Mesh Total Generalized Variation for Denoising

TL;DR

This paper introduces a novel numerical framework for discretizing second-order Total Generalized Variation (TGV) on triangular meshes and applies it to mesh denoising, effectively preserving sharp features and smooth regions.

Contribution

It develops the first numerical method for second-order TGV on triangular meshes and proposes a TGV-based variational model for mesh denoising with an efficient optimization algorithm.

Findings

Outperforms state-of-the-art methods visually and numerically

Effectively preserves sharp features and smooth regions

Demonstrates robustness on synthetic and real data

Abstract

Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating TGV over triangular meshes. In this paper, we develop a novel numerical framework to discretize the second-order TGV over triangular meshes. Further, we propose a TGV-based variational model to restore the face normal field for mesh denoising. The TGV regularization in the proposed model is represented by a combination of a first- and second-order term, which can be automatically balanced. This TGV regularization is able to locate sharp features and preserve them via the first-order term, while recognize smoothly curved regions and recover them via the second-order term. To solve the optimization problem, we introduce an efficient iterative algorithm based on variable-splitting and augmented Lagrangian method. Extensive results and comparisons on synthetic and real scanning data validate that the proposed method outperforms the state-of-the-art methods visually and numerically.