Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising

TL;DR

This paper introduces a new second-order total generalized variation (TGV) model for normal vectors on 3D meshes, using a specialized finite element space, and demonstrates its effectiveness in mesh denoising.

Contribution

It extends discrete TGV models to manifold-valued normal vectors on meshes by developing a tangential Raviart-Thomas finite element space.

Findings

The proposed TGV model improves mesh denoising quality.

The new formulation outperforms existing methods in experiments.

The finite element approach effectively handles manifold-valued data.

Abstract

We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV models for piecewise constant scalar data that utilize a Raviart-Thomas function space. To extend this formulation to the manifold setting, a tailor-made tangential Raviart-Thomas type finite element space is constructed in this work. The new regularizer is compared to existing methods in mesh denoising experiments.