Parametric morphological filters for pattern restoration

Summary form only given. A theoretical study of parametric morphological filters that best preserve the crucial topological structure of an input binary image from its noisy version is reported. The topological structure of the input binary image is given, and an arbitrary restoration filter is considered. A collection C of necessary and sufficient conditions for this filter to guarantee the restoration of a binary image from its noisy version, such that the input and restored images have identical topological structure, is derived. It is proved that each of the constraints in C generates a morphological filter. The approach used is to obtain a parametric filter that simultaneously satisfies as many of the constraints in C as possible