Two Models for Surface Segmentation using the Total Variation of the Normal Vector

TL;DR

This paper introduces two variational models for surface segmentation based on total variation regularization of the normal vector field, comparing their effectiveness and computational efficiency.

Contribution

It proposes and compares two total variation based regularizers for surface segmentation and introduces a manifold Newton method to improve computational efficiency.

Findings

The second regularizer produces better segmentation results, especially in noise removal.

The manifold Newton scheme significantly reduces computational cost.

The approach effectively segments surfaces with constant curvature regions.

Abstract

We consider the problem of surface segmentation, where the goal is to partition a surface represented by a triangular mesh. The segmentation is based on the similarity of the normal vector field to a given set of label vectors. We propose a variational approach and compare two different regularizers, both based on a total variation measure. The first regularizer penalizes the total variation of the assignment function directly, while the second regularizer penalizes the total variation in the label space. In order to solve the resulting optimization problems, we use variations of the split Bregman (ADMM) iteration adapted to the problem at hand. While computationally more expensive, the second regularizer yields better results in our experiments. In particular it removes noise more reliably in regions of constant curvature. In order to mitigate the computational cost, we present a manifold Newton scheme for the most expensive subproblem, which is related to the Riemannian center of mass on a sphere. This significantly improves the computational cost.