Operators for multi-resolution morse complexes in arbitrary dimensions

Abstract

Ascending and descending Morse complexes, defined by the critical points and integral lines of a scalar field f defined on a manifold M, induce a subdivision of M into regions of uniform gradient flow, and thus provide a compact description of the morphology of f on M. We propose a dual representation for the ascending and descending Morse complexes of f in arbitrary dimensions in terms of an incidence graph. We describe atomic simplification and refinement operators on the Morse complexes and we investigate the effect of those operators on the graph-based representation of the two complexes. Simplification and refinement operators form a basis for a hierarchical multi-resolution representation of Morse complexes, from which it will be possible to dynamically extract representations of the morphology of the scalar field f over M, at both uniform and variable resolutions. Copyright UNION Agency - Science Press.