" could resolved this error. ^_^, but at least we'll never get stuck in it. Oh my god, Thanks!

You must read following articles:

Concretely, I cut & paste the vital code here:

Error Message
This application has failed to start because MSVCR80.dll was not found. Re-installing the application may fix this problem.

Typically this error occurs because you are mixing retail and debug components. A very common scenario is a debug build of a application which is pulling in a retail version of a static library. The scenario could be the exact reverse and the error message in this case would reference msvcr80d.dll

Solution
This can be worked around by adding reference to retail CRT in the application manifest manually. Or by adding the following to a header.

#pragma comment(linker, "\"/manifestdependency:type='Win32' name='Microsoft.VC80.CRT' version='8.0.50608.0' processorArchitecture='X86' publicKeyToken='1fc8b3b9a1e18e3b' language='*'\"")

Note: Proceed with caution when providing this solution.

Bless you.

Hausdorff distance between convex polygons

2007-04-15T01:13:00.000-07:00

Normand Grégoire and Mikael Bouillot

1. Introduction
2. What is Hausdorff distance ?
3. Computing Hausdorff distance
3.1 Assumptions
3.2 Lemmas
3.3 Algorithm
3.4 Complexity
3.5 Interactive applet
4. Application examples

Glossary
References

Web project presented to Mr. Godfried Toussaint
for the course CS 507 Computational Geometry
McGill University, fall 1998

Fractals and the Fractal Dimension

2007-04-15T00:44:00.000-07:00

Fractals and the Fractal Dimension

Mandelbrot and Nature

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."(Mandelbrot, 1983).

The Concept of Dimension

So far we have used "dimension" in two senses:

The three dimensions of Euclidean space (D=1,2,3)
The number of variables in a dynamic system

Fractals, which are irregular geometric objects, require a third meaning:

The Hausdorff Dimension

If we take an object residing in Euclidean dimension D and reduce its linear size by 1/r in each spatial direction, its measure (length, area, or volume) would increase to N=r^D times the original. This is pictured in the next figure.

We consider N=r^D, take the log of both sides, and get log(N) = D log(r). If we solve for D. D = log(N)/log(r) The point: examined this way, D need not be an integer, as it is in Euclidean geometry. It could be a fraction, as it is in fractal geometry. This generalized treatment of dimension is named after the German mathematician, Felix Hausdorff. It has proved useful for describing natural objects and for evaluating trajectories of dynamic systems.

The length of a coastline

Mandelbrot began his treatise on fractal geometry by considering the question: "How long is the coast of Britain?" The coastline is irregular, so a measure with a straight ruler, as in the next figure, provides an estimate. The estimated length, L, equals the length of the ruler, s, multiplied by the N, the number of such rulers needed to cover the measured object. In the next figure we measure a part of the coastline twice, the ruler on the right is half that used on the left.

Measuring the length of a coastline using rulers of varying lengths.

But the estimate on the right is longer. If the the scale on the left is one, we have six units, but halving the unit gives us 15 rulers (L=7.5), not 12 (L=6). If we halved the scale again, we would get a similar result, a longer estimate of L. In general, as the ruler gets diminishingly small, the length gets infinitely large. The concept of length, begins to make little sense.

The "Richardson Effect"

Lewis Fry Richardson first noted the regularity between the length of national boundaries and scale size. As shown next, the relation between length estimate and length of scale is linear on a log-log plot.

The Richardson Effect.

Mandelbrot assigned the term (1-D) to the slope, so the functions are:
log[L(s)] = (1-D)log(s) + b where D is the Fractal Dimension.
For Great Britain, 1 - D = -.24, approximately. D = 1-(-.24) = 1.24, a fractional value.The coastline of South Africa is very smooth, virtually an arc of a circle. The slope estimated above is very near zero. D = 1-0 = 1. This makes sense because the coastline is very nearly a regular Euclidean object, a line, which has dimensionality of one. In general, the "rougher' the line, the steeper the slope, the larger the fractal dimension.

Examples of geometric objects with non-integer dimensions

Koch Curve

We begin with a straight line of length 1, called the initiator. We then remove the middle third of the line, and replace it with two lines that each have the same length (1/3) as the remaining lines on each side. This new form is called the generator, because it specifies a rule that is used to generate a new form.

The Initiator and Generator for constructing the Koch Curve.

The rule says to take each line and replace it with four lines, each one-third the length of the original.

Level 2 in the construction of the Koch Curve.

Level 3 in the construction of the Koch Curve.

We do this iteratively ... without end. The Koch Curve.

What is the length of the Koch curve?

The length of the curve increases with each iteration. It has infinite length. But if we treat the Koch curve as we did the coastline, ...

The relation between log(L(s)) and log(s) for the Koch curve ...

we find its fractal dimension to be 1.26. The same result obtained from D = log(N)/log(r) D = log(4)/log(3) = 1.26.

Cantor Dust

Iteratively removing the middle third of an initiating straight line, as in the Koch curve, ...

Initiator and Generator for constructing Cantor Dust. ...

this time without replacing the gap...

Levels 2, 3, and 4 in the construction of Cantor Dust.

Calculating the dimension ... D = log(N)/log(r) D = log(2)/log(3) = .63 We have an object with dimensionality less than one, between a point (dimensionality of zero and a line (dimensionality 1).

Sierpinski Triangle

We start with an equilateral triangle, connect the mid-points of the three sides and remove the resulting inner triangle.

Constructing the Sierpinski Triangle.

Iterating the first step.

Constructing the Sierpinski Triangle.

The Sierpinski Triangle.

Calculating the dimension... D = log(N)/log(r) = log(3)/log(2) = 1.585. This time we get a value between 1 and 2.

The dimensionality of a strange attractor

The trajectory of a strange attractor cannot intersect with itself. (Why?)
Nearby trajectories diverge exponentially. (Why?)
But the attractor is bounded to the phase space.
The trajectory does not fill the phase space.

A strange attractor is a fractal, and its fractal dimension is less than the dimensions of its phase space.

Self-similarity

An important (defining) property of a fractal is self-similarity, which refers to an infinite nesting of structure on all scales. Strict self- similarity refers to a characteristic of a form exhibited when a substructure resembles a superstructure in the same form.

Mandelbrot Set

Found by iterating
z_n+1 = z_n² + c.
where z is a complex number. z₀=0.
For different values of c, the trajectories either: stay near the origin, or "escape".
The Mandelbrot set is the set of points that are not in the Escape Set.

The Mandelbrot set. The points in the set are painted black.

The Escape Set differs in rate of escape, graphically depicted with different colors or altitudes ...

Constructed using the computer program "The Beauty of Fractal Lab", by Thomas Eberhardt.

So, what is a fractal?

An irregular geometric object with an infinite nesting of structure at all scales.

Why do we care about fractals?

Natural objects are fractals.
Chaotic trajectories (strange attractors) are fractals.
Assessing the fractal properties of an observed time series is informative.

Next Section: Nonlinear Statistical Tools

Thư viện xử lý ảnh và thị giác máy tính

2006-12-24T05:09:00.000-08:00

CVIP
ImageJ
OpenCV
IM
IPL 98

Tải về ở mục "Tổ chim của tôi"

HTK Training

2006-11-27T04:43:00.000-08:00

VõĐình Phong

Khoa học máy tính

MSSV: 0312060

Huấn luyện HTK 3.2.1

Nhận dạng tự động tiếng nói (ASR)

Lý do

Anh em học môn ASR đã khổ sở hơn một tháng nay vào việc huấn luyện HTK. Vấn đề không khó nhưng cần sự tỉ mỉ, kiên trì và hướng dẫn từ thầy Hạ. Sau khi hoàn thành việc huấn luyện ở trường, mình nghĩ nên làm một cái tool, trước hết là phục vụ cho mình, và cho những ai chưa huấn luyện xong HTK. Với quĩ thời gian một ngày rưỡi ngắn ngủi tranh thủ “xuất bản” để tất cả chúng ta có kịp thời gian nộp bài vào thứ 7 tới, mình đã vọc lại mớ dòng lệnh và tìm hiểu thêm ý nghĩa của nó. Những gì trình bày dưới đây là từ hướng dẫn của thầy Hạ và những kinh nghiệm làm sai của mình lẫn bạn bè. Ngoài ra mình có giải thích thêm một số ý nghĩa thông qua việc đọc HTK Book. Nhiều vấn đề còn chưa hiểu thấu đáo cũng như vốn từ dịch thuật củ chuối chắc chắn để lại nhiều thắc mắc các bạn khi đọc bài này. Nhưng rất mong các bạn đóng góp cho sự hoàn thiện của tutorial để anh em ta có thể đỡ “trâu bò” hơn cũng như các bạn năm sau đỡ khổ. Mong anh em ủng hộ. Xin cảm ơn.

Thông tin chung

1.Cấu trúc thư mục

Tạo thư mục ngoài cùng với tên tùy ý (trong bài này giả định tất cả để trong thư mục gốc C:\, tuy nhiên điều này không được khuyến khích).

Các thư mục con gồm có

· hmm0 – hmm15: các thư mục chứa file MMF.

· cfg (config): chứa các file config cho một số lệnh.

· ins (instruction): chứa các file .hed và .led.

· mlf (master label file): chứa các file .mlf.

· ph (phones): chứa các file phones: mono, tri.

· pl (Perl script): chứa các file script viết bằng Perl.

· txt (other files): chứa các file linh tinh như từ điển, danh sách file, wdnet, gram, train…

· wave: chứa các file Wave và mfcc.

2.Một vài lưu ý

Nhớ thiết lập biến môi trường cho HTKTools và Perl.

Các hướng dẫn trong bài này đều giả sử các tập tin âm thanh đã được thu trước đó.

Các tiến trình là bán tự động, yêu cầu người dùng gõ các lệnh thi hành các file Perl.

Thư mục yourproject chứa một số tập tin khời đầu tối thiểu để người dùng có thể bắt đầu thực hiện theo chỉ dẫn.

Thư mục sample chứa các tập tin đã hoàn chỉnh các bước trong bài này.

Bạn có thể dùng allin1.bat (all in one) để chạy tự động các lệnh.

Ngườì dùng nếu tìm thấy lỗi làm ơn thông báo đến mọi người khác, và nếu có thể, xin gởi mail về địa chỉ phongkhtn@yahoo.com. Xin cảm ơn nhiều.

Chuẩn bị dữ liệu

1.Tạo cấu trúc văn phạm

Cấu trúc văn phạm là một đồ thị có hướng tổng quát. Nó chứa các cấu trúc câu có thể có trong ngữ cảnh của ứng dụng mà ta muốn dùng ASR. Ví dụ nếu ta muốn áp dụng ASR trong môi trường chứng khoán, cấu trúc văn phạm phải có những từ (word) và câu (sentence, cấu thành từ word) được thiết kế sao cho nó có thể trình bày tất cả các mẫu câu mà một người trong ngữ cảnh đó có thể nói về.

