Fundamentals of digital image processing : a practical approach with examples in Matlab

Fundamentals of Digital Image Processing: A Practical Approach with Examples in Matlab......Page 2
Contents......Page 8
Preface......Page 14
Using the book website......Page 18
1.1.1 Image layout......Page 20
1.1.2 Image colour......Page 21
1.2 Resolution and quantization......Page 22
1.2.1 Bit-plane splicing......Page 23
1.3 Image formats......Page 24
1.3.1 Image data types......Page 25
1.3.2 Image compression......Page 26
1.4 Colour spaces......Page 28
1.4.1 RGB......Page 29
1.4.1.1 RGB to grey-scale image conversion......Page 30
1.4.2 Perceptual colour space......Page 31
1.5.1 Reading, writing and querying images......Page 33
1.5.2 Basic display of images......Page 34
1.5.3 Accessing pixel values......Page 35
1.5.4 Converting image types......Page 36
Exercises......Page 37
2.1 How is an image formed?......Page 40
2.2.1 Introduction......Page 41
2.2.2 Linear imaging systems......Page 42
2.2.3 Linear superposition integral......Page 43
2.2.4 The Dirac delta or impulse function......Page 44
2.2.5 The point-spread function......Page 47
2.2.6 Linear shift-invariant systems and the convolution integral......Page 48
2.2.7 Convolution: its importance and meaning......Page 49
2.2.9 Digital convolution......Page 53
2.3 The engineering of image formation......Page 56
2.3.1 The camera......Page 57
2.3.2.1 Quantization......Page 59
2.3.2.2 Digitization hardware......Page 61
2.3.2.3 Resolution versus performance......Page 62
2.3.3 Noise......Page 63
Exercises......Page 65
3.1 What is a pixel?......Page 68
3.2 Operations upon pixels......Page 69
3.2.1.1 Image addition and subtraction......Page 70
3.2.1.2 Image multiplication and division......Page 72
3.2.2 Logical operations on images......Page 73
3.2.3 Thresholding......Page 75
3.3.1 Logarithmic transform......Page 76
3.3.2 Exponential transform......Page 78
3.3.3 Power-law (gamma) transform......Page 80
3.3.3.1 Application: gamma correction......Page 81
3.4 Pixel distributions: histograms......Page 82
3.4.1 Histograms for threshold selection......Page 84
3.4.2 Adaptive thresholding......Page 85
3.4.3 Contrast stretching......Page 86
3.4.4.1 Histogram equalization theory......Page 88
3.4.4.2 Histogram equalization theory: discrete case......Page 89
3.4.4.3 Histogram equalization in practice......Page 90
3.4.5.1 Histogram matching theory......Page 92
3.4.5.2 Histogram matching theory: discrete case......Page 93
3.4.5.3 Histogram matching in practice......Page 94
3.4.6 Adaptive histogram equalization......Page 95
3.4.7 Histogram operations on colour images......Page 98
Exercises......Page 100
4.1.1 Enhancement via image filtering......Page 104
4.2 Pixel neighbourhoods......Page 105
4.3 Filter kernels and the mechanics of linear filtering......Page 106
4.4 Filtering for noise removal......Page 109
4.4.1 Mean filtering......Page 110
4.4.2 Median filtering......Page 111
4.4.3 Rank filtering......Page 113
4.4.4 Gaussian filtering......Page 114
4.5.1 Derivative filters for discontinuities......Page 116
4.5.2 First-order edge detection......Page 118
4.5.2.1 Linearly separable filtering......Page 120
4.5.3.1 Laplacian edge detection......Page 121
4.5.3.2 Laplacian of Gaussian......Page 122
4.5.3.3 Zero-crossing detector......Page 123
4.6.1 Laplacian edge sharpening......Page 124
4.6.2 The unsharp mask filter......Page 126
Exercises......Page 128
5.1 Frequency space: a friendly introduction......Page 132
5.2 Frequency space: the fundamental idea......Page 133
5.2.1 The Fourier series......Page 134
5.4 Complex Fourier series......Page 137
5.5 The 1-D Fourier transform......Page 138
5.6 The inverse Fourier transform and reciprocity......Page 140
5.7 The 2-D Fourier transform......Page 142
5.8 Understanding the Fourier transform: frequency-space filtering......Page 145
5.10 The convolution theorem......Page 148
5.11 The optical transfer function......Page 150
5.12 Digital Fourier transforms: the discrete fast Fourier transform......Page 153
5.13 Sampled data: the discrete Fourier transform......Page 154
5.14 The centred discrete Fourier transform......Page 155
6.1 Imaging models......Page 160
6.2 Nature of the point-spread function and noise......Page 161
6.3 Restoration by the inverse Fourier filter......Page 162
6.4 The Wiener–Helstrom filter......Page 165
6.5 Origin of the Wiener–Helstrom filter......Page 166
6.7 Constrained deconvolution......Page 170
6.8 Estimating an unknown point-spread function or optical transfer function......Page 173
6.9 Blind deconvolution......Page 175
