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

arXiv: https://arxiv.org/abs/2412.00445 · HTML: https://mlsanity.com/paper/2412.00445/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 30 Nov 2024.

## Builds on (most cited first, 6 of 6)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [MeshCNN: A Network with an Edge](https://mlsanity.com/paper/1809.05910/) (2018)
- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [Image Labeling by Assignment](https://mlsanity.com/paper/1603.05285/) (2016)
- [From the simplex to the sphere: Faster constrained optimization using the Hadamard parametrization](https://mlsanity.com/paper/2112.05273/) (2021)

## Built on by (most cited first, 1 of 1)

- [Geometry Denoising with Preferred Normal Vectors](https://mlsanity.com/paper/2511.04848/) (2025)

## Abstract (arXiv)

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.