We define the robustness of a level set homology class of a function f : X R as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theor...
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozo...
Given a continuous function f : X → IR on a topological space X, its level set f−1 (a) changes continuously as the real value a changes. Consequently, the connected components...
We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived from the levelsets of a real-valued function on a top...
Abstract. This paper presents a new hybrid split-and-merge image segmentation method based on computational geometry and topology using persistent homology. The algorithm uses edge...
—We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to a continuous function, we study the robustness of homology c...
Paul Bendich, Herbert Edelsbrunner, Michael Kerber