Hierarchy of Stable Morse Decompositions

Andrzej Szymczak
2013 IEEE Transactions on Visualization and Computer Graphics  
We introduce an algorithm for construction of the Morse hierarchy, i.e. a hierarchy of Morse decompositions of a piecewise constant vector field on a surface driven by stability of the Morse sets with respect to perturbation of the vector field. Our approach builds upon earlier work on stable Morse decompositions, which can be used to obtain Morse sets of user-prescribed stability. More stable Morse decompositions are coarser, i.e. they consist of larger Morse sets. In this work, we develop an
more » ... ork, we develop an algorithm for tracking the growth of Morse sets and topological events (mergers) that they undergo as their stability is gradually increased. The resulting Morse hierarchy can be explored interactively. We provide examples demonstrating that it can provide a useful coarse overview of the vector field topology. Index Terms-Morse decomposition, persistence, vector field 3 • A. Szymczak is with the
doi:10.1109/tvcg.2012.147 pmid:22732684 fatcat:tmpxr3t3ebc43ci44zlzyv7bji