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Isaac Newton Institute for Mathematical Sciences

Total Variation Regularization for Functions with Values in a Manifold


Presenter: Jan Lellmann (University of Cambridge/DAMTP)

Co-authors: Evgeny Strekalovskiy (TU Munich), Sabrina Koetter (TU Munich), Daniel Cremers (TU Munich)


While the total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. We propose an algorithm based on a convex relaxation method for solving such problems for arbitrary Riemannian manifolds. The framework can be adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain more accurate solutions than labelling methods. We show several applications including variational processing of chromaticity values, normal fields, and camera trajectories.

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