Tập tin cấu trúc văn phạm

//gram.txt

(<$digit>)

C:\>HParse txt/gram.txt txt/wdnet.txt

wordnet tạo ra sẽ có định dạng giống file lattice:

//wdnet.txt

VERSION=1.0

N=13 L=31

I=0 W=khoong

I=1 W=!NULL

I=2 W=chisn

I=3 W=tasm

I=4 W=bary

I=5 W=sasu

I=6 W=nawm

I=7 W=boosn

I=8 W=ba

I=9 W=hai

I=10 W=moojt

I=11 W=!NULL

I=12 W=!NULL

J=0 S=1 E=0

J=1 S=12 E=0

J=2 S=0 E=1

J=3 S=2 E=1

J=4 S=3 E=1

J=5 S=4 E=1

J=6 S=5 E=1

J=7 S=6 E=1

J=8 S=7 E=1

J=9 S=8 E=1

J=10 S=9 E=1

J=11 S=10 E=1

J=12 S=1 E=2

J=13 S=12 E=2

J=14 S=1 E=3

J=15 S=12 E=3

J=16 S=1 E=4

J=17 S=12 E=4

J=18 S=1 E=5

J=19 S=12 E=5

J=20 S=1 E=6

J=21 S=12 E=6

J=22 S=1 E=7

J=23 S=12 E=7

J=24 S=1 E=8

J=25 S=12 E=8

J=26 S=1 E=9

J=27 S=12 E=9

J=28 S=1 E=10

J=29 S=12 E=10

J=30 S=1 E=11

Để rõ hơn, xem cấu trúc file lattice SLF trong chương 20 phần phụ lục HTK Book.

2.Tạo từ điển

Muốn xây dựng từ điển thì bước đầu tiên là tập hợp tất cả các từ được dùng trong ngữ cảnh. Các từ này được xếp thứ tự alphabet trong tập tin và phải được phiên âm tương ứng. Qui cách phiên âm rất quan trọng, có thể hạ thấp chất lượng nhận dạng nếu không cẩn thận.

#dict.dct

ba b a sp
bary b ar y sp
boosn b oos n sp
chisn ch is n sp
hai h a i sp
khoong kh oo ng sp
moojt m ooj t sp
nawm n aw m sp
sasu s as u sp
tasm t as m sp
silence sil

Lưu ý có phone sp (short pause) trong từ điển.

Đối với bộ từ vựng nhỏ thì tốt nhất là gõ tay hoặc copy từ bộ từ điển có sẵn.
Sau khi có từ điển thì chúng ta có thể tạo ra bộ phiên âm, gọi là monophones0

HDMan -m -w txt/wlist -n ph/monophones -l dlog txt/dict txt/dict.dct

Giải thích

wlist: đầu vào, đơn giản là danh sách các từ được sử dụng trong wordnet, mỗi từ một dòng. wlist vẫn chưa có cho đến khi ta đến bước này. Để tạo wlist, ta cần có prompts. Prompts là gì ? Đây là một tập tin chứa các đoạn text yêu cầu utterance đọc vào. Utterance phải đọc từng câu trong prompts và lưu vào file .wav có tên tương ứng.

Tạo Prompts

C:\>HSGen.exe -l -n 10 txt/wdnet.txt txt/dict.dct >> txt/prompts

Ở đây ta tạo tập tin prompt có tất cả 10 câu.

#prompts

001 bary chisn chisn hai boosn moojt khoong
002 khoong boosn tasm bary bary nawm khoong
003 ba nawm moojt chisn sasu bary khoong
004 bary boosn bary tasm nawm sasu nawm
005 bary nawm ba chisn boosn chisn nawm
006 bary boosn boosn khoong moojt tasm nawm
007 moojt hai bary moojt bary tasm khoong
008 khoong boosn hai bary sasu bary nawm
009 moojt ba ba hai chisn nawm nawm
010 tasm nawm sasu tasm bary bary nawm

Sau khi đã tạo prompts thì ta sẽ tạo được wlist bằng Perl script như sau:

C:\> perl pl/prompts2wlist.pl txt/prompts txt/wlist

Như vậy ta đã có wlist, có cấu trúc như sau:

#wlist

ba
bary
boosn
chisn
hai
khoong
khoong
moojt
nawm
sasu
tasm

monophones1: đầu ra, danh sách các phones được dùng để phiên âm trong từ điển.

#monophones1

sil
b
a
sp
ar
y
oos
n
ch
is
h
i
kh
oo
ng
m
ooj
t
aw
s
as
u

beep: Đầu vào, từ điển phiên âm.

names: Đầu vào, từ điển tên riêng (tùy chọn).
dict: Đầu ra, từ điển mới được tạo, tổng hợp từ beep. names và wlist.

Lưu ý: Nếu beep có silence thì HDMan sẽ bỏ silence đi, làm cho dict mới bị thiếu silence. Vì sao ? Bởi vì HDMan sẽ tìm trong tất cả các từ trong beep mà nó có trong wlist. Mà wlist lại được tạo từ prompts. Prompts không chứa silence. Do đó, wlist, và hầu quả là, dict mới tạo cũng không chứa silence. Tốt nhất là ta cứ tạo dict cho có hình thức, nhưng không dùng. Ta chỉ dùng monophones0 mà nó tạo ra. Ở các bước sau ta chỉ dùng beep thôi. Nhưng nếu beep thực sự quá lớn trong khi wlist lại nhỏ, ta hiệu chỉnh lại dict để dùng. Việc hiệu chỉnh rất đơn giản, chỉ cần thêm silence – sil là được. Việc này được tự động hóa bằng Perl script.

Thêm nữa, việc đặt tên monophones0 hay monophones1 trong dòng tham số lệnh là không quan trọng. Dù thế nào thì sau khi tạo, monophones# sẽ luôn có âm sp và thiếu sil. Thêm sil và giữ nguyên sp thì có được monophones1.

Thêm sil và xóa sp thì có được monophones0.

C:\>perl pl/mkMonophones.pl ph/monophones ph/monophones0 ph/monophones1

Giải thích

createMonophones.pl: Đầu vào, perl script.

monophones: Đầu vào, tập tin monophones sau được tạo ở HDMan.

monophones0: Đầu ra, tập tin monophones0 sau khi hiệu chỉnh.

monophones1: Đầu ra, tập tin monophones0 sau khi hiệu chỉnh.

3.Thu dữ liệu

Bước này bao gồm các công việc sau:

1) Thu âm giọng đọc lưu trữ thành các tập tin .wav.

2) Viết tập tin transcript tương ứng với mỗi file.

hoặc:

1) Tạo tập tin transcript (đã được tạo tự động bằng HSGen trong bước trước, chính là tập tin prompts).

2) Thu âm giọng đọc lưu trữ thành các tập tin .wav bằng cách đọc theo transcription trong tập tin prompts.

Như vậy ta có tất cả 2 cách thu dữ liệu:

n Tự động tạo prompts và ghi âm theo.

n Ghi âm và tạo prompts sau.

4.Tạo tập tin transcription

HTK không sử dụng file prompts cho xử lý sau này. Ta cần tạo ra một số file khác, cụ thể là dạng file MLF (Master Label File, tham khảo thêm trong HTK Book).

Có hai loại tập tin MLF cần tạo ra:

MLF ở mức từ (word), tức là tập tin words.mlf định dạng tập tin prompts theo chuẩn MLF:

//words.mlf

#!MLF!#
"*/001.lab"
bary
chisn
chisn
hai
boosn
moojt
khoong
.
"*/002.lab"
khoong
boosn
tasm
bary
bary
nawm
khoong
................

Làm sao tạo ?

C:\> Perl pl/prompts2mlf.pl mlf/words.mlf txt/prompts

MLF ở mức âm (phones), tức là định dạng tập tin phones0.mlf và phones1.mlf theo MLF:

//phones1.mlf

"*/002.lab"
sil
kh
oo
ng
b
oos
n
t
as
m
b
ar
y
b
ar
y
n
aw
m
kh
oo
ng
sil
.

Thực ra, phones#.mlf là dạng khai triển của words.mlf ở mức âm.

Làm sao tạo?

C:\> HLEd -l * -d txt/dict.dct -i mlf/phones0.mlf ins/mkphones0.led mlf/words.mlf

Giải thích

-d dict: đầu vào, từ điển ta đã có từ trước.
words.mlf: đầu vào, vừa được tạo ở trên.
-i phones0.mlf: đầu ra.
mkphones0.led: chứa các lệnh script để chuyển words.mlf thành phones0.mlf

#mkphones0.led
EX
IS sil sil
DE sp

Giải thích

EX: Thay thế mỗi từ trong words.mlf bằng phiên âm tương ứng trong từ điển dict.
IS: Chèn mô hình lặng (silence - sil) vào đầu và cuối của một từ.
DE: Xóa tất cả các short pause (sp) được thêm vào sau lệnh EX.

Tạo phones1.mlf

Vì sao lại cần phones0.mlf và phones1.mlf ? Ai mà biết HTK muốn gì ! Nhưng đại khái là phones0.mlf không chứa âm sp, còn phones1.mlf thì có. Thêm sp vào chắc với mục đích tăng tính hiệu quả cho quá trình nhận dạng sau này.

Cách tạo phones1.mlf ?

C:\> HLEd -l * -d txt/dict.dct -i mlf/phones1.mlf ins/mkphones1.led mlf/words.mlf

Giải thích

-d dict: đầu vào, từ điển ta đã có từ trước.
words.mlf: đầu vào, vừa được tạo ở trên.
-i phones1.mlf: đầu ra.
mkphones1.led: chứa các lệnh script để chuyển words.mlf thành phones1.mlf

//mkphones1.led
EX
IS sil sil

Nhận xét: phones1.mlf được tạo đơn giản bằng cách bỏ lệnh xóa sp trong mkphones1.led.

5.Mã hóa dữ liệu

Tại bước này, các file âm thanh mà ta đã thu ở bước 3 sẽ được rút đặc trưng. HTK hỗ trợ 2 dạng đặc trưng MFCC và LPC. MFCC nên được sử dụng vì nó tốt hơn (không tin thì thử LPC xem). Các thông tin cấu hình khác được lưu trong tập tin cấu hình config_HCopy.txt:

#config_HCopy.txt
#coding parameters - HCopy
SOURCEKIND = WAVEFORM
SOURCEFORMAT = WAV
TARGETKIND = MFCC_0_D_A
TARGETRATE = 100000.0
SAVECOMPRESSED = T
SAVEWITHCRC = T
WINDOWSIZE = 250000.0
USEHAMMING = T
PREEMCOEF = 0.97
NUMCHANS = 26
CEPLIFTER = 22
NUMCEPS = 12
ENORMALISE = F

C:\>HCopy -T 1 -C cfg/HCopy.cfg -S txt/listwavmfc

Giải thích

-S listwavmfc: Đầu vào, chứa danh sách file wave - file mfc tương ứng.

Làm sao tạo ?

C:>perl pl/listwavmfc.pl wave txt/listwavmfc

Giải thích

listwavmfc.pl: Tập tin script.
Wave: Đầu vào, thư mục chứa các tập tin .wav, ở đây giả sử là nằm ở thư mục C:\.
listwavmfc: Đầu ra, tập tin text chứa danh sách file wave.

Tạo monophone HMMs

Ở giai đoạn này, chúng ta sẽ tạo và huấn luyện cho monophones HMM xấp xỉ bằng một hàm Gauss. Đầu tiên, tất cả các xấp xỉ của các âm đều có hàm Gauss như nhau (kỳ vọng và phương sai). Sau khi được huấn luyện, âm sp và silence lần lượt được thêm vào. Cuối cùng, chúng được huấn luyện lại.

1.Tạo Flat Start Monophones

Tại bước này, chúng ta sẽ định nghĩa ra một “đề cương” cho HMM (chữ đề cương “dịch ” từ chữ prototype). Việc gán thông tin nào cho prototype là không quan trọng, chủ yếu là xây dựng một cái khung. Một mô hình tốt mà HTK Book đề xuất là mô hình 3 trạng thái trái – giữa – phải tuần tự.

