Anisotropic Mesh Filtering by Homogeneous MLS Fitting

TL;DR

This paper introduces a novel anisotropic mesh filtering method based on homogeneous MLS fitting, which preserves features and handles various noise types effectively.

Contribution

The paper proposes a new H-MLS filter that improves mesh filtering by using homogeneous least squares fitting without requiring pre-filtered normals.

Findings

Exact recovery of spheres and cylinders.

High fidelity preservation of original mesh features.

Effective filtering of noisy and irregular meshes.

Abstract

In this paper we present a novel geometric filter, a homogeneous moving least squares fitting-based filter (H-MLS filter), for anisotropic mesh filtering. Instead of fitting the noisy data by a moving parametric surface and projecting the noisy data onto the surface, we compute new positions of mesh vertices as the solutions to homogeneous least squares fitting of moving constants to local neighboring vertices and tangent planes that pass through the vertices. The normals for defining the tangent planes need not be filtered beforehand but the parameters for balancing the influences between neighboring vertices and neighboring tangent planes are computed robustly from the original data under the assumption of quadratic precision in each tangent direction. The weights for respective neighboring points for the least squares fitting are computed adaptively for anisotropic filtering. The filter is easy to implement and has distinctive features for mesh filtering. (1) The filter is locally implemented and has circular precision, spheres and cylinders can be recovered exactly by the filter. (2) The filtered mesh has a high fidelity to the original data without any position constraint and salient or sharp features can be preserved well. (3) The filter can be used to filter meshes with various kinds of noise as well as meshes with highly irregular triangulation.