Non-linear multiscale filtering using mathematical morphology

Mathematical Morphology is a new branch of mathematics powerful enough to study some vision problems like multiscale filtering. Due to the fact morphological openings smooth the signal while preserving the edges, and using the three Matheron's axioms, an important result is obtained: morphological openings do not introduce additional zero-crossing as one moves to a coarser scales. With these results a multiscale filtering scheme is developed. The choice of the structuring element is constrained to the sub-space of convex, compact and homothetic ones. In this paper we will report a procedure for choosing the structuring element based on the pre-filtering effects of morphological openings and the subsequent detection of edges.