#proto

~o 39

~h "proto"

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0.0 1.0 0.0 0.0 0.0

0.0 0.6 0.4 0.0 0.0

0.0 0.0 0.6 0.4 0.0

0.0 0.0 0.0 0.7 0.3

0.0 0.0 0.0 0.0 0.0

Giải thích thêm

Số chiều Vector đặc trưng MFCC_0_D_A là 39 = 13 tĩnh (MFCC_0) + 13 hệ số delta + 13 hệ số acceleration.

Tuy là có 5 trạng thái nhưng 2 trạng thái đầu và cuối không xét.

Các vector kỳ vọng (mean) và phương sai (variance) đều bằng nhau.

Ma trận xác suất chuyển được khởi tạo theo kinh nghiệm.

1.1.Làm sao tạo proto?

C:\>HCompV –C cfg/HCompV.cfg –f 0.01 –m –S txt/train.scp –M hmm0 hmm0/proto

Giải thích

-C HCompV.cfg: Đầu vào, tập tin cấu hình để HCompV tham khảo, có nội dung như sau:

#HCompV.cfg

TARGETKIND = MFCC_0_D_A

TARGETRATE = 100000.0

SAVECOMPRESSED = T

SAVEWITHCRC = T

WINDOWSIZE = 250000.0

USEHAMMING = T

PREEMCOEF = 0.97

NUMCHANS = 26

CEPLIFTER = 22

NUMCEPS = 12

ENORMALISE = F

-f 0.01: Tham số đầu vào, yêu cầu xuất file vFloor chứa vector floor có giá trị bằng 0.01 vector variance.

-S train.scp: Đầu vào, chứa danh sách các tập tin đặc trưng mfc. Cách đơn giản để tạo file train.scp là dùng lệnh dir của hệ thống (có thể dùng Perl).

Làm sao?

C:\Wave>dir /B *.mfc > ../train.scp

Hoặc

C:\>dir /B Wave\*.mfc > train.scp

Tuy nhiên ta phải điều chỉnh tập tin train.scp bằng tay để thêm đường dẫn tuyệt đối cho từng tập tin .mfc được liệt kê trong đó. Ta có thể tránh điều này bằng cách sử dụng Perl script:

C:\>perl pl/mkTrainFile.pl wave txt/train.scp

Giải thích

CreateTrainFile.pl: Đầu vào, file script Perl.

Wave: Đầu vào, thư mục chứa các tập tin .mfc.

train.scp: Đầu ra, tên tập tin chứa danh sách file .mfc.

-M hmm0: Đầu vào, thư mục mà HCompV sẽ dùng để chứa proto (phải được tạo trước).

Hmm0/proto.txt: Đầu vào, tập tin chứa cấu trúc proto như phần trên đã trình bày (nhớ là lưu trong thư mục hmm0).

1.2.

Sau khi chạy HCompV, hai tập tin proto và vFloors được tạo ra trong thư mục hmm0. Thông thường, tiết mục tiếp theo là “cắt may” thủ công tập tin hmmdefs từ proto và monophones0. Tuy nhiên, chúng ta có script để tự động hóa chuyện này.

Tạo macros tự động

C:\>perl pl/mkMacrosFile.pl hmm0/vFloors hmm0/macros

Giải thích

createMacrosFile.pl: Đầu vào, perl script.

hmm0/vFloors: Đầu vào, file vFloors được tạo từ lệnh HCompV ở trên.

hmm0/macros: Đầu ra, file macros cần tạo.

Tạo hmmdefs tự động

C:\>perl pl/mkHmmdefsFile.pl hmm0/proto ph/monophones0 hmm0/hmmdefs

Giải thích

createHmmdefsFile.pl: Đầu vào, perl script;

hmm0/proto: Đầu vào, tập tin proto có được từ bước trước.

monophones0: Đầu vào, tập tin monophones0 có từ bước .

hmm0/hmmdefs: Đầu ra, tên tập tin hmm.

Sau khi đã có được hmmdefs và macros, chúng ta sử dụng HERest để tái ước lượng các tham số trong hmmdefs. Vì sao phải ước lượng lại ? Cần nhớ là khi ta tạo tập tin hmmdefs ở trên, mô hình xấp xỉ Gauss là như nhau cho mọi phones (mean và variance đều giống nhau và giống mô hình trong file proto). Với HERest, nó sẽ sử dụng thông tin trong các tập tin đặc trưng .mfc để ước lượng lại thông số hàm xấp xỉ.

C:\> HERest -C cfg/HERest.cfg -I mlf/phones0.mlf -t 250.0 150.0 1000.0 -S txt/train.scp -H hmm0/macros -H hmm0/hmmdefs -M hmm1 ph/monophones0

Giải thích

-C HERest.cfg: Đầu vào, tập tin cấu hình

#HERest.cfg

# Coding parameters

TARGETKIND = MFCC_D_A_0

TARGETRATE = 100000.0

SAVECOMPRESSED = T

SAVEWITHCRC = T

WINDOWSIZE = 250000.0

USEHAMMING = T

PREEMCOEF = 0.97

NUMCHANS = 26

CEPLIFTER = 22

NUMCEPS = 12

ENORMALISE = F

-I mlf/phones0.mlf: Đầu vào, tập tin MLF được tạo từ trước.

-t 250.0 150.0 1000.0: Đầu vào, tham số prunning.

-S txt/train.scp: Đầu vào, danh sách các file .mfc.

-H hmm0/macros: Đầu vào, vừa tạo.

-H hmm0/hmmdefs: Đầu vào, vừa tạo.

-M hmm1: Đầu ra, chứa tập tin hmmdefs và macros mới.

ph/monophones0: Đầu vào, danh sách các phones (ngoại trừ sp).

Sau khi đã có hmm1, ta huấn luyện tiếp hmm2 và hmm3 bằng HERest. Lưu ý là khi huấn luyện hmm2 thì hmmdefs và macros là của hmm1, tương tự như vậy với hmm3, là các file của hmm2.

2.Fixing the Silence Models

Bước này thêm vào mô hình silence hai bước chuyển từ trạng thái 2 đến trạng thái 4 và ngược lại (như hình). Mô hình short pause (sp) cũng được thêm vào trạng thái trung tâm của mô hình sil. Vì sao làm vậy và tác dụng ra sao thì chưa được rõ.

Có hai bước nhỏ phải thực hiện:

Thêm mô hình sp vào hmmdefs4

C:\>perl pl/makesp.pl hmm3/hmmdefs hmm4/hmmdefs hmm3/macros hmm4/macros

Chạy HHEd để thực hiện việc “trói buộc” mô hình sil và sp với nhau, đồng thời thêm các xác suất chuyển cho mô hình sil.

C:\> HHEd -H hmm4/macros -H hmm4/hmmdefs -M hmm5 ins/sil.hed ph/monophones1

Giải thích

-H hmm4/macros: Đầu vào, tập tin macros trong hmm4.

-H hmm4/hmmdefs: Đầu vào, tập tin hmmdefs trong hmm4.

-M hmm5: Đầu ra hmm5.

ph/monophones1: Đầu vào, tập tin sanh sách âm, có chứa sil và sp.

ins/sil.hed: Đầu vào, tập tin chứa lệnh điều chỉnh.

#sil.hed

AT 2 4 0.2 {sil.transP}

AT 4 2 0.2 {sil.transP}

AT 1 3 0.3 {sp.transP}

TI silst {sil.state[3],sp.state[2]}

Giải thích lệnh

AT: thêm các xác suất dịch chuyển cho các dịch chuyển 2 – 4, 4 – 2 trong ma trận transition của mô hình sil (mở file hmm5/hmmdefs để kiểm chứng).

#hmm5/hmmdefs

~h "sil"

…

5.238852e+001

~s "silst"

…

1.008743e+002

0.000000e+000 1.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000

0.000000e+000 7.391776e-001 6.082239e-002 2.000000e-001 0.000000e+000

0.000000e+000 0.000000e+000 3.656323e-001 6.343677e-001 0.000000e+000

0.000000e+000 2.000000e-001 0.000000e+000 4.123393e-001 3.876607e-001

0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000 0.000000e+000

AT 1 3 0.3 {sp.transP}: thêm xác suất dịch chuyển 1 -3 cho mô hình sp.

#hmm5/hmmdefs

~h "sp"

~s "silst"

0.000000e+000 7.000000e-001 3.000000e-001

0.000000e+000 5.000000e-001 5.000000e-001

0.000000e+000 0.000000e+000 0.000000e+000

Dễ thấy trạng thái 2 của sp cũng bị buộc với mô hình silst vừa mới tạo.

TI: thực hiện trói buộc sp và sil bằng silst, được lưu ở đầu file hmmdefs. Quan sát mô hình sil, có thể thấy trạng thái 3 liên kết với mô hình silst mới này.

#hmm5/hmmdefs

~s "silst"

-1.233204e+001 9.116629e-001 3.020478e-001 2.393242e+000 3.001888e+000 3.456290e+000 3.706096e+000 2.861026e+000 6.466328e-001 9.644089e-001 7.715054e-001 6.577221e-001 7.104364e+001 -5.122911e-002 -2.084613e-002 2.598116e-001 -2.869415e-001 1.950579e-001 -3.822781e-002 -8.443902e-002 -1.072719e-001 -4.904599e-002 8.692242e-002 8.164209e-003 1.979581e-002 2.325216e-001 1.303717e-001 -4.080342e-002 4.128299e-002 -2.011553e-001 -7.077198e-002 -2.321420e-001 -9.913503e-002 -9.830537e-002 -1.752981e-001 -1.535826e-001 -1.363883e-001 -1.232475e-001 2.405691e-001

1.300436e+001 1.042869e+001 1.641352e+001 1.574066e+001 1.265830e+001 1.167596e+001 1.477261e+001 1.271613e+001 1.887716e+001 1.765516e+001 1.965426e+001 1.868261e+001 6.421104e+000 9.842667e-001 1.060887e+000 1.250746e+000 1.715912e+000 1.131693e+000 1.550215e+000 1.346661e+000 1.496958e+000 1.858089e+000 2.148503e+000 1.762000e+000 1.668207e+000 8.345646e-001 1.546411e-001 1.906256e-001 2.265411e-001 2.813516e-001 2.009885e-001 2.763181e-001 2.499908e-001 2.784255e-001 2.954797e-001 3.488080e-001 3.192161e-001 2.714097e-001 1.329405e-001

9.173016e+001

Ta nhận ra rằng silst đơn thuần là một hàm Gauss với mean và variance như trên.

Thực hiện HERest thêm 2 lần nữa để tạo ra hmm6 và hmm7.

3.Canh chỉnh lại dữ liệu huấn luyện

Trong từ điển phát âm có một số từ có nhiều kiểu phát âm khác nhau. Ở bước trước, HLEd chọn tùy ý một trong các kiểu phát âm. Ở bước này, chúng ta sẽ canh chỉnh lại tập tin transcription words.mlf. Nó sẽ chọn cách phiên âm nào khớp nhất so với dữ liệu ngữ âm. Đồng thời, nó sẽ thêm mô hình silence vào đầu và cuối mỗi utterance. Nên nhớ ta phải có entry silence sil trong từ điển (Điều này đã được giải quyết từ bước trước, nếu không nhớ xem lại bước tạo từ điển).

