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10.0 EDGES MATTER⧉

A blur can mix a bright sky into a dark mountain. A pasted object can carry a visible brightness step around its boundary. Resizing can bend a straight building edge. Each problem needs a different treatment of image structure.

Chapter 10.1, Bilateral filtering and its relatives reduce averaging between pixels judged dissimilar. The similarity may come from intensity, a patch, or a separate guide. These are models of which samples should influence one another; they do not identify every object boundary correctly. Chapter 10.3, Edge-preserving optimization — colorization and Chapter 10.5, Matting Laplacian use local models in global solves to propagate sparse constraints.

Chapter 10.8, Poisson image editing instead fits an image to a prescribed gradient field and boundary values. It can reduce a compositing seam, but the reconstructed colors may change. Chapter 10.9, Seam optimization chooses where to switch sources, select a region, or remove a path. Its costs depend on the application: selection often follows a strong edge, while seam carving Avidan & Shamir 2007 usually avoids removing one.

The methods build on convolution, pyramids and sparse linear systems. Chapter 10.10, Recap: which edge-aware technique when? compares their costs and failure modes. For detailed noise models and modern denoisers, use Chapter 2.8, Noise, signal-to-noise ratio and dynamic range and Part 13, Denoising.

Edges are useful partly because smooth regions are often locally predictable, while a boundary tells us that a prediction from one side may fail on the other. Local contrast also matters strongly to appearance. This does not make smooth shading or absolute color expendable; it explains why an operation that mishandles a narrow boundary can spoil an otherwise plausible image.

Two ideas connect these methods. Affinity specifies which samples should influence one another: a filter uses it to form an average, while an optimization can use it to penalize disagreement between related pixels. The objective specifies what the result should preserve. A gradient reconstruction penalizes disagreement with a desired gradient field; a seam algorithm assigns costs to possible boundaries or removed paths. The optimizer can remain the same while changing those costs produces a different editing tool.

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