Well-Composed Sets

Abstract A special class of subsets of binary digital images called "well-composed sets" is defined. The sets of this class have very nice topological properties; for example, the Jordan Curve Theorem holds for them, their Euler characteristic is locally computable, and they have only one connectedness relation, since 4- and 8-connectedness are equivalent. This implies that many basic algorithms used in computer vision become simpler. There are real advantages in applying thinning algorithms to well-composed sets, For example, thinning is an internal operation on these sets and the problems with irreducible "thick" sets disappear. Furthermore, we prove that the skeletons obtained are "one point thick" and we give a formal definition of this concept. We also show that these skeletons have a graph structure and we define what this means.

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