C:\> HVite -l * -o SWT -b silence -a -H hmm7/macros -H hmm7/hmmdefs -i mlf/aligned.mlf -m -t 250.0 -y lab -I mlf/words.mlf -S txt/train.scp txt/dict.dct ph/monophones1

Giải thích

-b silence: Đầu vào, chèn thêm sil vào đầu và cuối utterance.

HERest được thực hiện thêm 2 lần nữa để tạo hmm8 và hmm9.

Lưu ý là ta không dùng phones1.mlf nữa mà chuyển sang aligned.mlf.

C:\> HERest -B -C cfg/HERest.cfg -I mlf/aligned.mlf -t 250.0 150.0 1000.0 -s stats -S txt/train.scp -H hmm7/macros -H hmm7/hmmdefs -M hmm8 ph/monophones1

C:\> HERest -B -C cfg/HERest.cfg -I mlf/aligned.mlf -t 250.0 150.0 1000.0 -s stats -S txt/train.scp -H hmm8/macros -H hmm8/hmmdefs -M hmm9 ph/monophones1

Tạo triphones

Giai đoạn cuối cùng trong việc xây dựng mô hình HMM là tạo các triphones phụ thuộc vào ngữ cảnh. Có hai bước nhỏ. Thứ nhất, monophones transcription (transcription đơn âm) được chuyển thành triphones transcription (transcription 3-âm). Các mô hình triphones được ước lượng lại từ mô hình monophones. Thứ hai, các trạng thái triphones được “tied” với nhau để quá trình ước lượng tốt hơn. Tied là gì ? Nhớ lại bước trước, khi mà ta thêm mô hình sp cho hmmdefs, tied (tạm dịch là trói buộc) nghĩa là 2 ay nhiều mô hình HMM sẽ dùng chung một bộ các tham số (mean hay variance chẳng hạn).

1.Tạo triphones từ monophones

1.1

C:\> HLEd -n ph/triphones1 -l * -i mlf/wintri.mlf ins/mktri.led mlf/aligned.mlf

Giải thích

-n ph/triphones1: Đầu ra, danh sách các triphones.

-i mlf/wintri.mlf: Đầu ra, triphones transcription.

mlf/aligned.mlf: Đầu vào, monophones transcription đã được ước lượng lại.

ins/mktri.led: Đầu vào, chứa lệnh tạo triphones từ monophones.

#mktri.led

WB sp

WB sil

Giải thích lệnh

WB: coi như sp và sil là những từ ở biên (word boundary symbol), và do đó, không chuyển chúng thành triphones.

TC: chuyển tất cả các monophones thành triphones trừ các WB. Một điều đáng lưu ý là cũng có các biphones được tạo ra trong quá trình này, bởi vì chúng có một bên nằm sát biên. Xem xét ví dụ sau để hiểu rõ hơn:

sil th ih s sp m ae n sp

sil th+ih th-ih+s ih-s sp m+ae m-ae+n ae-n sp

biphones

triphones

word boundary symbol

Mô hình trên đây gọi là Word internal. Còn có hai mô hình nữa, chúng ta sẽ đề cập trong một dịp khác.

1.2.

Tiếp theo, chúng ta sẽ “nhái” mô hình monophones trong hmm9 thành triphones trong hmm10

C:\> HHEd -B -H hmm9/macros -H hmm9/hmmdefs -M hmm10 ins/mktri.hed ph/monophones1

Giải thích

-H hmm9/macros -H hmm9/hmmdefs: Đầu vào, hmm của monophones.

-M hmm10: Đầu ra, hmm10 được huấn luyện thành triphones.

Ins/mktri.hed: Đầu vào, tập tin chứa lệnh thực hiện “trói buộc” các ma trận chuyển của mỗi triphone trong tập tin triphones1.

-B: Đầu vào, lưu trữ hmmdefs ở dạng nhị phân thay vì text (giảm không gian chiếm dụng).

Làm sao tạo mktri.hed?

C:\>perl pl/mkTriHed.pl ph/monophones1 ph/triphones1 ins/mktri.hed

Lý giải cách làm việc của makeTriHed.pl (chưa có).

Chúng ta sẽ nhận được một số WARNING về T_sil và T_sp. Không sao cả, chuyền này rất bình thường.

1.3.

Sau khi đã “nhái” xong, việc tiếp theo là tái ước lượng mô hình triphones này. Chúng ta cũng vẫn sử dụng HERest.

C:\> HERest -B -C cfg/HERest.cfg -I mlf/wintri.mlf -t 250.0 150.0 1000.0 -s stats -S txt/train.scp -H hmm10/macros -H hmm10/hmmdefs -M hmm11 ph/triphones1

Thực hiện thêm một lần nữa để có hmm12.

C:\> HERest -B -C cfg/HERest.cfg -I mlf/wintri.mlf -t 250.0 150.0 1000.0 -s stats -S txt/train.scp -H hmm11/macros -H hmm11/hmmdefs -M hmm12 ph/triphones1

2.Tạo trạng thái ràng buộc cho triphones (tied state triphones)

Công việc cuối cùng trong việc xây dựng mô hình là ràng buộc các các trạng thái trong các tập triphones, từ đó chia sẻ dữ liệu trong từng tập và kết quả nhận dạng sẽ tốt hơn. Mặc dù bước trước đã ràng buộc, quá trình này đỏi hỏi phải tinh tế hơn một chút vì nó sẽ ảnh hưởng rất lớn đến hiệu suất nhận dạng. Ở bước này chúng ta sẽ sử dụng HHEd để gom nhóm (clusterring) các trạng thái và sau đó trói buộc các trạng thái trong cùng một nhóm với nhau. HHEd đưa ra hai tùy chọn : i) Dùng độ đo tính tương đồng giữa các trạng thái để gom nhóm (cách này gọi là hướng dữ liệu); ii) Dùng cây quyết định, dựa trên việc đưa ra các câu hỏi về trạng thái trái (left) và phải (right) của ngữ cảnh (context) của từng triphones. Cây quyết định sẽ thử tìm những ngữ cảnh (context) nào tạo ra sự khác biệt lớn nhất đối với ngữ âm và sử dụng nó để gom nhóm.

C:\> HHEd -B -H hmm12/macros -H hmm12/hmmdefs -M hmm13 ins/tree.hed ph/triphones1 > log

Khoan thực hiện lệnh này, nó sẽ được thực hiện sau khi đọc toàn bộ.

Giải thích

tree.hed: là tập hợp các chỉ thị tìm kiếm các ngữ cảnh phù hợp cho việc gom nhóm.

Hiểu & dùng tập tin tree.hed

Trong tree.hed có một số lệnh như: RO, TR, QS, TB, AU, CO, ST.

RO 100.0: Thiết lập ngưỡng ngoài là 100 (không hiểu: The outlier threshold determines the minimum occupancy of any cluster and prevents a single outlier state forming a singleton cluster just because it is acoustically very different to all the other states.) và nạp file thống kế stats đã tạo ở bước trước.

TR 0: Thiết lập trace về 0.

QS *: Nạp câu hỏi. QS (question) là do người dùng tự định nghĩa. Và định nghĩa thế nào cho hiệu quả là cả một vấn đề lớn. Perl script của ta chỉ thực hiện những việc thiết yếu đối với QS: QS cho ngữ cảnh Left và Right. Một hình dung dễ hiểu về QS là gì có thể thông qua ví dụ sau:

QS "L_Class-Stop" {p-*,b-*,t-*,d-*,k-*,g-*}

Mỗi QS (câu hỏi) được định nghĩa bằng một tập các ngữ cảnh theo sau nó, đặt trong hai dấu ngoặc nhọn. Câu hỏi “L_Class_Stop” sẽ TRUE nếu ngữ cảnh bên trái là p,b,t,d,k hoặc g.

Các câu hỏi cụ thể hơn về consonant, vowel, nasal, diphthong,… có thể không cần nhưng nếu có sẽ tốt hơn.

TR: .

TB: Hoạt động như sau: tất cả các triphones được cho chung vào một pool (đơn giản nghĩa là một chỗ chứa). Tất cả các QS lần lượt được nạp và được dùng để phân đôi pool này làm hai pool con. QS nào làm cực đại logarit likelihood của dữ liệu huấn luyện sẽ được chọn làm nhánh đầu tiên trong cây quyết định. Quá trình này được lặp lại cho đến khi với bất cứ QS nào, mức tăng log likelihood nhỏ hơn ngưỡng mà chúng ta qui định. Giá trị ngưỡng là con số đi theo sau TB

(VD: TB 40 "st_y_4_" {("y","*-y+*","y+*","*-y").state[4]}).

AU “fulllist”: tập tin chứa danh sách đầy đủ các phones: mono,bi và tri.

CO “tiedlist”: có một số mô hình sẽ giống nhau cả ba trạng thái và ma trận chuyển. Lệnh này tìm kiếm các mô hình giống nhau và nén lại bằng cách trói buộc chúng với nhau (khái niệm tie đã trình bày trước đây), tạo ra một danh sách mới các mô hình, lưu trữ trong tiedlist.

Như vậy, chúng ta phải tạo fulllist.

C:\>perl pl/mkFullList.pl ph/monophones0

Tạo tập tin tree.hed

C:\>perl pl/mkTree.pl 40 ph/monophones0 ins/tree.hed

Giải thích

40: ngưỡng qui định đối với TB, có thể thay đổi tùy ý.

ins/tree.hed: Đầu ra, tập tin tree.hed cần tạo.

Đến đây thì ta có thể yên tâm thực hiện lệnh HHEd.

Ta tiếp tục chạy HERest thêm 2 lần nữa cho hmm14 và hmm15.

C:\>HERest -B -C cfg/HERest.cfg -I mlf/wintri.mlf -t 250.0 150.0 1000.0 -s stats -S txt/train.scp -H hmm13/macros -H hmm13/hmmdefs -M hmm14 ph/triphones1

C:\>HERest -B -C cfg/HERest.cfg -I mlf/wintri.mlf -t 250.0 150.0 1000.0 -s stats -S txt/train.scp -H hmm14/macros -H hmm14/hmmdefs -M hmm15 ph/triphones1

Đánh giá nhận dạng

Bộ nhận dạng bây giờ đã hoàn hoàn thành và có thể được sử dụng. Bao nhiêu công sức bỏ ra và bây giờ là giai đoạn đánh giá [^.^].

1.Nhận dạng dữ liệu test

Giả sử chúng ta muốn nhận dạng thử bộ dữ liệu gồm 10 utterances.

C:\> HVite –C cfg/Hvite.cfg -H hmm15/macros -H hmm15/hmmdefs -S test/test.scp -i test/recout.mlf -w txt/wdnet.txt txt/dict.dct tiedlist

Giải thích

–C cfg/Hvite.cfg: Đầu vào, tập tin cấu hình.

-H hmm15/macros -H hmm15/hmmdefs: Đầu vào

-S test/test.scp: Đầu vào, tập tin chứa danh sách các file .mfc cần nhận dạng.

-i test/recout.mlf: Đầu ra, transcription nhận dạng được.

-w txt/wdnet.txt: Đầu vào, wordnet được tạo từ những bước đầu.

txt/dict.dct: Đầu vào, từ điển phiên âm.

tiedlist: Đầu vào, danh sách phones tạo được từ lệnh CO “tiedlist” trong tree.hed.

