no code implementations • 24 Apr 2014 • Benjamin Charlier, Nicolas Charon, Alain Trouvé
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis.
no code implementations • 22 Apr 2013 • Nicolas Charon, Alain Trouvé
More specifically, problems occur with structures like acute pikes because of canceling effects of currents or with data that consists in many disconnected pieces like fiber bundles for which currents require a consistent orientation of all pieces.
1 code implementation • 5 Aug 2016 • Nicolas Charon, Benjamin Charlier, Alain Trouvé
In this paper, we describe in detail a model of geometric-functional variability between fshapes.
Optimization and Control Differential Geometry 49M25, 49Q20, 58B32, 58E50, 68U05, 68U10
no code implementations • 5 Jul 2021 • Jean Feydy, Pierre Roussillon, Alain Trouvé, Pietro Gori
The parameters -- blur and reach -- of our method are meaningful, defining the minimum and maximum distance at which two fibers are compared with each other.
1 code implementation • 18 Oct 2018 • Jean Feydy, Thibault Séjourné, François-Xavier Vialard, Shun-ichi Amari, Alain Trouvé, Gabriel Peyré
Comparing probability distributions is a fundamental problem in data sciences.
Statistics Theory Statistics Theory 62
4 code implementations • 28 Oct 2019 • Thibault Séjourné, Jean Feydy, François-Xavier Vialard, Alain Trouvé, Gabriel Peyré
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems.