In this paper, we study four mesh denoising methods: linear filtering, a heat diffusion method, Sobolev regularization, and, to a lesser extent, a barycentric approach based on the Sinkhorn algorithm. We illustrate that, for a simple image denoising task, a naive choice of a Gibbs kernel can lead to unsatisfactory results. We demonstrate that while Sobolev regularization is the fastest method in our implementation, it produces slightly less faithful denoised meshes than the best results obtained with iterative filtering or heat diffusion. We empirically show that, for the large mesh considered, the heat diffusion method is slower and not more effective than filtering, whereas on a small mesh an appropriate choice of diffusion parameters can improve the quality. Finally, we observe that all three mesh-based methods perform markedly better on the large mesh than on the small one.

翻译：本文研究了四种网格去噪方法：线性滤波、热扩散方法、Sobolev正则化，以及（在较小程度上）一种基于Sinkhorn算法的重心方法。我们阐明，对于简单的图像去噪任务，Gibbs核的朴素选择可能导致不理想的结果。我们证明，虽然Sobolev正则化在我们的实现中是最快的方法，但其产生的去噪网格在保真度上略逊于迭代滤波或热扩散所获得的最佳结果。我们通过实验表明，对于所考虑的大型网格，热扩散方法比滤波更慢且效果并未更优；而在小型网格上，扩散参数的适当选择可以提升质量。最后，我们观察到所有三种基于网格的方法在大型网格上的表现均明显优于在小型网格上的表现。