Table of Contents
Preface vii
Chapter 1 Introduction 1
1.1 Wavelet: A Novel Mathematical Tool for Pattern Recognition 1
1.2 Brief Review of Pattern Recognition with Wavelet Theory 18
1.2.1 Iris Pattern Recognition 21
1.2.2 Face Recognition Using Wavelet Transform 22
1.2.3 Hand Gestures Classification 28
1.2.4 Classification and Clustering 31
1.2.5 Document Analysis with Wavelets 37
1.2.6 Analysis and Detection of Singularities with Wavelets 43
1.2.7 Wavelet Descriptors for Shapes of the Objects 46
1.2.8 Invariant Representation of Patterns 49
1.2.9 Handwritten and Printed Character Recognition 56
1.2.10 Texture Analysis and Classification 61
1.2.11 Image Indexing and Retrieval 67
1.2.12 Wavelet-Based Image Fusion 70
1.2.13 Others 72
Chapter 2 Continuous Wavelet Transforms 75
2.1 General Theory of Continuous Wavelet Transforms 75
2.2 The Continuous Wavelet Transform as a Filter 91
2.3 Characterization of Lipschitz Regularity of Signal by Wavelet 94
2.4 Some Examples of Basic Wavelets 98
Chapter 3 Multiresolution Analysis and Wavelet Bases 105
3.1 Multiresolution Analysis 105
3.1.1 Basic Concept of Multiresolution Analysis (MRA) 105
3.1.2 The Solution of Two-Scale Equation 109
3.2 The Construction of MRAs 120
3.2.1 The Biorthonormal MRA 127
3.2.2 Examples of Constructing MRA 133
3.3 The Construction of Biorthonormal Wavelet Bases 143
3.4 S. Mallat Algorithms 148
Chapter 4 Some Typical Wavelet Bases 153
4.1 Orthonormal Wavelet Bases 156
4.1.1 Haar Wavelet 156
4.1.2 Littlewood-Paley (LP) Wavelet 158
4.1.3 Meyer Wavelet 160
4.1.4 Battle-Lemaré-spline Wavelet 162
4.1.5 Daubechies' Compactly Supported Orthonormal Wavelets 166
4.1.6 Coiflet 178
4.2 Nonorthonormal Wavelet Bases 181
4.2.1 Cardinal Spline Wavelet 181
4.2.2 Compactly Supported Spline Wavelet 196
Chapter 5 Step-Edge Detection by Wavelet Transform 201
5.1 Edge Detection with Local Maximal Modulus of Wavelet Transform 202
5.2 Calculation of Wsf(x) and Wsf(x, y) 211
5.2.1 Calculation of Wsf(x) 213
5.2.2 Calculation of Wsf(x, y) 215
5.3 Wavelet Transform for Contour Extraction and Background Removal 220
5.3.1 Basic Edge Structures 225
5.3.2 Analysis of the Basic Edge Structures with Wavelet Transform 228
5.3.3 Scale-Independent Algorithm 239
5.3.4 Experiments 242
Chapter 6 Characterization of Dirac-Edges with Quadratic Spline Wavelet Transform 251
6.1 Selection of Wavelet Functions by Derivation 252
6.1.1 Scale Wavelet Transform 253
6.1.2 Construction of Wavelet Function by Derivation of the Low-Pass Function 255
6.2 Characterization of Dirac-Structure Edges by Wavelet Transform 258
6.2.1 Slope Invariant 263
6.2.2 Grey-Level Invariant 265
6.2.3 Width Light-Dependent 267
6.3 Experiments 272
Chapter 7 Construction of New Wavelet Function and Application to Curve Analysis 279
7.1 Construction of New Wavelet Function - Tang-Yang Wavelet 282
7.2 Characterization of Curves through New Wavelet Transform 285
7.3 Comparison with Other Wavelets 295
7.3.1 Comparison with Gaussian Wavelets 296
7.3.2 Comparison with Quadratic Spline Wavelets 300
7.4 Algorithm and Experiments 301
7.4.1 Algorithm 301
7.4.2 Experiments 305
Chapter 8 Skeletonization of Ribbon-like Shapes with New Wavelet Function 311
8.1 Tang-Yang Wavelet Function 315
8.2 Characterization of the Boundary of a Shape by Wavelet Transform 317
8.3 Wavelet Skeletons and Its Implementation 322
8.3.1 Wavelet, Transform in the Discrete Domain 322
8.3.2 Generation of Wavelet Skeleton in the Discrete Domain 325
8.3.3 Modification of Primary Wavelet Skeleton 327
8.4 Algorithm and Experiment 331
8.4.1 Algorithm 331
8.4.2 Experiments 332
Chapter 9 Feature Extraction by Wavelet Sub-Patterns and Divider Dimensions 343
9.1 Dimensionality Reduction of Two-Dimensional Patterns with Ring-Projection 346
9.2 Wavelet Orthonormal Decomposition to Produce Sub-Patterns 351
9.3 Wavelet-Fractal Scheme 358
9.3.1 Basic Concepts of Fractal Dimension 359
9.3.2 The Divider Dimension of One-Dimensional Patterns 365
9.4 Experiments 367
9.4.1 Experimental Procedure 367
9.4.2 Experimental Results 368
Chapter 10 Document Analysis by Reference Line Detection with 2-D Wavelet Transform 381
10.1 Two-Dimensional MRA and Mallat Algorithm 383
10.2 Detection of Reference Line from Sub-Images by the MRA 387
10.3 Experiments 390
Chapter 11 Chinese Character Processing with B-Spline Wavelet Transform 399
11.1 Compression of Chinese Character 404
11.1.1 Algorithm 1 (Global Approach) 404
11.1.2 Algorithm 2 (Local Approach) 406
11.1.3 Experiments 407
11.2 Enlargement of Type Size with Arbitrary Scale Based on Wavelet Transform 408
11.2.1 Algorithms 409
11.2.2 Experiments 414
11.3 Generation of Chinese Type Style Based on Wavelet Transform 415
11.3.1 Modification 416
11.3.2 Composition 424
Chapter 12 Classifier Design Based on Orthogonal Wavelet Series 429
12.1 Fundamentals 429
12.2 Minimum Average Lose Classifier Design 433
12.3 Minimum Error-Probability Classifier Design 435
12.4 Probability Density Estimation Based on Orthogonal Wavelet Series 437
12.4.1 Kernel Estimation of a Density Function 437
12.4.2 Orthogonal Series Probability Density Estimators 439
12.4.3 Orthogonal Wavelet Series Density Estimators 441
List of Symbols 449
Bibliography 451
Index 461