Lưu ý

Với việc cấu tạo triphones theo kiểu word internal như đã nói phần trước, trong tập tin cấu hình Hvite.cfg cần có thêm 2 tham số FORCECXTEXP = T và ALLOWXWRDEXP=F. Muốn hiểu tại sao, xem chương 12 HTK Book.

Có thêm một vài tham số của Hvite như p, s, tùy người dùng điều chỉnh.

2.Xuất kết quả

C:\>HResults –f –t -I mlf/words.mlf tiedlist test/recout.mlf > test/result

Kết quả nhận dạng 20 utterances đầu trong train.scp

------------------------ Overall Results --------------------SENT: %Correct=40.00 [H=8, S=12, N=20]

WORD: %Corr=100.00, Acc=89.29 [H=140, D=0, S=0, I=15, N=140]

=============================================================

Kết quả không khả quan mấy, nhưng chạy được là tốt rồi.[^_^].

Công việc tiếp theo

Bước tiếp theo là tăng số hàm Gauss dùng để xấp xỉ mô hình HMM từ 1 lên 3, 5, 7,. Đọc Mixture Incrementing trong slide môn học.

Xa hơn là Adapting HMMs.

Hy vọng hai chủ đề này sẽ sớm được cập nhật.

Inverse Polish notation

2006-11-22T22:45:00.000-08:00

5 * ( ( ( 9 + 8 ) * ( 4 * 6 ) + 7)
push(5)
push(9)
push(8)
push(pop + pop)
push(4)
push(6)
push(pop*pop)
push(pop*pop)
push(7)
push(pop+pop)
push(pop*pop)

----------------

stackinit();
repeat
repeat read(c) until c<>' ' ;

if(c == ')') then write(chr(pop));
if(c == '+') then push(ord(pop));
if(c == '*') then push(ord(pop));
if(c == '/') then push(orf(pop));

while(c>='0' and c<= '9') do
begin
write(c);
read(c);
end;

if(c<>'(') then write(' ');
untl eofn;

repeat
c = 0;
repeat read(c) until c<> ' ';
if c == '*' then x = pop*pop;
if c == '+' then x = pop + pop;
while c>= '0' and c <= '9' do
begin
x = 10*x + ord(c) - ord('0');
read(c);
end;
push(x);
until eoln;

The Wavelet Tutorial IV

2006-11-17T05:16:00.000-08:00

The Wavelet Tutorial

Part IV

Why is the Discrete Wavelet Transform Needed?

Although the discretized continuous wavelet transform enables the computation of the continuous wavelet transform by computers, it is not a true discrete transform. As a matter of fact, the wavelet series is simply a sampled version of the CWT, and the information it provides is highly redundant as far as the reconstruction of the signal is concerned. This redundancy, on the other hand, requires a significant amount of computation time and resources. The discrete wavelet transform (DWT), on the other hand, provides sufficient information both for analysis and synthesis of the original signal, with a significant reduction in the computation time.

The DWT is considerably easier to implement when compared to the CWT. The basic concepts of the DWT will be introduced in this section along with its properties and the algorithms used to compute it. As in the previous chapters, examples are provided to aid in the interpretation of the DWT.

THE DISCRETE WAVELET TRANSFORM (DWT)

The foundations of the DWT go back to 1976 when Croiser, Esteban, and Galand devised a technique to decompose discrete time signals. Crochiere, Weber, and Flanagan did a similar work on coding of speech signals in the same year. They named their analysis scheme as subband coding. In 1983, Burt defined a technique very similar to subband coding and named it pyramidal coding which is also known as multiresolution analysis. Later in 1989, Vetterli and Le Gall made some improvements to the subband coding scheme, removing the existing redundancy in the pyramidal coding scheme. Subband coding is explained below. A detailed coverage of the discrete wavelet transform and theory of multiresolution analysis can be found in a number of articles and books that are available on this topic, and it is beyond the scope of this tutorial.

The Subband Coding and The Multiresolution Analysis

The main idea is the same as it is in the CWT. A time-scale representation of a digital signal is obtained using digital filtering techniques. Recall that the CWT is a correlation between a wavelet at different scales and the signal with the scale (or the frequency) being used as a measure of similarity. The continuous wavelet transform was computed by changing the scale of the analysis window, shifting the window in time, multiplying by the signal, and integrating over all times. In the discrete case, filters of different cutoff frequencies are used to analyze the signal at different scales. The signal is passed through a series of high pass filters to analyze the high frequencies, and it is passed through a series of low pass filters to analyze the low frequencies.

The resolution of the signal, which is a measure of the amount of detail information in the signal, is changed by the filtering operations, and the scale is changed by upsampling and downsampling (subsampling) operations. Subsampling a signal corresponds to reducing the sampling rate, or removing some of the samples of the signal. For example, subsampling by two refers to dropping every other sample of the signal. Subsampling by a factor n reduces the number of samples in the signal n times.

Upsampling a signal corresponds to increasing the sampling rate of a signal by adding new samples to the signal. For example, upsampling by two refers to adding a new sample, usually a zero or an interpolated value, between every two samples of the signal. Upsampling a signal by a factor of n increases the number of samples in the signal by a factor of n.

Although it is not the only possible choice, DWT coefficients are usually sampled from the CWT on a dyadic grid, i.e., s₀ = 2 and t ₀ = 1, yielding s=2^j and t =k*2^j, as described in Part 3. Since the signal is a discrete time function, the terms function and sequence will be used interchangeably in the following discussion. This sequence will be denoted by x[n], where n is an integer.

The procedure starts with passing this signal (sequence) through a half band digital lowpass filter with impulse response h[n]. Filtering a signal corresponds to the mathematical operation of convolution of the signal with the impulse response of the filter. The convolution operation in discrete time is defined as follows:

A half band lowpass filter removes all frequencies that are above half of the highest frequency in the signal. For example, if a signal has a maximum of 1000 Hz component, then half band lowpass filtering removes all the frequencies above 500 Hz.

The unit of frequency is of particular importance at this time. In discrete signals, frequency is expressed in terms of radians. Accordingly, the sampling frequency of the signal is equal to 2p radians in terms of radial frequency. Therefore, the highest frequency component that exists in a signal will be p radians, if the signal is sampled at Nyquist’s rate (which is twice the maximum frequency that exists in the signal); that is, the Nyquist’s rate corresponds to p rad/s in the discrete frequency domain. Therefore using Hz is not appropriate for discrete signals. However, Hz is used whenever it is needed to clarify a discussion, since it is very common to think of frequency in terms of Hz. It should always be remembered that the unit of frequency for discrete time signals is radians.

After passing the signal through a half band lowpass filter, half of the samples can be eliminated according to the Nyquist’s rule, since the signal now has a highest frequency of p/2 radians instead of p radians. Simply discarding every other sample will subsample the signal by two, and the signal will then have half the number of points. The scale of the signal is now doubled. Note that the lowpass filtering removes the high frequency information, but leaves the scale unchanged. Only the subsampling process changes the scale. Resolution, on the other hand, is related to the amount of information in the signal, and therefore, it is affected by the filtering operations. Half band lowpass filtering removes half of the frequencies, which can be interpreted as losing half of the information. Therefore, the resolution is halved after the filtering operation. Note, however, the subsampling operation after filtering does not affect the resolution, since removing half of the spectral components from the signal makes half the number of samples redundant anyway. Half the samples can be discarded without any loss of information. In summary, the lowpass filtering halves the resolution, but leaves the scale unchanged. The signal is then subsampled by 2 since half of the number of samples are redundant. This doubles the scale.

This procedure can mathematically be expressed as

Having said that, we now look how the DWT is actually computed: The DWT analyzes the signal at different frequency bands with different resolutions by decomposing the signal into a coarse approximation and detail information. DWT employs two sets of functions, called scaling functions and wavelet functions, which are associated with low pass and highpass filters, respectively. The decomposition of the signal into different frequency bands is simply obtained by successive highpass and lowpass filtering of the time domain signal. The original signal x[n] is first passed through a halfband highpass filter g[n] and a lowpass filter h[n]. After the filtering, half of the samples can be eliminated according to the Nyquist’s rule, since the signal now has a highest frequency of p /2 radians instead of p . The signal can therefore be subsampled by 2, simply by discarding every other sample. This constitutes one level of decomposition and can mathematically be expressed as follows:

where y_high[k] and y_low[k] are the outputs of the highpass and lowpass filters, respectively, after subsampling by 2.

This decomposition halves the time resolution since only half the number of samples now characterizes the entire signal. However, this operation doubles the frequency resolution, since the frequency band of the signal now spans only half the previous frequency band, effectively reducing the uncertainty in the frequency by half. The above procedure, which is also known as the subband coding, can be repeated for further decomposition. At every level, the filtering and subsampling will result in half the number of samples (and hence half the time resolution) and half the frequency band spanned (and hence double the frequency resolution). Figure 4.1 illustrates this procedure, where x[n] is the original signal to be decomposed, and h[n] and g[n] are lowpass and highpass filters, respectively. The bandwidth of the signal at every level is marked on the figure as "f".

Figure 4.1. The Subband Coding Algorithm As an example, suppose that the original signal x[n] has 512 sample points, spanning a frequency band of zero to p rad/s. At the first decomposition level, the signal is passed through the highpass and lowpass filters, followed by subsampling by 2. The output of the highpass filter has 256 points (hence half the time resolution), but it only spans the frequencies p/2 to p rad/s (hence double the frequency resolution). These 256 samples constitute the first level of DWT coefficients. The output of the lowpass filter also has 256 samples, but it spans the other half of the frequency band, frequencies from 0 to p/2 rad/s. This signal is then passed through the same lowpass and highpass filters for further decomposition. The output of the second lowpass filter followed by subsampling has 128 samples spanning a frequency band of 0 to p/4 rad/s, and the output of the second highpass filter followed by subsampling has 128 samples spanning a frequency band of p/4 to p/2 rad/s. The second highpass filtered signal constitutes the second level of DWT coefficients. This signal has half the time resolution, but twice the frequency resolution of the first level signal. In other words, time resolution has decreased by a factor of 4, and frequency resolution has increased by a factor of 4 compared to the original signal. The lowpass filter output is then filtered once again for further decomposition. This process continues until two samples are left. For this specific example there would be 8 levels of decomposition, each having half the number of samples of the previous level. The DWT of the original signal is then obtained by concatenating all coefficients starting from the last level of decomposition (remaining two samples, in this case). The DWT will then have the same number of coefficients as the original signal.

The frequencies that are most prominent in the original signal will appear as high amplitudes in that region of the DWT signal that includes those particular frequencies. The difference of this transform from the Fourier transform is that the time localization of these frequencies will not be lost. However, the time localization will have a resolution that depends on which level they appear. If the main information of the signal lies in the high frequencies, as happens most often, the time localization of these frequencies will be more precise, since they are characterized by more number of samples. If the main information lies only at very low frequencies, the time localization will not be very precise, since few samples are used to express signal at these frequencies. This procedure in effect offers a good time resolution at high frequencies, and good frequency resolution at low frequencies. Most practical signals encountered are of this type.

The frequency bands that are not very prominent in the original signal will have very low amplitudes, and that part of the DWT signal can be discarded without any major loss of information, allowing data reduction. Figure 4.2 illustrates an example of how DWT signals look like and how data reduction is provided. Figure 4.2a shows a typical 512-sample signal that is normalized to unit amplitude. The horizontal axis is the number of samples, whereas the vertical axis is the normalized amplitude. Figure 4.2b shows the 8 level DWT of the signal in Figure 4.2a. The last 256 samples in this signal correspond to the highest frequency band in the signal, the previous 128 samples correspond to the second highest frequency band and so on. It should be noted that only the first 64 samples, which correspond to lower frequencies of the analysis, carry relevant information and the rest of this signal has virtually no information. Therefore, all but the first 64 samples can be discarded without any loss of information. This is how DWT provides a very effective data reduction scheme.

