Total Variation of the Normal Vector Field as Shape Prior

Abstract

An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vector field is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. It is shown that spheres are stationary points when the total variation of the normal is minimized under an area constraint. Shape calculus is used to characterize the relevant derivatives. Since the total variation functional is non-differentiable whenever the boundary contains flat regions, an extension of the split Bregman method to manifold valued functions is proposed.

References in corpus (4)

• A Parallel Douglas Rachford Algorithm for Minimizing ROF-like Functionals on Images with Values in Symmetric Hadamard Manifolds
• Primal-Dual Optimization Algorithms over Riemannian Manifolds: an Iteration Complexity Analysis
• First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
• Fenchel Duality Theory and A Primal-Dual Algorithm on Riemannian Manifolds

Cited by in corpus (1)

• Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach