A new numerical scheme for constrained total variation flows and its convergence

In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained in a Riemannian manifold. The difficulty of this problem is that the underlying function space is not convex and it is hard to calculate the minimizer of the functional with the manifold constraint. We overcome this difficulty by "localization technique" using the exponential map and prove the finite-time error estimate in general situation. Finally, we show a few numerical results for the cases that the target manifolds are $S^2$ and $SO(3)$.

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