Bilateral mesh denoising

Abstract

We present an anisotropic mesh denoising algorithm that is effective, simple and fast. This is accomplished by filtering vertices of the mesh in the normal direction using local neighborhoods. Motivated by the impressive results of bilateral filtering for image denoising, we adopt it to denoise 3D meshes; addressing the specific issues required in the transition from two-dimensions to manifolds in three dimensions. We show that the proposed method successfully removes noise from meshes while preserving features. Furthermore, the presented algorithm excels in its simplicity both in concept and implementation.

Mesh denoising via L 0 minimization

“…Fleishman et al [2003] propose a bilateral filter inspired approach that filters vertices of the mesh in the normal direction of the surface using local neighborhoods. Jones et al [2003] present a similar approach as well based on robust statistics.…”

Neighborhood Filters and the Recovery of 3D Information

“…Filtering without losing the sharp features is as critical for surfaces as it is for images, and a first adaptation of the bilateral filter to surface meshes was proposed by Fleishman, Drori, and Cohen-Or in [15]. Consider a meshed surface M with known normals n v at each vertex position v. Let N .v/ be the one-ring neighborhood of v (i.e., the set of vertices sharing an edge with v).…”

“…Each point p gets a parameter p;k which measures the degree of membership of p to a cluster k. Let m p be the number of points in the spherical neighborhood of a point p. If m p < threshold, the point is deleted. Otherwise, a fuzzy C-means clustering center c p is associated with p. The normal at point c p is computed as the normal to the regression plane of the data set in a spherical neighborhood of p. Fleishman's bilateral filter [15] is used to filter c i which yields the denoised point. This hybrid and complex method is doubly bilateral.…”

“…For example, the bilateral predictor used in [15] is … p .v/ D vC..p v/ n v /n v , and in [20], the used predictor is … p .v/ D vC..p v/ n p /n p which is the projection of v on the tangent plane passing by p. With this last predictor the corners are less smoothed out, yet there is a tangential drift due to the fact that the motion is not in the normal direction n v but in an averaged direction of the n p for p 2 N .v/. Therefore a new predictor is introduced:…”

Mason: morphological simplification

“…The computer graphics literature contains several methods for smoothing meshes, typically to remove acquisition artifacts from laser range scanning or isosurface extraction. Some techniques seek to preserve the sharp features that regularization would remove [27,28,29]. Others [30,31,32] eliminate sharp features, but like the energy-minimizing techniques they differ from regularization in that they do not simplify topology and they typically preserve thin structures.…”