This paper presents the first segmentation operation defined within the 3D topological map framework. Firstly we show how a traditional segmentation algorithm, found in the literat...
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...
In this study we concentrate on qualitative topological analysis of the local behavior of the space of natural images. To this end, we use a space of 3 by 3 high-contrast patches ...
Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, A...
Abstract. Graph-based algorithms have become increasingly popular for medical image segmentation. The fundamental process for each of these algorithms is to use the image content t...
We present a novel framework for characterizing signals in images using techniques from computational algebraic topology. This technique is general enough for dealing with noisy mu...