Feature Extraction & Image Processing (eBook)

Cover 1
Title page 4
Copyright Page 5
Table of Contents 6
Preface 12
Chapter 1 Introduction 18
1.1 Overview 18
1.2 Human and computer vision 18
1.3 The human vision system 20
1.3.1 The eye 21
1.3.2 The neural system 23
1.3.3 Processing 24
1.4 Computer vision systems 26
1.4.1 Cameras 27
1.4.2 Computer interfaces 29
1.4.3 Processing an image 31
1.5 Mathematical systems 32
1.5.1 Mathematical tools 33
1.5.2 Hello Mathcad, hello images! 33
1.5.3 Hello Matlab! 38
1.6 Associated literature 41
1.6.1 Journals and magazines 41
1.6.2 Textbooks 42
1.6.3 The web 45
1.7 Conclusions 46
1.8 References 46
Chapter 2 Images, sampling and frequency domain processing 50
2.1 Overview 50
2.2 Image formation 51
2.3 The Fourier transform 54
2.4 The sampling criterion 60
2.5 The discrete Fourier transform 64
2.5.1 One-dimensional transform 64
2.5.2 Two-dimensional transform 66
2.6 Other properties of the Fourier transform 71
2.6.1 Shift invariance 71
2.6.2 Rotation 73
2.6.3 Frequency scaling 73
2.6.4 Superposition (linearity) 74
2.7 Transforms other than Fourier 75
2.7.1 Discrete cosine transform 75
2.7.2 Discrete Hartley transform 76
2.7.3 Introductory wavelets: the Gabor wavelet 78
2.7.4 Other transforms 80
2.8 Applications using frequency domain properties 81
2.9 Further reading 82
2.10 References 83
Chapter 3 Basic image processing operations 86
3.1 Overview 86
3.2 Histograms 87
3.3 Point operators 88
3.3.1 Basic point operations 88
3.3.2 Histogram normalization 91
3.3.3 Histogram equalization 92
3.3.4 Thresholding 94
3.4 Group operations 98
3.4.1 Template convolution 98
3.4.2 Averaging operator 101
3.4.3 On different template size 104
3.4.4 Gaussian averaging operator 105
3.5 Other statistical operators 107
3.5.1 More on averaging 107
3.5.2 Median filter 108
3.5.3 Mode filter 111
3.5.4 Anisotropic diffusion 113
3.5.5 Force field transform 118
3.5.6 Comparison of statistical operators 119
3.6 Mathematical morphology 120
3.6.1 Morphological operators 121
3.6.2 Grey-level morphology 124
3.6.3 Grey-level erosion and dilation 125
3.6.4 Minkowski operators 126
3.7 Further reading 129
3.8 References 130
Chapter 4 Low-level feature extraction (including edge detection) 132
4.1 Overview 132
4.2 First order edge detection operators 134
4.2.1 Basic operators 134
4.2.2 Analysis of the basic operators 136
4.2.3 Prewitt edge detection operator 138
4.2.4 Sobel edge detection operator 140
4.2.5 Canny edge detection operator 146
4.3 Second order edge detection operators 154
4.3.1 Motivation 154
4.3.2 Basic operators: the Laplacian 154
4.3.3 Marr–Hildreth operator 156
4.4 Other edge detection operators 161
4.5 Comparison of edge detection operators 162
4.6 Further reading on edge detection 163
4.7 Phase congruency 164
4.8 Localized feature extraction 169
4.8.1 Detecting image curvature (corner extraction) 170
4.8.1.1 Definition of curvature 170
4.8.1.2 Computing differences in edge direction 171
4.8.1.3 Measuring curvature by changes in intensity (differentiation) 173
4.8.1.4 Moravec and Harris detectors 176
4.8.1.5 Further reading on curvature 180
4.8.2 Modern approaches: region/patch analysis 180
4.8.2.1 Scale invariant feature transform 180
4.8.2.2 Saliency 183
4.8.2.3 Other techniques and performance issues 184
4.9 Describing image motion 184
4.9.1 Area-based approach 185
4.9.2 Differential approach 188
4.9.3 Further reading on optical flow 194
4.10 Conclusions 195
4.11 References 195
Chapter 5 Feature extraction by shape matching 200
5.1 Overview 200
5.2 Thresholding and subtraction 201
5.3 Template matching 203
5.3.1 Definition 203
