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An analogue of the total variation prior for the normal vector field alongthe boundary of smooth shapes in 3D is introduced. The analysis of the totalvariation of the normal vector field is based on a differential geometricsetting in which the unit normal vector is viewed as an element of thetwo-dimensional sphere manifold. It is shown that spheres are stationary pointswhen the total variation of the normal is minimized under an area constraint.Shape calculus is used to characterize the relevant derivatives. Since thetotal variation functional is non-differentiable whenever the boundary containsflat regions, an extension of the split Bregman method to manifold valuedfunctions is proposed.

Total Variation of the Normal Vector Field as Shape Prior