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Creators/Authors contains: "Charon, Nicolas"

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  1. Free, publicly-accessible full text available January 1, 2024
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  5. This paper studies a longitudinal shape transformation model in which shapes are deformed in response to an internal growth potential that evolves according to an advection reaction diffusion process. This model extends prior works that considered a static growth potential, i.e., the initial growth potential is only advected by diffeomorphisms. We focus on the mathematical study of the corresponding system of coupled PDEs describing the joint dynamics of the diffeomorphic transformation together with the growth potential on the moving domain. Specifically, we prove the uniqueness and long time existence of solutions to this system with reasonable initial and boundary conditions as well as regularization on deformation fields. In addition, we provide a few simple simulations of this model in the case of isotropic elastic materials in 2D.
    Free, publicly-accessible full text available March 1, 2023
  6. Chen, K ; Schönlieb, CB ; Tai, XC ; Younces, L (Ed.)
  7. This paper introduces an extension of diffeomorphic registration to enable the morphological analysis of data structures with inherent density variations and imbalances. Building on the framework of Large Diffeomorphic Metric Matching (LDDMM) registration and measure representations of shapes, we propose to augment previous measure deformation approaches with an additional density (or mass) transformation process. We then derive a variational formulation for the joint estimation of optimal deformation and density change between two measures. Based on the obtained optimality conditions, we deduce a shooting algorithm to numerically estimate solutions and illustrate the practical interest of this model for several types of geometric data such as fiber bundles with inconsistent fiber densities or incomplete surfaces.