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An efficient kernel product for automatic differentiation libraries, with applications to measure transport

Presented by: 
Jean Feydy École Normale Supérieure, ENS de Cachan
Monday 13th November 2017 - 11:00 to 11:30
INI Seminar Room 1
Authors : Benjamin Charlier, Jean Feydy, Joan Alexis Glaunès and Alain Trouvé This paper presents a memory-efficient implementation of the kernel matrix-vector product, which is suitable for use with automatic differentiation libraries -- in our case, PyTorch. This piece of software alleviates the major bottleneck of autodiff libraries as far as diffeomorphic image registration is concerned: symbolic python code can now scale up to large point clouds and shapes (100,000+ vertices). To showcase the value of automatic differentiation to the LDDMM community, we introduce the "normalized Hamiltonian" setting and show that it corresponds to a spatially regularized optimal transport of mass distributions: made tractable by autodiff libraries, the kernel normalization trick turns an extrinsic image deformation routine into an intrinsic measure transportation program.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons