Well-composed sets

Well-composed sets define exactly the class of subsets of Zn whose continuous analog in &Rdbl;nhas the boundary that is n-1D manifold. The continuous analog has an intuitive and natural meaning in computer vision and computer graphics. Each point in a digital image has a dual nature. For algorithmic processing, it is necessary to treat each point in a digital image as a point with integer coordinates, that is, as a topological object of dimension zero. The class of well-composed sets seems to be general enough, in the sense that it is possible to determine the digital sets in digital images obtained in practical applications in such a way that they are well-composed sets. A 3D digital set is well-composed if the boundary surface of its continuous analog is a 2D manifold, that is, it looks locally like a planar open set. The concept of 2D well-composed sets is extended in two directions to an arbitrary grid system and to segmented images with objects labeled with more than two gray values.