38 citations · 134 across the 17 of their papers we have counts for
5 papers · 1 filter
Discretization of functionals involving the Monge-Ampère operator
Jean-David Benamou, Guillaume Carlier, Quentin Mérigot +1
Gradient flows in the Wasserstein space have become a powerful tool in the analysis of diffusion equations, following the seminal work of Jordan, Kinderlehrer and Otto (JKO). The n…
Robust Geometry Estimation using the Generalized Voronoi Covariance Measure
Louis Cuel, Jacques-Olivier Lachaud, Quentin Mérigot +1
The Voronoi Covariance Measure of a compact set K of R^d is a tensor-valued measure that encodes geometric information on K and which is known to be resilient to Hausdorff noise bu…
Handling convexity-like constraints in variational problems
Quentin Mérigot, Edouard Oudet
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the spa…
Intersection of paraboloids and application to Minkowski-type problems
Pedro Machado Manhães De Castro, Quentin Mérigot, Boris Thibert
In this article, we study the intersection (or union) of the convex hull of N confocal paraboloids (or ellipsoids) of revolution. This study is motivated by a Minkowski-type proble…
On the reconstruction of convex sets from random normal measurements
Hiba Abdallah, Quentin Mérigot
We study the problem of reconstructing a convex body using only a finite number of measurements of outer normal vectors. More precisely, we suppose that the normal vectors are meas…