Publications

Journal Articles

Characterization of the Homology and Cohomology Bases Computed by Standard Methods

Yann-Situ Gazull, Aldo Gonzalez-Lorenzo, Alexandra Bac
Journal of Mathematical Imaging and Vision, 2026
Published Version | Bibtex

This paper is an extension of the paper Characterization of the Computed Homology and Cohomology Bases. We characterize the homology and cohomology bases computed by standard computational homology methods. We also characterize the pair of homology and cohomology bases that can be computed simultaneously. Read more

Stability and extension of steady and ranging persistence

Yann-Situ Gazull
Journal of Applied and Computational Topology, 2025
Published Version | HAL Version | Code | Bibtex

We extend steady and ranging persistence from graphs to other categories, and provide a characterization of the features that give rise to stable steady and ranging persistent diagrams. We show examples for hypergraphs. Read more

A constructive approach of Alexander duality

Aldo Gonzalez-Lorenzo, Alexandra Bac, Yann-Situ Gazull
Journal of Applied and Computational Topology, 2024
Published Version | HAL Version | Bibtex

We prove a combinatorial and geometric version of Alexander duality with a constructive proof, based on HDVFs. This allows us to define four different representations of homological holes, named homology quartets. Read more

Computing Geometrical Measures of Topological Holes

Yann-Situ Gazull, Alexandra Bac, Aldo Gonzalez-Lorenzo
Computer-Aided Design, 2023 (SPM 2023 second best paper award)
Published Version | HAL Version | Code | Bibtex

We define and compute two specific balls for every hole of a geometric object. One ball corresponds to the thickness (~fragility, in red), whereas the other corresponds to the breadth (~size, in blue) of the hole. Read more

Conference Papers

Characterization of the Computed Homology and Cohomology Bases

Yann-Situ Gazull, Aldo Gonzalez-Lorenzo, Alexandra Bac
Proceedings of International Conference on Discrete Geometry and Mathematical Morphology, 2025
Published Version | HAL Version | Bibtex

We provide a combinatorial characterization of the homology bases computed by standard computational homology methods (discrete Morse theory, standard persistent homology, modified Smith normal form, tri-partitions), using homological discrete vector fields. Read more

Preprints

On the Graph of Homology Computations and its Connectedness

Yann-Situ Gazull, Aldo Gonzalez-Lorenzo, Alexandra Bac
preprint, 2025
| HAL Version | Bibtex

This preprint is a study about the graph of perfect HDVFs. We provide an algorithm relating two perfect HDVFs, showing this graph is connected. We also provide an algorithm to adapt a HDVF to a given explicit basis. Read more