Figure 4.2 Example of a DWT

We will revisit this example, since it provides important insight to how DWT should be interpreted. Before that, however, we need to conclude our mathematical analysis of the DWT.

One important property of the discrete wavelet transform is the relationship between the impulse responses of the highpass and lowpass filters. The highpass and lowpass filters are not independent of each other, and they are related by

where g[n] is the highpass, h[n] is the lowpass filter, and L is the filter length (in number of points). Note that the two filters are odd index alternated reversed versions of each other. Lowpass to highpass conversion is provided by the (-1)ⁿ term. Filters satisfying this condition are commonly used in signal processing, and they are known as the Quadrature Mirror Filters (QMF). The two filtering and subsampling operations can be expressed by

The reconstruction in this case is very easy since halfband filters form orthonormal bases. The above procedure is followed in reverse order for the reconstruction. The signals at every level are upsampled by two, passed through the synthesis filters g’[n], and h’[n] (highpass and lowpass, respectively), and then added. The interesting point here is that the analysis and synthesis filters are identical to each other, except for a time reversal. Therefore, the reconstruction formula becomes (for each layer)

However, if the filters are not ideal halfband, then perfect reconstruction cannot be achieved. Although it is not possible to realize ideal filters, under certain conditions it is possible to find filters that provide perfect reconstruction. The most famous ones are the ones developed by Ingrid Daubechies, and they are known as Daubechies’ wavelets.

Note that due to successive subsampling by 2, the signal length must be a power of 2, or at least a multiple of power of 2, in order this scheme to be efficient. The length of the signal determines the number of levels that the signal can be decomposed to. For example, if the signal length is 1024, ten levels of decomposition are possible.

Interpreting the DWT coefficients can sometimes be rather difficult because the way DWT coefficients are presented is rather peculiar. To make a real long story real short, DWT coefficients of each level are concatenated, starting with the last level. An example is in order to make this concept clear:

Suppose we have a 256-sample long signal sampled at 10 MHZ and we wish to obtain its DWT coefficients. Since the signal is sampled at 10 MHz, the highest frequency component that exists in the signal is 5 MHz. At the first level, the signal is passed through the lowpass filter h[n], and the highpass filter g[n], the outputs of which are subsampled by two. The highpass filter output is the first level DWT coefficients. There are 128 of them, and they represent the signal in the [2.5 5] MHz range. These 128 samples are the last 128 samples plotted. The lowpass filter output, which also has 128 samples, but spanning the frequency band of [0 2.5] MHz, are further decomposed by passing them through the same h[n] and g[n]. The output of the second highpass filter is the level 2 DWT coefficients and these 64 samples precede the 128 level 1 coefficients in the plot. The output of the second lowpass filter is further decomposed, once again by passing it through the filters h[n] and g[n]. The output of the third highpass filter is the level 3 DWT coefficiets. These 32 samples precede the level 2 DWT coefficients in the plot.

The procedure continues until only 1 DWT coefficient can be computed at level 9. This one coefficient is the first to be plotted in the DWT plot. This is followed by 2 level 8 coefficients, 4 level 7 coefficients, 8 level 6 coefficients, 16 level 5 coefficients, 32 level 4 coefficients, 64 level 3 coefficients, 128 level 2 coefficients and finally 256 level 1 coefficients. Note that less and less number of samples is used at lower frequencies, therefore, the time resolution decreases as frequency decreases, but since the frequency interval also decreases at low frequencies, the frequency resolution increases. Obviously, the first few coefficients would not carry a whole lot of information, simply due to greatly reduced time resolution. To illustrate this richly bizarre DWT representation let us take a look at a real world signal. Our original signal is a 256-sample long ultrasonic signal, which was sampled at 25 MHz. This signal was originally generated by using a 2.25 MHz transducer, therefore the main spectral component of the signal is at 2.25 MHz. The last 128 samples correspond to [6.25 12.5] MHz range. As seen from the plot, no information is available here, hence these samples can be discarded without any loss of information. The preceding 64 samples represent the signal in the [3.12 6.25] MHz range, which also does not carry any significant information. The little glitches probably correspond to the high frequency noise in the signal. The preceding 32 samples represent the signal in the [1.5 3.1] MHz range. As you can see, the majority of the signal’s energy is focused in these 32 samples, as we expected to see. The previous 16 samples correspond to [0.75 1.5] MHz and the peaks that are seen at this level probably represent the lower frequency envelope of the signal. The previous samples probably do not carry any other significant information. It is safe to say that we can get by with the 3^rd and 4^th level coefficients, that is we can represent this 256 sample long signal with 16+32=48 samples, a significant data reduction which would make your computer quite happy.

One area that has benefited the most from this particular property of the wavelet transforms is image processing. As you may well know, images, particularly high-resolution images, claim a lot of disk space. As a matter of fact, if this tutorial is taking a long time to download, that is mostly because of the images. DWT can be used to reduce the image size without losing much of the resolution. Here is how:

For a given image, you can compute the DWT of, say each row, and discard all values in the DWT that are less then a certain threshold. We then save only those DWT coefficients that are above the threshold for each row, and when we need to reconstruct the original image, we simply pad each row with as many zeros as the number of discarded coefficients, and use the inverse DWT to reconstruct each row of the original image. We can also analyze the image at different frequency bands, and reconstruct the original image by using only the coefficients that are of a particular band. I will try to put sample images hopefully soon, to illustrate this point.

Another issue that is receiving more and more attention is carrying out the decomposition (subband coding) not only on the lowpass side but on both sides. In other words, zooming into both low and high frequency bands of the signal separately. This can be visualized as having both sides of the tree structure of Figure 4.1. What result is what is known as the wavelet packages. We will not discuss wavelet packages in this here, since it is beyond the scope of this tutorial. Anyone who is interested in wavelet packages, or more information on DWT can find this information in any of the numerous texts available in the market.

And this concludes our mini series of wavelet tutorial. If I could be of any assistance to anyone struggling to understand the wavelets, I would consider the time and the effort that went into this tutorial well spent. I would like to remind that this tutorial is neither a complete nor a through coverage of the wavelet transforms. It is merely an overview of the concept of wavelets and it was intended to serve as a first reference for those who find the available texts on wavelets rather complicated. There might be many structural and/or technical mistakes, and I would appreciate if you could point those out to me. Your feedback is of utmost importance for the success of this tutorial.

Thank you very much for your interest in The Wavelet Tutorial .

The Wavelet Tutorial III

2006-11-17T05:15:00.000-08:00

The Wavelet Tutorial

Part III

MULTIRESOLUTION ANALYSIS
&
THE CONTINUOUS WAVELET TRANSFORM

by
Robi Polikar

MULTIRESOLUTION ANALYSIS

Although the time and frequency resolution problems are results of a physical phenomenon (the Heisenberg uncertainty principle) and exist regardless of the transform used, it is possible to analyze any signal by using an alternative approach called the multiresolution analysis (MRA) . MRA, as implied by its name, analyzes the signal at different frequencies with different resolutions. Every spectral component is not resolved equally as was the case in the STFT.

MRA is designed to give good time resolution and poor frequency resolution at high frequencies and good frequency resolution and poor time resolution at low frequencies. This approach makes sense especially when the signal at hand has high frequency components for short durations and low frequency components for long durations. Fortunately, the signals that are encountered in practical applications are often of this type. For example, the following shows a signal of this type. It has a relatively low frequency component throughout the entire signal and relatively high frequency components for a short duration somewhere around the middle.

THE CONTINUOUS WAVELET TRANSFORM

The continuous wavelet transform was developed as an alternative approach to the short time Fourier transform to overcome the resolution problem. The wavelet analysis is done in a similar way to the STFT analysis, in the sense that the signal is multiplied with a function, {\it the wavelet}, similar to the window function in the STFT, and the transform is computed separately for different segments of the time-domain signal. However, there are two main differences between the STFT and the CWT:

1. The Fourier transforms of the windowed signals are not taken, and therefore single peak will be seen corresponding to a sinusoid, i.e., negative frequencies are not computed.

2. The width of the window is changed as the transform is computed for every single spectral component, which is probably the most significant characteristic of the wavelet transform.

The continuous wavelet transform is defined as follows

Equation 3.1

As seen in the above equation , the transformed signal is a function of two variables, tau and s , the translation and scale parameters, respectively. psi(t) is the transforming function, and it is called the mother wavelet . The term mother wavelet gets its name due to two important properties of the wavelet analysis as explained below:

The term wavelet means a small wave . The smallness refers to the condition that this (window) function is of finite length ( compactly supported). The wave refers to the condition that this function is oscillatory . The term mother implies that the functions with different region of support that are used in the transformation process are derived from one main function, or the mother wavelet. In other words, the mother wavelet is a prototype for generating the other window functions.

The term translation is used in the same sense as it was used in the STFT; it is related to the location of the window, as the window is shifted through the signal. This term, obviously, corresponds to time information in the transform domain. However, we do not have a frequency parameter, as we had before for the STFT. Instead, we have scale parameter which is defined as $1/frequency$. The term frequency is reserved for the STFT. Scale is described in more detail in the next section.

The Scale

The parameter scale in the wavelet analysis is similar to the scale used in maps. As in the case of maps, high scales correspond to a non-detailed global view (of the signal), and low scales correspond to a detailed view. Similarly, in terms of frequency, low frequencies (high scales) correspond to a global information of a signal (that usually spans the entire signal), whereas high frequencies (low scales) correspond to a detailed information of a hidden pattern in the signal (that usually lasts a relatively short time). Cosine signals corresponding to various scales are given as examples in the following figure .

Figure 3.2

Fortunately in practical applications, low scales (high frequencies) do not last for the entire duration of the signal, unlike those shown in the figure, but they usually appear from time to time as short bursts, or spikes. High scales (low frequencies) usually last for the entire duration of the signal.

Scaling, as a mathematical operation, either dilates or compresses a signal. Larger scales correspond to dilated (or stretched out) signals and small scales correspond to compressed signals. All of the signals given in the figure are derived from the same cosine signal, i.e., they are dilated or compressed versions of the same function. In the above figure, s=0.05 is the smallest scale, and s=1 is the largest scale.

In terms of mathematical functions, if f(t) is a given function f(st) corresponds to a contracted (compressed) version of f(t) if s > 1 and to an expanded (dilated) version of f(t) if s <>.

However, in the definition of the wavelet transform, the scaling term is used in the denominator, and therefore, the opposite of the above statements holds, i.e., scales s > 1 dilates the signals whereas scales s <>, compresses the signal. This interpretation of scale will be used throughout this text.

COMPUTATION OF THE CWT

Interpretation of the above equation will be explained in this section. Let x(t) is the signal to be analyzed. The mother wavelet is chosen to serve as a prototype for all windows in the process. All the windows that are used are the dilated (or compressed) and shifted versions of the mother wavelet. There are a number of functions that are used for this purpose. The Morlet wavelet and the Mexican hat function are two candidates, and they are used for the wavelet analysis of the examples which are presented later in this chapter.

