Page 8 -

vi

2.5 Notes . . . . . ... .. .. ... .. .. ... .. ... .. .. ... . 61

3 Color 68
3.1 Human Color Perception .. ... .. .. ... .. ... .. .. ... . 68
3.1.1 Color Matching . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1.2 Color Receptors . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.2 The Physics of Color . . . . ... .. .. ... .. ... .. .. ... . 73
3.2.1 The Color of Light Sources . . . . .. .. ... .. .. ... . 73
3.2.2 The Color of Surfaces .. .. .. ... .. ... .. .. ... . 76
3.3 Representing Color . .. .. ... .. .. ... .. ... .. .. ... . 77
3.3.1 Linear Color Spaces . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.2 Non-linear Color Spaces . . . . . . . . . . . . . . . . . . . . . 83
3.4 A Model of Image Color . . . .. .. .. ... .. ... .. .. ... . 86
3.4.1 The Diffuse Term .. ... .. .. ... .. ... .. .. ... . 88
3.4.2 The Specular Term . ... .. .. ... .. ... .. .. ... . 90
3.5 Inference from Color . . . . ... .. .. ... .. ... .. .. ... . 90
3.5.1 Finding Specularities Using Color . . . . . . . . . . . . . . . 90
3.5.2 Shadow Removal Using Color . . . .. .. ... .. .. ... . 92
3.5.3 Color Constancy: Surface Color from Image Color . . . . . . 95
3.6 Notes . . . . . ... .. .. ... .. .. ... .. ... .. .. ... . 99

II EARLY VISION: JUST ONE IMAGE 105

4 Linear Filters 107
4.1 Linear Filters and Convolution . . . . . . . . . . . . . . . . . . . . . 107
4.1.1 Convolution . .. .. ... .. .. ... .. ... .. .. ... . 107
4.2 Shift Invariant Linear Systems . . . . . . . . . . . . . . . . . . . . . 112
4.2.1 Discrete Convolution ... .. .. ... .. ... .. .. ... . 113
4.2.2 Continuous Convolution . .. .. ... .. ... .. .. ... . 115
4.2.3 Edge Effects in Discrete Convolutions .. ... .. .. ... . 118
4.3 Spatial Frequency and Fourier Transforms . . . . . . . . . . . . . . . 118
4.3.1 Fourier Transforms . ... .. .. ... .. ... .. .. ... . 119
4.4 Sampling and Aliasing . . . ... .. .. ... .. ... .. .. ... . 121
4.4.1 Sampling .. .. .. ... .. .. ... .. ... .. .. ... . 122
4.4.2 Aliasing ... .. .. ... .. .. ... .. ... .. .. ... . 125
4.4.3 Smoothing and Resampling . . . . . . . . . . . . . . . . . . . 126
4.5 Filters as Templates . . . . . .. .. .. ... .. ... .. .. ... . 131
4.5.1 Convolution as a Dot Product . ... .. ... .. .. ... . 131
4.5.2 Changing Basis . .. ... .. .. ... .. ... .. .. ... . 132
4.6 Technique: Normalized Correlation and Finding Patterns . . . . . . 132