Manifold Shape: From Differential Geometry to Mathematical Morphology

摘要

The authors study the question of shape desription of patterns on arbitrary (smooth) surfaces based on mathematical morphology. The primary interest in the paper is to outline the mathematical structure of the description. Some concepts of differential geometry, in particular those of parallel transport and covariant differentiation are used to replace the more restricted concept of invariance used so far in mathematical morphology. The corresponding morphological operators are constructed which leave the geometry on the surface invariant.