In an earlier submission, we considered 2-D and 3-D digital binary images topologically characterized by their well-composedness. Well-composed images exhibit important topological and geometrical properties not shared by their ill-composed counterparts. These properties have important implications for various algorithms used by the ITK community such as thinning algorithms and Marching Cubes.

A natural follow-up inquiry to our original submission concerns the possible extension of the binary algorithm to accommodate images with multiple labels. In this paper, we describe such a generalization of our previous submission which also subsumes the binary approach. For completeness and clarity of exposition, we develop the idea of well-composedness within the binary image context and later generalize the discussion to include those images with multiple labels.