8 Neighbourhood operations and image filtering
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8.1 Convolution and correlation
8.1.1 Discrete convolution in two dimensions
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8.1.2 Separable and rank-one kernels
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8.1.3 Boundary handling: zero, reflect, replicate, wrap
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8.1.4 Computational cost and efficient implementations
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8.2 Smoothing filters
8.2.1 Box (mean) filter and integral images
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8.2.2 Gaussian filter and σ selection
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8.2.3 Median and rank-order filters
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8.2.4 Bilateral and edge-preserving filters
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8.2.5 Non-local means
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8.3 Derivative and edge filters
8.3.1 First-order operators: Sobel, Prewitt, Scharr
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8.3.2 Second-order operators: Laplacian and Laplacian of Gaussian
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8.3.3 Gradient magnitude and orientation
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8.3.4 Sub-pixel edge localisation
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8.4 The frequency domain
8.4.1 The 2D discrete Fourier transform
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8.4.2 Magnitude, phase and their perceptual roles
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8.4.3 The convolution theorem
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8.4.4 Low-pass, high-pass and band-pass filtering
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8.4.5 Frequency-domain inspection of periodic structure
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8.4.6 The sampling theorem and aliasing
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8.5 Scale space and image pyramids
8.5.1 Scale-space theory in outline
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8.5.2 The Gaussian pyramid
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8.5.3 The Laplacian pyramid
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8.5.4 Multi-resolution processing patterns
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8.6 Choosing a filtering strategy
8.6.1 Matching a filter to the noise model and the feature
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8.6.2 Preserving edges while suppressing noise
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8.6.3 Spatial versus frequency-domain: when each wins
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8.6.4 Ordering operations in a preprocessing pipeline
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