In this talk, we propose to rescale the classical kernel cometric tensor of LDDMM theory to impose a stochasticity condition. We show that this operation breaks the right-invariance property of LDDMM metrics on spaces of diffeomorphisms, and replaces it with an awareness to the mass of the transported shape. Made computationally tractable by automatic differentiation libraries, the kernel normalization trick turns an extrinsic image deformation routine into an intrinsic measure transportation program.

This presentation is part of Minisymposium “MS75 - Geometric methods for shape analysis with applications to biomedical imaging and computational anatomy, Part II (2 parts)”
organized by: Joan Alexis Glaunès (MAP5, Université Paris Descartes) , Sergey Kushnarev (Singapore University of Technology and Design) , Mario Micheli (Harvey Mudd College) .

Authors:

Jean Feydy (Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure Paris-Saclay)

Keywords:

diffeomorphic registration, image registration, lddmm, shape analysis, transportation theory