Nonlinear multiscale filtering using mathematical morphology

A multiscale filtering scheme based on the three Matheron axioms for morphological openings is developed. It is shown that opening a signal with a gray scale operator does not introduce additional zero-crossings as one moves to coarser scales. Within this framework, the problem of choosing an appropriate structuring element is studied. In order to obtain a measure of the performance of different structuring elements, the statistical properties of gray scale opening are studied, using a powerful tool in mathematical morphology, namely, basis functions