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Chapter 3

Image processing

3.1 Point operators ................................. 89
3.1.1 Pixel transforms ............................ 91
3.1.2 Color transforms ............................ 92
3.1.3 Compositing and matting ........................ 92
3.1.4 Histogram equalization ......................... 94
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

R. Szeliski, Computer Vision: Algorithms and Applications, Texts in Computer Science, 87
DOI 10.1007/978-1-84882-935-0_3, © Springer-Verlag London Limited 2011