Once the mother wavelet is chosen the computation starts with s=1 and the continuous wavelet transform is computed for all values of s , smaller and larger than ``1''. However, depending on the signal, a complete transform is usually not necessary. For all practical purposes, the signals are bandlimited, and therefore, computation of the transform for a limited interval of scales is usually adequate. In this study, some finite interval of values for s were used, as will be described later in this chapter.

For convenience, the procedure will be started from scale s=1 and will continue for the increasing values of s , i.e., the analysis will start from high frequencies and proceed towards low frequencies. This first value of s will correspond to the most compressed wavelet. As the value of s is increased, the wavelet will dilate.

The wavelet is placed at the beginning of the signal at the point which corresponds to time=0. The wavelet function at scale ``1'' is multiplied by the signal and then integrated over all times. The result of the integration is then multiplied by the constant number 1/sqrt{s} . This multiplication is for energy normalization purposes so that the transformed signal will have the same energy at every scale. The final result is the value of the transformation, i.e., the value of the continuous wavelet transform at time zero and scale s=1 . In other words, it is the value that corresponds to the point tau =0 , s=1 in the time-scale plane.

The wavelet at scale s=1 is then shifted towards the right by tau amount to the location t=tau , and the above equation is computed to get the transform value at t=tau , s=1 in the time-frequency plane.

This procedure is repeated until the wavelet reaches the end of the signal. One row of points on the time-scale plane for the scale s=1 is now completed.

Then, s is increased by a small value. Note that, this is a continuous transform, and therefore, both tau and s must be incremented continuously . However, if this transform needs to be computed by a computer, then both parameters are increased by a sufficiently small step size. This corresponds to sampling the time-scale plane.

The above procedure is repeated for every value of s. Every computation for a given value of s fills the corresponding single row of the time-scale plane. When the process is completed for all desired values of s, the CWT of the signal has been calculated.

The figures below illustrate the entire process step by step.

Figure 3.3

In Figure 3.3, the signal and the wavelet function are shown for four different values of tau . The signal is a truncated version of the signal shown in Figure 3.1. The scale value is 1 , corresponding to the lowest scale, or highest frequency. Note how compact it is (the blue window). It should be as narrow as the highest frequency component that exists in the signal. Four distinct locations of the wavelet function are shown in the figure at to=2 , to=40, to=90, and to=140 . At every location, it is multiplied by the signal. Obviously, the product is nonzero only where the signal falls in the region of support of the wavelet, and it is zero elsewhere. By shifting the wavelet in time, the signal is localized in time, and by changing the value of s , the signal is localized in scale (frequency).

If the signal has a spectral component that corresponds to the current value of s (which is 1 in this case), the product of the wavelet with the signal at the location where this spectral component exists gives a relatively large value. If the spectral component that corresponds to the current value of s is not present in the signal, the product value will be relatively small, or zero. The signal in Figure 3.3 has spectral components comparable to the window's width at s=1 around t=100 ms.

The continuous wavelet transform of the signal in Figure 3.3 will yield large values for low scales around time 100 ms, and small values elsewhere. For high scales, on the other hand, the continuous wavelet transform will give large values for almost the entire duration of the signal, since low frequencies exist at all times.

Figure 3.4

Figure 3.5

Figures 3.4 and 3.5 illustrate the same process for the scales s=5 and s=20, respectively. Note how the window width changes with increasing scale (decreasing frequency). As the window width increases, the transform starts picking up the lower frequency components.

As a result, for every scale and for every time (interval), one point of the time-scale plane is computed. The computations at one scale construct the rows of the time-scale plane, and the computations at different scales construct the columns of the time-scale plane.

Now, let's take a look at an example, and see how the wavelet transform really looks like. Consider the non-stationary signal in Figure 3.6. This is similar to the example given for the STFT, except at different frequencies. As stated on the figure, the signal is composed of four frequency components at 30 Hz, 20 Hz, 10 Hz and 5 Hz.

Figure 3.6

Figure 3.7 is the continuous wavelet transform (CWT) of this signal. Note that the axes are translation and scale, not time and frequency. However, translation is strictly related to time, since it indicates where the mother wavelet is located. The translation of the mother wavelet can be thought of as the time elapsed since t=0 . The scale, however, has a whole different story. Remember that the scale parameter s in equation 3.1 is actually inverse of frequency. In other words, whatever we said about the properties of the wavelet transform regarding the frequency resolution, inverse of it will appear on the figures showing the WT of the time-domain signal.

Figure 3.7

Note that in Figure 3.7 that smaller scales correspond to higher frequencies, i.e., frequency decreases as scale increases, therefore, that portion of the graph with scales around zero, actually correspond to highest frequencies in the analysis, and that with high scales correspond to lowest frequencies. Remember that the signal had 30 Hz (highest frequency) components first, and this appears at the lowest scale at a translations of 0 to 30. Then comes the 20 Hz component, second highest frequency, and so on. The 5 Hz component appears at the end of the translation axis (as expected), and at higher scales (lower frequencies) again as expected.

Figure 3.8

Now, recall these resolution properties: Unlike the STFT which has a constant resolution at all times and frequencies, the WT has a good time and poor frequency resolution at high frequencies, and good frequency and poor time resolution at low frequencies. Figure 3.8 shows the same WT in Figure 3.7 from another angle to better illustrate the resolution properties: In Figure 3.8, lower scales (higher frequencies) have better scale resolution (narrower in scale, which means that it is less ambiguous what the exact value of the scale) which correspond to poorer frequency resolution . Similarly, higher scales have scale frequency resolution (wider support in scale, which means it is more ambitious what the exact value of the scale is) , which correspond to better frequency resolution of lower frequencies.

The axes in Figure 3.7 and 3.8 are normalized and should be evaluated accordingly. Roughly speaking the 100 points in the translation axis correspond to 1000 ms, and the 150 points on the scale axis correspond to a frequency band of 40 Hz (the numbers on the translation and scale axis do not correspond to seconds and Hz, respectively , they are just the number of samples in the computation).

TIME AND FREQUENCY RESOLUTIONS

In this section we will take a closer look at the resolution properties of the wavelet transform. Remember that the resolution problem was the main reason why we switched from STFT to WT.

The illustration in Figure 3.9 is commonly used to explain how time and frequency resolutions should be interpreted. Every box in Figure 3.9 corresponds to a value of the wavelet transform in the time-frequency plane. Note that boxes have a certain non-zero area, which implies that the value of a particular point in the time-frequency plane cannot be known. All the points in the time-frequency plane that falls into a box is represented by one value of the WT.

Figure 3.9

Let's take a closer look at Figure 3.9: First thing to notice is that although the widths and heights of the boxes change, the area is constant. That is each box represents an equal portion of the time-frequency plane, but giving different proportions to time and frequency. Note that at low frequencies, the height of the boxes are shorter (which corresponds to better frequency resolutions, since there is less ambiguity regarding the value of the exact frequency), but their widths are longer (which correspond to poor time resolution, since there is more ambiguity regarding the value of the exact time). At higher frequencies the width of the boxes decreases, i.e., the time resolution gets better, and the heights of the boxes increase, i.e., the frequency resolution gets poorer.

Before concluding this section, it is worthwhile to mention how the partition looks like in the case of STFT. Recall that in STFT the time and frequency resolutions are determined by the width of the analysis window, which is selected once for the entire analysis, i.e., both time and frequency resolutions are constant. Therefore the time-frequency plane consists of squares in the STFT case.

Regardless of the dimensions of the boxes, the areas of all boxes, both in STFT and WT, are the same and determined by Heisenberg's inequality . As a summary, the area of a box is fixed for each window function (STFT) or mother wavelet (CWT), whereas different windows or mother wavelets can result in different areas. However, all areas are lower bounded by 1/4 \pi . That is, we cannot reduce the areas of the boxes as much as we want due to the Heisenberg's uncertainty principle. On the other hand, for a given mother wavelet the dimensions of the boxes can be changed, while keeping the area the same. This is exactly what wavelet transform does.

THE WAVELET THEORY: A MATHEMATICAL APPROACH

This section describes the main idea of wavelet analysis theory, which can also be considered to be the underlying concept of most of the signal analysis techniques. The FT defined by Fourier use basis functions to analyze and reconstruct a function. Every vector in a vector space can be written as a linear combination of the basis vectors in that vector space , i.e., by multiplying the vectors by some constant numbers, and then by taking the summation of the products. The analysis of the signal involves the estimation of these constant numbers (transform coefficients, or Fourier coefficients, wavelet coefficients, etc). The synthesis, or the reconstruction, corresponds to computing the linear combination equation.

All the definitions and theorems related to this subject can be found in Keiser's book, A Friendly Guide to Wavelets but an introductory level knowledge of how basis functions work is necessary to understand the underlying principles of the wavelet theory. Therefore, this information will be presented in this section.

Basis Vectors

Note: Most of the equations include letters of the Greek alphabet. These letters are written out explicitly in the text with their names, such as tau, psi, phi etc. For capital letters, the first letter of the name has been capitalized, such as, Tau, Psi, Phi etc. Also, subscripts are shown by the underscore character _ , and superscripts are shown by the ^ character. Also note that all letters or letter names written in bold type face represent vectors, Some important points are also written in bold face, but the meaning should be clear from the context.

A basis of a vector space V is a set of linearly independent vectors, such that any vector v in V can be written as a linear combination of these basis vectors. There may be more than one basis for a vector space. However, all of them have the same number of vectors, and this number is known as the dimension of the vector space. For example in two-dimensional space, the basis will have two vectors.

Equation 3.2

Equation 3.2 shows how any vector v can be written as a linear combination of the basis vectors b_k and the corresponding coefficients nu^k .

This concept, given in terms of vectors, can easily be generalized to functions, by replacing the basis vectors b_k with basis functions phi_k(t), and the vector v with a function f(t). Equation 3.2 then becomes

Equation 3.2a

The complex exponential (sines and cosines) functions are the basis functions for the FT. Furthermore, they are orthogonal functions, which provide some desirable properties for reconstruction.

Let f(t) and g(t) be two functions in L^2 [a,b]. ( L^2 [a,b] denotes the set of square integrable functions in the interval [a,b]). The inner product of two functions is defined by Equation 3.3:

Equation 3.3

According to the above definition of the inner product, the CWT can be thought of as the inner product of the test signal with the basis functions psi_(tau ,s)(t):

Equation 3.4

where,

Equation 3.5

This definition of the CWT shows that the wavelet analysis is a measure of similarity between the basis functions (wavelets) and the signal itself. Here the similarity is in the sense of similar frequency content. The calculated CWT coefficients refer to the closeness of the signal to the wavelet at the current scale .

This further clarifies the previous discussion on the correlation of the signal with the wavelet at a certain scale. If the signal has a major component of the frequency corresponding to the current scale, then the wavelet (the basis function) at the current scale will be similar or close to the signal at the particular location where this frequency component occurs. Therefore, the CWT coefficient computed at this point in the time-scale plane will be a relatively large number.

Inner Products, Orthogonality, and Orthonormality

Two vectors v , w are said to be orthogonal if their inner product equals zero:

Equation 3.6

Similarly, two functions $f$ and $g$ are said to be orthogonal to each other if their inner product is zero:

Equation 3.7

A set of vectors {v_1, v_2, ....,v_n} is said to be orthonormal , if they are pairwise orthogonal to each other, and all have length ``1''. This can be expressed as:

Equation 3.8

Similarly, a set of functions {phi_k(t)}, k=1,2,3,..., is said to be orthonormal if

Equation 3.9

and

Equation 3.10

or equivalently

Equation 3.11

where, delta_{kl} is the Kronecker delta function, defined as:

Equation 3.12

As stated above, there may be more than one set of basis functions (or vectors). Among them, the orthonormal basis functions (or vectors) are of particular importance because of the nice properties they provide in finding these analysis coefficients. The orthonormal bases allow computation of these coefficients in a very simple and straightforward way using the orthonormality property.

