122 citations · 234 across the 29 of their papers we have counts for
10 papers · 1 filter
A Benamou-Brenier Proximal Splitting Method for Constrained Unbalanced Optimal Transport
Mao Nishino, Martin Bauer, Tom Needham +1
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity…
Path constrained unbalanced optimal transport
Martin Bauer, Nicolas Charon, Tom Needham +1
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kin…
Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric
Hsi-Wei Hsieh, Nicolas Charon
This paper introduces and studies a metamorphosis framework for geometric measures known as varifolds, which extends the diffeomorphic registration model for objects such as curves…
A new variational model for shape graph registration with partial matching constraints
Yashil Sukurdeep, Martin Bauer, Nicolas Charon
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape…
Mechanistic Modeling of Longitudinal Shape Changes: equations of motion and inverse problems
Dai-Ni Hsieh, Sylvain Arguillère, Nicolas Charon +1
This paper examines a longitudinal shape evolution model in which a 3D volume progresses through a family of elastic equilibria in response to the time-derivative of an internal fo…
Metrics, quantization and registration in varifold spaces
Hsi-Wei Hsieh, Nicolas Charon
This paper is concerned with the theory and applications of varifolds to the representation, approximation and diffeomorphic registration of shapes. One of its purpose is to synthe…
A Model for Elastic Evolution on Foliated Shapes
Dai-Ni Hsieh, Sylvain Arguillère, Nicolas Charon +2
We study a shape evolution framework in which the deformation of shapes from time t to t + dt is governed by a regularized anisotropic elasticity model. More precisely, we assume t…
Global Optimality in Separable Dictionary Learning with Applications to the Analysis of Diffusion MRI
Evan Schwab, Benjamin D. Haeffele, René Vidal +1
Sparse dictionary learning is a popular method for representing signals as linear combinations of a few elements from a dictionary that is learned from the data. In the classical s…
Diffeomorphic registration of discrete geometric distributions
Hsi-Wei Hsieh, Nicolas Charon
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete di…
Metamorphoses of functional shapes in Sobolev spaces
Nicolas Charon, Benjamin Charlier, Alain Trouvé
In this paper, we describe in detail a model of geometric-functional variability between fshapes. These objects were introduced for the first time by the authors in [Charlier et al…