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4.6.1 Controlling the Television by Finding Hands by Normalized
Correlation . . . . . ... .. .. ... .. ... .. .. ... . 133
4.7 Technique: Scale and Image Pyramids . . . . . . . . . . . . . . . . . 134
4.7.1 The Gaussian Pyramid . . . . . . .. .. ... .. .. ... . 135
4.7.2 Applications of Scaled Representations . . . . . . . . . . . . . 136
4.8 Notes . . . . . . .. .. .. ... .. .. ... .. ... .. .. ... . 137

5 Local Image Features 141
5.1 Computing the Image Gradient . . . . . ... .. ... .. .. ... . 141
5.1.1 Derivative of Gaussian Filters . . . .. .. ... .. .. ... . 142
5.2 Representing the Image Gradient .. .. ... .. ... .. .. ... . 144
5.2.1 Gradient-Based Edge Detectors . ... .. ... .. .. ... . 145
5.2.2 Orientations . .. .. ... .. .. ... .. ... .. .. ... . 147
5.3 Finding Corners and Building Neighborhoods . . . . . . . . . . . . . 148
5.3.1 Finding Corners . . . .. .. .. ... .. ... .. .. ... . 149
5.3.2 Using Scale and Orientation to Build a Neighborhood . . . . 151
5.4 Describing Neighborhoods with SIFT and HOG Features . . . . . . 155
5.4.1 SIFT Features . .. ... .. .. ... .. ... .. .. ... . 157
5.4.2 HOG Features . . . ... .. .. ... .. ... .. .. ... . 159
5.5 Computing Local Features in Practice . ... .. ... .. .. ... . 160
5.6 Notes . . . . . . .. .. .. ... .. .. ... .. ... .. .. ... . 160

6 Texture 164
6.1 Local Texture Representations Using Filters . .. ... .. .. ... . 166
6.1.1 Spots and Bars . . . . .. .. .. ... .. ... .. .. ... . 167
6.1.2 From Filter Outputs to Texture Representation . . . . . . . . 168
6.1.3 Local Texture Representations in Practice . . . . . . . . . . . 170
6.2 Pooled Texture Representations by Discovering Textons . . . . . . . 171
6.2.1 Vector Quantization and Textons . . . . . . . . . . . . . . . . 172
6.2.2 K-means Clustering for Vector Quantization . . . . . . . . . . 172
6.3 Synthesizing Textures and Filling Holes in Images . . . . . . . . . . 176
6.3.1 Synthesis by Sampling Local Models . . . . . . . . . . . . . . 176
6.3.2 Filling in Holes in Images . . . . . . . . . . . . . . . . . . . . 179
6.4 Image Denoising .. .. .. ... .. .. ... .. ... .. .. ... . 182
6.4.1 Non-local Means . . ... .. .. ... .. ... .. .. ... . 183
6.4.2 Block Matching 3D (BM3D) . . . . . . . . . . . . . . . . . . 183
6.4.3 Learned Sparse Coding . . . . . ... .. ... .. .. ... . 184
6.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.5 Shape from Texture . . . . . .. .. .. ... .. ... .. .. ... . 187
6.5.1 Shape from Texture for Planes . ... .. ... .. .. ... . 187
6.5.2 Shape from Texture for Curved Surfaces . ... .. .. ... . 190