For orthonormal bases, the coefficients, mu_k , can be calculated as

Equation 3.13

and the function f(t) can then be reconstructed by Equation 3.2_a by substituting the mu_k coefficients. This yields

Equation 3.14

Orthonormal bases may not be available for every type of application where a generalized version, biorthogonal bases can be used. The term ``biorthogonal'' refers to two different bases which are orthogonal to each other, but each do not form an orthogonal set.

In some applications, however, biorthogonal bases also may not be available in which case frames can be used. Frames constitute an important part of wavelet theory, and interested readers are referred to Kaiser's book mentioned earlier.

Following the same order as in chapter 2 for the STFT, some examples of continuous wavelet transform are presented next. The figures given in the examples were generated by a program written to compute the CWT.

Before we close this section, I would like to include two mother wavelets commonly used in wavelet analysis. The Mexican Hat wavelet is defined as the second derivative of the Gaussian function:

Equation 3.15

which is

Equation 3.16

The Morlet wavelet is defined as

Equation 3.16a

where a is a modulation parameter, and sigma is the scaling parameter that affects the width of the window.

EXAMPLES

All of the examples that are given below correspond to real-life non-stationary signals. These signals are drawn from a database signals that includes event related potentials of normal people, and patients with Alzheimer's disease. Since these are not test signals like simple sinusoids, it is not as easy to interpret them. They are shown here only to give an idea of how real-life CWTs look like.

The following signal shown in Figure 3.11 belongs to a normal person.

Figure 3.11

and the following is its CWT. The numbers on the axes are of no importance to us. those numbers simply show that the CWT was computed at 350 translation and 60 scale locations on the translation-scale plane. The important point to note here is the fact that the computation is not a true continuous WT, as it is apparent from the computation at finite number of locations. This is only a discretized version of the CWT, which is explained later on this page. Note, however, that this is NOT discrete wavelet transform (DWT) which is the topic of Part IV of this tutorial.

Figure 3.12

and the Figure 3.13 plots the same transform from a different angle for better visualization.

Figure 3.13

Figure 3.14 plots an event related potential of a patient diagnosed with Alzheimer's disease

Figure 3.14

and Figure 3.15 illustrates its CWT:

Figure 3.15

and here is another view from a different angle

Figure 3.16

THE WAVELET SYNTHESIS

The continuous wavelet transform is a reversible transform, provided that Equation 3.18 is satisfied. Fortunately, this is a very non-restrictive requirement. The continuous wavelet transform is reversible if Equation 3.18 is satisfied, even though the basis functions are in general may not be orthonormal. The reconstruction is possible by using the following reconstruction formula:

Equation 3.17 Inverse Wavelet Transform

where C_psi is a constant that depends on the wavelet used. The success of the reconstruction depends on this constant called, the admissibility constant , to satisfy the following admissibility condition :

Equation 3.18 Admissibility Condition

where psi^hat(xi) is the FT of psi(t). Equation 3.18 implies that psi^hat(0) = 0, which is

Equation 3.19

As stated above, Equation 3.19 is not a very restrictive requirement since many wavelet functions can be found whose integral is zero. For Equation 3.19 to be satisfied, the wavelet must be oscillatory.

Discretization of the Continuous Wavelet Transform: The Wavelet Series

In today's world, computers are used to do most computations (well,...ok... almost all computations). It is apparent that neither the FT, nor the STFT, nor the CWT can be practically computed by using analytical equations, integrals, etc. It is therefore necessary to discretize the transforms. As in the FT and STFT, the most intuitive way of doing this is simply sampling the time-frequency (scale) plane. Again intuitively, sampling the plane with a uniform sampling rate sounds like the most natural choice. However, in the case of WT, the scale change can be used to reduce the sampling rate.

At higher scales (lower frequencies), the sampling rate can be decreased, according to Nyquist's rule. In other words, if the time-scale plane needs to be sampled with a sampling rate of N_1 at scale s_1 , the same plane can be sampled with a sampling rate of N_2 , at scale s_2 , where, s_1 <>(corresponding to frequencies f1>f2 ) and N_2 <>. The actual relationship between N_1 and N_2 is

Equation 3.20

Equation 3.21

In other words, at lower frequencies the sampling rate can be decreased which will save a considerable amount of computation time.

It should be noted at this time, however, that the discretization can be done in any way without any restriction as far as the analysis of the signal is concerned. If synthesis is not required, even the Nyquist criteria does not need to be satisfied. The restrictions on the discretization and the sampling rate become important if, and only if, the signal reconstruction is desired. Nyquist's sampling rate is the minimum sampling rate that allows the original continuous time signal to be reconstructed from its discrete samples. The basis vectors that are mentioned earlier are of particular importance for this reason.

As mentioned earlier, the wavelet psi(tau,s) satisfying Equation 3.18, allows reconstruction of the signal by Equation 3.17. However, this is true for the continuous transform. The question is: can we still reconstruct the signal if we discretize the time and scale parameters? The answer is ``yes'', under certain conditions (as they always say in commercials: certain restrictions apply !!!).

The scale parameter s is discretized first on a logarithmic grid. The time parameter is then discretized with respect to the scale parameter , i.e., a different sampling rate is used for every scale. In other words, the sampling is done on the dyadic sampling grid shown in Figure 3.17 :

Figure 3.17

Think of the area covered by the axes as the entire time-scale plane. The CWT assigns a value to the continuum of points on this plane. Therefore, there are an infinite number of CWT coefficients. First consider the discretization of the scale axis. Among that infinite number of points, only a finite number are taken, using a logarithmic rule. The base of the logarithm depends on the user. The most common value is 2 because of its convenience. If 2 is chosen, only the scales 2, 4, 8, 16, 32, 64,...etc. are computed. If the value was 3, the scales 3, 9, 27, 81, 243,...etc. would have been computed. The time axis is then discretized according to the discretization of the scale axis. Since the discrete scale changes by factors of 2 , the sampling rate is reduced for the time axis by a factor of 2 at every scale.

Note that at the lowest scale (s=2), only 32 points of the time axis are sampled (for the particular case given in Figure 3.17). At the next scale value, s=4, the sampling rate of time axis is reduced by a factor of 2 since the scale is increased by a factor of 2, and therefore, only 16 samples are taken. At the next step, s=8 and 8 samples are taken in time, and so on.

Although it is called the time-scale plane, it is more accurate to call it the translation-scale plane, because ``time'' in the transform domain actually corresponds to the shifting of the wavelet in time. For the wavelet series, the actual time is still continuous.

Similar to the relationship between continuous Fourier transform, Fourier series and the discrete Fourier transform, there is a continuous wavelet transform, a semi-discrete wavelet transform (also known as wavelet series) and a discrete wavelet transform.

Expressing the above discretization procedure in mathematical terms, the scale discretization is s = s_0^j , and translation discretization is tau = k.s_0^j.tau_0 where s_0>1 and tau_0>0 . Note, how the translation discretization is dependent on scale discretization with s_0 .

The continuous wavelet function

Equation 3.22

Equation 3.23

by inserting s = s_0^j , and tau = k.s_0^j.tau_0 .

If {psi_(j,k)} constitutes an orthonormal basis, the wavelet series transform becomes

Equation 3.24

Equation 3.25

A wavelet series requires that {psi_(j,k)} are either orthonormal, biorthogonal, or frame. If {psi_(j,k)} are not orthonormal, Equation 3.24 becomes

Equation 3.26

where hat{ psi_{j,k}^*(t)} , is either the dual biorthogonal basis or dual frame (Note that * denotes the conjugate).

If {psi_(j,k) } are orthonormal or biorthogonal, the transform will be non-redundant, where as if they form a frame, the transform will be redundant. On the other hand, it is much easier to find frames than it is to find orthonormal or biorthogonal bases.

The following analogy may clear this concept. Consider the whole process as looking at a particular object. The human eyes first determine the coarse view which depends on the distance of the eyes to the object. This corresponds to adjusting the scale parameter s_0^(-j). When looking at a very close object, with great detail, j is negative and large (low scale, high frequency, analyses the detail in the signal). Moving the head (or eyes) very slowly and with very small increments (of angle, of distance, depending on the object that is being viewed), corresponds to small values of tau = k.s_0^j.tau_0 . Note that when j is negative and large, it corresponds to small changes in time, tau , (high sampling rate) and large changes in s_0^-j (low scale, high frequencies, where the sampling rate is high). The scale parameter can be thought of as magnification too.

How low can the sampling rate be and still allow reconstruction of the signal? This is the main question to be answered to optimize the procedure. The most convenient value (in terms of programming) is found to be ``2'' for s_0 and "1" for tau. Obviously, when the sampling rate is forced to be as low as possible, the number of available orthonormal wavelets is also reduced.

The continuous wavelet transform examples that were given in this chapter were actually the wavelet series of the given signals. The parameters were chosen depending on the signal. Since the reconstruction was not needed, the sampling rates were sometimes far below the critical value where s_0 varied from 2 to 10, and tau_0 varied from 2 to 8, for different examples.

This concludes Part III of this tutorial. I hope you now have a basic understanding of what the wavelet transform is all about. There is one thing left to be discussed however. Even though the discretized wavelet transform can be computed on a computer, this computation may take anywhere from a couple seconds to couple hours depending on your signal size and the resolution you want. An amazingly fast algorithm is actually available to compute the wavelet transform of a signal. The discrete wavelet transform (DWT) is introduced in the final chapter of this tutorial, in Part IV.

Let's meet at the grand finale, shall we?

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Qt4 with Visual Studio

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Contents

Building Qt

Obtain and install the Qt source

Download and install the patch allowing Qt to be compiled with Visual Studio compilers

Open a command prompt in the Qt source directory

Patching the Qt sources

Configuring your Qt install (and building qmake)

Building the Qt library

Setting up your environment

Testing your install

Creating Visual Studio projects

Notes on Creating Visual Studio projects

Maintaining Visual Studio Projects

Another way for creating and maintaining Visual Studio Projects

Buildproblems with Visual Studio 2005 and service pack 1

Relationships Among MFC Objects

How to: Convert Between Various String Types

Converting from char *

Example

Output

Converting from wchar_t *

Example

Output

Converting from _bstr_t

Example

Output

Converting from CComBSTR

Example

Output

Converting from CString

Example

Output

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Example

Output

Converting from System::String

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Output

Computer Vision Software

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Error with MSVCR80.DLL !!!!!!!!!!!!

Hausdorff distance between convex polygons

Fractals and the Fractal Dimension

Fractals and the Fractal Dimension

Mandelbrot and Nature

The Concept of Dimension

The Hausdorff Dimension

The length of a coastline

The "Richardson Effect"

Examples of geometric objects with non-integer dimensions

Koch Curve

Cantor Dust

Sierpinski Triangle

The dimensionality of a strange attractor

Self-similarity

Mandelbrot Set

So, what is a fractal?

Why do we care about fractals?

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Configuring your Qt install (and building `qmake`)

The Wavelet Tutorial

Part III

MULTIRESOLUTION ANALYSIS
&
THE CONTINUOUS WAVELET TRANSFORM