289 citations · 628 across the 35 of their papers we have counts for
7 papers · 1 filter
Wrapping Cycles in Delaunay Complexes: Bridging Persistent Homology and Discrete Morse Theory
Ulrich Bauer, Fabian Roll
We study the connection between discrete Morse theory and persistent homology in the context of shape reconstruction methods. Specifically, we consider the construction of Wrap com…
Topologically faithful image segmentation via induced matching of persistence barcodes
Nico Stucki, Johannes C. Paetzold, Suprosanna Shit +2
Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentatio…
Multi-Parameter Persistence Modules are Generically Indecomposable
Ulrich Bauer, Luis Scoccola
Algebraic persistence studies persistence modules (typically, linear representations of the poset with ) and the algebraic relationships between persistenc…
Keeping it sparse: Computing Persistent Homology revisited
Ulrich Bauer, Talha Bin Masood, Barbara Giunti +3
In this work, we study several variants of matrix reduction via Gaussian elimination that try to keep the reduced matrix sparse. The motivation comes from the growing field of topo…
Relative Interlevel Set Cohomology Categorifies Extended Persistence Diagrams
Ulrich Bauer, Benedikt Fluhr
The extended persistence diagram introduced by Cohen-Steiner, Edelsbrunner, and Harer is an invariant of real-valued continuous functions, which are -tame in the sense…
A Unified View on the Functorial Nerve Theorem and its Variations
Ulrich Bauer, Michael Kerber, Fabian Roll +1
The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often nee…
Efficient Computation of Image Persistence
Ulrich Bauer, Maximilian Schmahl
We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These a…