Topology-Preserving Deformations of Fuzzy Digital Pictures

This chapter considers the topology of two-dimensional fuzzy digital pictures, and discusses topology-preserving deformations of these fuzzy pictures that generalize deformations of two-valued digital pictures. It is shown that an arbitrary fuzzy picture can be transformed by this type of deformation into a coherent fuzzy picture. As another application, it is shown that the genus of a fuzzy picture is a linear combination of local property values.