Tree-Based Encoding for Cancellations on Morse Complexes

Authors:
Lidija Čomić;Leila Floriani
Affiliations:
Faculty of Engineering, University of Novi Sad, Serbia;Department of Computer Science, University of Genova, Italy
Venue:
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Year:
2009

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Abstract

A scalar function f , defined on a manifold M , can be simplified by applying a sequence of removal and contraction operators, which eliminate its critical points in pairs, and simplify the topological representation of M , provided by Morse complexes of f . The inverse refinement operators, together with a dependency relation between them, enable a construction of a multi-resolution representation of such complexes. Here, we encode a sequence of simplification operators in a data structure called an augmented cancellation forest , which will enable procedural encoding of the inverse refinement operators, and reduce the dependency relation between modifications of the Morse complexes. In this way, this representation will induce a high flexibility of the hierarchical representation of the Morse complexes, producing a large number of Morse complexes at different resolutions that can be obtained from the hierarchy.