Image Processing: The Fundamentals, 2nd Edition

Preface xxiii

1 Introduction 1

2 Image Transformations 47

2.1 Singular value decomposition 51

2.2 Haar, Walsh and Hadamard transforms 74

2.3 Discrete Fourier transform 94

2.4 The even symmetric discrete cosine transform (EDCT) 138

2.5 The odd symmetric discrete cosine transform (ODCT) 149

2.6 The even antisymmetric discrete sine transform (EDST) 157

2.7 The odd antisymmetric discrete sine transform (ODST) 167

3 Statistical Description of Images 177

3.1 Random fields 178

3.2 Karhunen-Loeve transform 201

3.3 Independent component analysis 234

4 Image Enhancement 293

4.1 Elements of linear filter theory 294

4.2 Reducing high frequency noise 311

4.3 Reducing low frequency interference 351

4.4 Histogram manipulation 367

4.5 Generic deblurring algorithms 383

5 Image Restoration 395

5.1 Homogeneous linear image restoration: inverse filtering 396

5.2 Homogeneous linear image restoration: Wiener filtering 419

5.3 Homogeneous linear image restoration: Constrained matrix inversion 436

5.4 Inhomogeneous linear image restoration: the whirl transform 468

5.5 Nonlinear image restoration: MAP estimation 490

5.6 Geometric image restoration 513

6 Image Segmentation and Edge Detection 527

6.1 Image segmentation 528

6.2 Edge detection 591

6.3 Phase congruency and the monogenic signal 625

7 Image Processing for Multispectral Images 669

7.1 Image preprocessing for multispectral images 671

7.2 The physics and psychophysics of colour vision 700

7.3 Colour image processing in practice 742

Bibliographical notes 775

References 777

Index 781