Topological approaches to the data skeletonization problem
Topological data analysis is a rapidly growing field, combining
techniques coming from theoretical mathematics and computer science to
solve problems related to shape recognition. On concrete level given a
point cloud in a Euclidean space we consider the problem of
approximating the cloud by an embedded graph in the same space. We
will review past approaches to related data skeletonization problems
via Reeb graphs and a 1-dimensional Homologically Persistent Skeleton.
Then we will introduce a new approximate skeleton for detecting
topological shapes of micelles in n dimensions. The talk is based on
joint work with Vitaliy Kurlin at the University of Liverpool.