A Novel Mesh Denoising Method Based on Relaxed Second-Order Total Generalized Variation

In the paper, we develop a relaxed second-order total generalized variation model on triangulated surfaces, which couples the first-order gradient operator and the weighted divergence operator. An iterative two-stage mesh denoising method is proposed with the relaxed model, which contains facet normal filtering based on the relaxed model and robust vertex updating. The nondifferentiable optimization problem is solved by an iterative algorithm based on variable splitting and augmented Lagrangian method. Our denoising method is discussed and compared to several state-of-the-art techniques in terms of reconstruction quality, quantitative comparison, and computational costs. Experiments indicate that our approach is comparable to state-of-the-art algorithms at reasonable costs. It can produce denoising results with more structures, alleviate the staircase effect (false edges), and prevent edge flips. The quantitative errors also verify that the newly proposed algorithm is robust numerically.

Automated summary

The paper introduces a relaxed second-order total generalized variation model on triangulated surfaces and an iterative two-stage mesh denoising method based on this model. The proposed method shows good performance in terms of computational efficiency and high-quality denoising results.