5.3.2 Fourier transform implementation 210
5.3.3 Discussion of template matching 213
5.4 Hough transform 213
5.4.1 Overview 213
5.4.2 Lines 214
5.4.3 Hough transform for circles 220
5.4.4 Hough transform for ellipses 224
5.4.5 Parameter space decomposition 227
5.4.5.1 Parameter space reduction for lines 227
5.4.5.2 Parameter space reduction for circles 229
5.4.5.3 Parameter space reduction for ellipses 234
5.5 Generalized Hough transform 238
5.5.1 Formal definition of the GHT 238
5.5.2 Polar definition 240
5.5.3 The GHT technique 241
5.5.4 Invariant GHT 245
5.6 Other extensions to the Hough transform 252
5.7 Further reading 253
5.8 References 254
Chapter 6 Flexible shape extraction (snakes and other techniques) 258
6.1 Overview 258
6.2 Deformable templates 259
6.3 Active contours (snakes) 261
6.3.1 Basics 261
6.3.2 The greedy algorithm for snakes 263
6.3.3 Complete (Kass) snake implementation 269
6.3.4 Other snake approaches 274
6.3.5 Further snake developments 274
6.3.6 Geometric active contours 278
6.4 Shape skeletonization 283
6.4.1 Distance transforms 283
6.4.2 Symmetry 285
6.5 Flexible shape models: active shape and active appearance 289
6.6 Further reading 292
6.7 References 293
Chapter 7 Object description 298
7.1 Overview 298
7.2 Boundary descriptions 299
7.2.1 Boundary and region 299
7.2.2 Chain codes 300
7.2.3 Fourier descriptors 302
7.2.3.1 Basis of Fourier descriptors 303
7.2.3.2 Fourier expansion 304
7.2.3.3 Shift invariance 306
7.2.3.4 Discrete computation 307
7.2.3.5 Cumulative angular function 309
7.2.3.6 Elliptic Fourier descriptors 318
7.2.3.7 Invariance 322
7.3 Region descriptors 328
7.3.1 Basic region descriptors 328
7.3.2 Moments 332
7.3.2.1 Basic properties 332
7.3.2.2 Invariant moments 335
7.3.2.3 Zernike moments 337
7.3.2.4 Other moments 341
7.4 Further reading 342
7.5 References 343
Chapter 8 Introduction to texture description, segmentation and classification 346
8.1 Overview 346
8.2 What is texture? 347
8.3 Texture description 349
8.3.1 Performance requirements 349
8.3.2 Structural approaches 349
8.3.3 Statistical approaches 352
8.3.4 Combination approaches 354
8.4 Classification 356
8.4.1 The k-nearest neighbour rule 356
8.4.2 Other classification approaches 360
8.5 Segmentation 360
8.6 Further reading 362
8.7 References 363
Chapter 9 Appendix 1: Example worksheets 366
9.1 Example Mathcad worksheet for Chapter 3 366
9.2 Example Matlab worksheet for Chapter 4 369
Chapter 10 Appendix 2: Camera geometry fundamentals 372
10.1 Image geometry 372
10.2 Perspective camera 372
10.3 Perspective camera model 374
10.3.1 Homogeneous coordinates and projective geometry 374
10.3.1.1 Representation of a line and duality 375
10.3.1.2 Ideal points 375
10.3.1.3 Transformations in the projective space 376
10.3.2 Perspective camera model analysis 377
10.3.3 Parameters of the perspective camera model 380
10.4 Affine camera 381
10.4.1 Affine camera model 382
10.4.2 Affine camera model and the perspective projection 383
10.4.3 Parameters of the affine camera model 385
10.5 Weak perspective model 386
10.6 Example of camera models 388
10.7 Discussion 396
10.8 References 397
Chapter 11 Appendix 3: Least squares analysis 398
11.1 The least squares criterion 398
11.2 Curve fitting by least squares 399
Chapter 12 Appendix 4: Principal components analysis 402
12.1 Introduction 402
12.2 Data 402
12.3 Covariance 403
12.4 Covariance matrix 405
12.5 Data transformation 406
12.6 Inverse transformation 407
12.7 Eigenproblem 408
12.8 Solving the eigenproblem 409
12.9 PCA method summary 409
12.10 Example 410
12.11 References 415
Index 416