3D well-composed pictures

A special class of subsets of binary digital 3D pictures called `well-composed pictures' is defined by two simple conditions on a local voxel level. The pictures of this class have very nice topological and geometrical properties; for example, a very natural definition of a continuous analog leads to regular properties of surfaces, a digital version of the 3D separation theorem has a simple proof, and there is only one connectedness relation in a well-composed picture, since 6-, 18-, and 26-connectedness are equivalent. This implies that many algorithms used in computer vision and computer graphics and their descriptions can be simpler, and the algorithms can be faster.

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