Persistence-sensitive simplification of functions on 2-manlfolds
Herbert Edelsbrunner, Dmitriy Morozov, Valerio Pascucci · Symposium on Computational Geometry · 2006
We continue the study of topological persistence [5] by investigating the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an -simplification of another function f if ‖f − g‖∞ ≤ , and the persistence diagrams of g are the same as those of f except all points within L1-distance at most from the diagonal have been removed. We prove that for functions f on a 2-manifold such -simplification exists, and we give an algorithm to construct them in the piecewise linear case.