In this chapter, we discuss operations that “deform” a picture to derive new pictures from it while preserving geometric properties of the original picture, particularly topologic properties. We emphasize deformations of 2D binary pictures, but we also briefly discuss deformations of 3D and multivalued pictures.

16.1 Topology-Preserving Deformations and Simple Pixels

In this section, we assume that P is a 2D binary picture. We will usually use 8-adjacency for the 1s and 4-adjacency for the 0s, and we will assume that the set image of 1s is finite, but our results also hold (with appropriate modifications) under the opposite ...

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