6.10 Iterative deconvolution and the Lucy–Richardson algorithm......Page 177
6.11 Matrix formulation of image restoration......Page 180
6.12 The standard least-squares solution......Page 181
6.13 Constrained least-squares restoration......Page 182
6.15 The generalized Gauss–Markov estimator......Page 184
7.1 The description of shape......Page 188
7.2 Shape-preserving transformations......Page 189
7.3 Shape transformation and homogeneous coordinates......Page 190
10.2 Use of image properties and features in segmentation......Page 1
7.5 Affine transformation in homogeneous coordinates......Page 193
7.6 The procrustes transformation......Page 194
7.7 Procrustes alignment......Page 195
7.8 The projective transform......Page 199
7.9 Nonlinear transformations......Page 203
7.10 Warping: the spatial transformation of an image......Page 205
7.11 Overdetermined spatial transformations......Page 208
7.13 The piecewise affine warp......Page 210
7.14 Warping: forward and reverse mapping......Page 213
8.2 Binary images: foreground, background and connectedness......Page 216
8.3 Structuring elements and neighbourhoods......Page 217
8.4 Dilation and erosion......Page 219
8.5 Dilation, erosion and structuring elements within Matlab......Page 220
8.6 Structuring element decomposition and Matlab......Page 221
8.7 Effects and uses of erosion and dilation......Page 223
8.7.1 Application of erosion to particle sizing......Page 226
8.8 Morphological opening and closing......Page 228
8.8.1 The rolling-ball analogy......Page 229
8.9 Boundary extraction......Page 231
8.10 Extracting connected components......Page 232
8.11 Region filling......Page 234
8.12 The hit-or-miss transformation......Page 235
8.12.1 Generalization of hit-or-miss......Page 238
8.13 Relaxing constraints in hit-or-miss: ‘don’t care’ pixels......Page 239
8.14 Skeletonization......Page 241
8.15 Opening by reconstruction......Page 243
8.17 Grey-scale structuring elements: general case......Page 246
8.18 Grey-scale erosion and dilation with flat structuring elements......Page 247
8.19 Grey-scale opening and closing......Page 248
8.20 The top-hat transformation......Page 249
8.21 Summary......Page 250
Exercises......Page 252
9.1 Landmarks and shape vectors......Page 254
9.2 Single-parameter shape descriptors......Page 256
9.3 Signatures and the radial fourier expansion......Page 258
9.4 Statistical moments as region descriptors......Page 262
9.5 Texture features based on statistical measures......Page 265
9.7 Principal component analysis: an illustrative example......Page 266
9.8 Theory of principal component analysis: version 1......Page 269
9.9 Theory of principal component analysis: version 2......Page 270
9.11 Summary of properties of principal component analysis......Page 272
9.12 Dimensionality reduction: the purpose of principal component analysis......Page 275
9.14 Representation of out-of-sample examples using principal component analysis......Page 276
9.15 Key example: eigenfaces and the human face......Page 278
10.3 Intensity thresholding......Page 284
10.3.1 Problems with global thresholding......Page 285
10.5 Split-and-merge algorithm......Page 286
10.7 The laplacian of Gaussian and difference of Gaussians filters......Page 289
10.8 The Canny edge detector......Page 290
10.9 Interest operators......Page 293
10.10 Watershed segmentation......Page 298
10.11 Segmentation functions......Page 299
10.12 Image segmentation with markov random fields......Page 305
10.12.1 Parameter estimation......Page 307
10.12.2 Neighbourhood weighting parameter θn......Page 308
10.12.3 Minimizing U(x | y): the iterated conditional modes algorithm......Page 309
11.1 The purpose of automated classification......Page 310
11.3 Classification: a simple example......Page 311
11.4 Design of classification systems......Page 313
11.5 Simple classifiers: prototypes and minimum distance criteria......Page 315
11.6 Linear discriminant functions......Page 316
11.7 Linear discriminant functions in N dimensions......Page 320
11.8 Extension of the minimum distance classifier and the Mahalanobis distance......Page 321
11.9 Bayesian classification: definitions......Page 322
11.10 The Bayes decision rule......Page 323
11.11 The multivariate normal density......Page 325
11.12 Bayesian classifiers for multivariate normal distributions......Page 326
11.12.1 The Fisher linear discriminant......Page 329
11.12.2 Risk and cost functions......Page 330
11.13 Ensemble classifiers......Page 331
11.14 Unsupervised learning: k-means clustering......Page 332
Further reading......Page 336
Index......Page 338
Colour Plates......Page 348