Dimension-independent multi-resolution Morse complexes

Morse and Morse–Smale complexes have been recognized as a suitable model for representing topological information extracted from discrete scalar fields. Here, we propose a dimension-independent multi-resolution model for Morse complexes built on a graph representation of the complexes, that we call a Multi-Resolution Morse Incidence Graph (MMIG). We define data structures for encoding the MMIG and we discuss how to extract from an MMIG topological representations of the scalar field over its domain M at both uniform and variable resolutions. We present experimental results evaluating the storage cost of the data structures encoding the MMIG, and timings for building and querying an MMIG.

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► The Morse complexes of a scalar field f over a manifold M are encoded in the form of a “Morse Incidence Graph” (MIG).
► Simplification and refinement operators have been defined and implemented on the MIG.
► Multi-resolution model (Multi-Resolution Morse Incidence graph (MMIG)) for the MIG has been defined.
► Efficient encodings for the MMIG have been designed and implemented.
► A selective refinement algorithm for querying the MMIG has been developed and experimental results have been presented.