Tree-Based Encoding for Cancellations on Morse Complexes

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.