231 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Institut national de recherche en sciences et technologies du numériqueFR183 papers
- Centre National de la Recherche ScientifiqueFR44 papers
- Université Côte d'AzurFR37 papers
- Laboratoire Jean-Alexandre DieudonnéFR16 papers
- National Research CouncilLK11 papers
- Université Nice Sophia AntipolisFR11 papers
- Institute for Complex SystemsIT10 papers
- Laboratoire d'Informatique, Signaux et Systèmes de Sophia AntipolisFR10 papers
- École PolytechniqueFR8 papers
- MATHNEURO: Mathématiques pour les NeurosciencesFR8 papers
- Mathématiques, Informatique et Statistique pour l'Environnement et l'AgronomieFR7 papers
- Centre for Research and Information on Substance AbuseNG6 papers
18 papers · 1 filter
Manifolds of positive reach, differentiability, tangent variation, and attaining the reach
André Lieutier, Mathijs Wintraecken
This paper contains three main results. Firstly, we give an elementary proof of the following statement: Let be a (closed, in both the geometrical and topological sense of the…
A free lunch: manifolds of positive reach can be smoothed without decreasing the reach
Hana Dal Poz Kouřimská, André Lieutier, Mathijs Wintraecken
Assumptions on the reach are crucial for ensuring the correctness of many geometric and topological algorithms, including triangulation, manifold reconstruction and learning, homot…
Differentiability and Optimization of Multiparameter Persistent Homology
Luis Scoccola, Siddharth Setlur, David Loiseaux +2
Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topol…
Computing Persistent Homology with Various Coefficient Fields in a Single Pass
Jean-Daniel Boissonnat, Clément Maria
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-…
The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes
Jean-Daniel Boissonnat, Clément Maria
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored…
Discrete Morse Theory for Computing Zigzag Persistence
Clément Maria, Hannah Schreiber
We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology. From a zigzag filt…
An elementary approach to tangent space variation on Riemannian submanifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We give asymptotically tight estimates of tangent space variation on Riemannian submanifolds of Euclidean space with respect to the local feature size of the submanifolds. We show…
Building Efficient and Compact Data Structures for Simplicial Complexes
Jean-Daniel Boissonnat, Karthik C. S., Sébastien Tavenas
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range…
Only distances are required to reconstruct submanifolds
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh +1
In this paper, we give the first algorithm that outputs a faithful reconstruction of a submanifold of Euclidean space without maintaining or even constructing complicated data stru…
Domain Mapping for Volumetric Parameterization using Harmonic Functions
Vikash Gupta, Hari K. Voruganti, Bhaskar Dasgupta
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization whe…
Delaunay stability via perturbations
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We present an algorithm that takes as input a finite point set in Euclidean space, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting pert…
The Compressed Annotation Matrix: an Efficient Data Structure for Computing Persistent Cohomology
Jean-Daniel Boissonnat, Tamal K. Dey, Clément Maria
The persistent homology with coefficients in a field F coincides with the same for cohomology because of duality. We propose an implementation of a recently introduced algorithm fo…
The Stability of Delaunay Triangulations
Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh
We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of -generic point sets are thick. Equipped…
Geometric Tomography With Topological Guarantees
Omid Amini, Jean-Daniel Boissonnat, Pooran Memari
We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in from its cross-sections with a given set of cutting planes $\…
Algebraic methods for counting Euclidean embeddings of rigid graphs
Ioannis Z. Emiris, Elias P. Tsigaridas, Antonios Varvitsiotis
The study of (minimally) rigid graphs is motivated by numerous applications, mostly in robotics and bioinformatics. A major open problem concerns the number of embeddings of such g…
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
Frank Nielsen, Jean-Daniel Boissonnat, Richard Nock
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are…
Triangulating the Real Projective Plane
Mridul Aanjaneya, Monique Teillaud
We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 alwa…
Stability of boundary measures
Frédéric Chazal, David Cohen-Steiner, Quentin Mérigot
We introduce the boundary measure at scale r of a compact subset of the n-dimensional Euclidean space. We show how it can be computed for point clouds and suggest these measures ca…