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xiv Contents

3.1.5 Application: Tonal adjustment ..................... 97
3.2 Linear filtering ................................. 98
3.2.1 Separable filtering ........................... 102
3.2.2 Examples of linear filtering ....................... 103
3.2.3 Band-pass and steerable filters ..................... 104
3.3 More neighborhood operators .......................... 108
3.3.1 Non-linear filtering ........................... 108
3.3.2 Morphology .............................. 112
3.3.3 Distance transforms .......................... 113
3.3.4 Connected components ......................... 115
3.4 Fourier transforms ............................... 116
3.4.1 Fourier transform pairs ......................... 119
3.4.2 Two-dimensional Fourier transforms .................. 123
3.4.3 Wiener filtering ............................. 123
3.4.4 Application: Sharpening, blur, and noise removal ........... 126
3.5 Pyramids and wavelets ............................. 127
3.5.1 Interpolation .............................. 127
3.5.2 Decimation ............................... 130
3.5.3 Multi-resolution representations .................... 132
3.5.4 Wavelets ................................ 136
3.5.5 Application: Image blending ...................... 140
3.6 Geometric transformations ........................... 143
3.6.1 Parametric transformations ....................... 145
3.6.2 Mesh-based warping .......................... 149
3.6.3 Application: Feature-based morphing ................. 152
3.7 Global optimization ............................... 153
3.7.1 Regularization ............................. 154
3.7.2 Markov random fields ......................... 158
3.7.3 Application: Image restoration ..................... 169
3.8 Additional reading ............................... 169
3.9 Exercises .................................... 171

4 Feature detection and matching 181
4.1 Points and patches ................................ 183
4.1.1 Feature detectors ............................ 185
4.1.2 Feature descriptors ........................... 196
4.1.3 Feature matching ............................ 200
4.1.4 Feature tracking ............................ 207
4.1.5 Application: Performance-driven animation .............. 209
4.2 Edges ...................................... 210
4.2.1 Edge detection ............................. 210
4.2.2 Edge linking .............................. 215
4.2.3 Application: Edge editing and enhancement .............. 219
4.3 Lines ...................................... 220
4.3.1 Successive approximation ....................... 220
4.3.2 Hough transforms ............................ 221