Variational Mesh Denoising Using Total Variation and Piecewise Constant Function Space

Abstract

Mesh surface denoising is a fundamental problem in geometry processing. The main challenge is to remove noise while preserving sharp features (such as edges and corners) and preventing generating false edges. We propose in this paper to combine total variation (TV) and piecewise constant function space for variational mesh denoising. We first give definitions of piecewise constant function spaces and associated operators. A variational mesh denoising method will then be presented by combining TV and piecewise constant function space. It is proved that, the solution of the variational problem (the key part of the method) is in some sense continuously dependent on its parameter, indicating that the solution is robust to small perturbations of this parameter. To solve the variational problem, we propose an efficient iterative algorithm (with an additional algorithmic parameter) based on variable splitting and augmented Lagrangian method, each step of which has closed form solution. Our denoising method is discussed and compared to several typical existing methods in various aspects. Experimental results show that our method outperforms all the compared methods for both CAD and non-CAD meshes at reasonable costs. It can preserve different levels of features well, and prevent generating false edges in most cases, even with the parameters evaluated by our estimation formulae.

Tensor Voting Guided Mesh Denoising

“…The three regions of irregular surface sampling are highlighted. The denoised results of Wu et al [3] with parameters (50,5), Zhang et al [4] (0.2, 80, 10, 1), and ours.…”

Survey on sparsity in geometric modeling and processing

“…In many mesh reconstruction and editting applications, sharp features shoud be preserved after processing. As sharp feature is always sparse, sparsity formulation catches this observation well and achieve state-of-art performance [13,14,15,75].…”

“…6(b) gives one denoised result with sharp features. [17] robust to noises, outliers WLOP [18] robust to noises, outliers CLOP [19] robust to noises, outliers TV( 1 ) based/ [20] robust to noises, outliers Subdivision [21] robust to noises, outliers Mesh Denoising 0 -norm of Edge Operator [13] sharp feature preserving 1 -analysis Compressed Sensing [14] sharp feature preserving TV( 1 ) based [15] sharp feature preserving Shape Matching…”

“…Instead, Zhang et al [15] adopt the sparsity of face normals differences and propose a two-phase method including f ace normal filtering and vertex updating. They filter face normals with a TV based variational denoising method based on another kind of differential operators on triangulated surfaces…”

“…One might justifiably wonder whether sparsity based regularization and sparse representation can be useful at all for geometry processing tasks. The answer has been largely positive: in the past few years, variations and extensions of 1 minimization have been applied to many geometry processing tasks, including mesh denoising [13,14,15], point surface reconstruction [16], point cloud consolidation [17,18,19,20,21], mesh segmentation [22,23,24,25], and point cloud registration [26]. In almost all of these applications, using sparsity as a prior leads to stateof-the-art results.…”