Denoising Manifold and Non-Manifold Point Clouds

Abstract

The faithful reconstruction of 3-D models from irregular and noisy point samples is a task central to many applications of computer vision and graphics. We present an approach to denoising that naturally handles intersections of manifolds, thus preserving high-frequency details without oversmoothing. This is accomplished through the use of a modified locally weighted regression algorithm that models a neighborhood of points as an implicit product of linear subspaces. By posing the problem as one of energy minimization subject to constraints on the coefficients of a higher order polynomial, we can also incorporate anisotropic error models appropriate for data acquired with a range sensor. We demonstrate the effectiveness of our approach through some preliminary results in denoising synthetic data in 2-D and 3-D domains. *

Scale Selection for Geometric Fitting in Noisy Point Clouds

“…Such objects possess sharp features such as corners and edges which are created when these smooth surfaces intersect. One way to overcome this is may be to use a modified local regression technique, such as presented in [35], that models sharp intersections as an implicit product of lower dimensional subspaces. The geometric fitting of these sharp features may be done by iteratively first solving a generalized eigenvector problem to fit a smooth surface and then subjecting the solution to some non-linear constraints required for the model parameters to represent a degenerate surface.…”

Algorithmic Solutions for Computing Precise Maximum Likelihood 3D Point Clouds from Mobile Laser Scanning Platforms

“…These approaches are usually time expensive, due to the enlarged state space. Aiming to reduce noise, Unnikrishnan and Hebert locally fit high-order polynomials to 3D data [17]. However, large-scale deformations will not be corrected by such a local approach.…”

Robust Segmentation of Multiple Intersecting Manifolds from Unoriented Noisy Point Clouds

“…surface smoothness, water tightness, viewpoint invariance and topology [BMR*99, AC01, Flö09, DG03, CSD04, JR07, DLRW09, TOZ*11, SSZCO10, KBH06]. For noisy clouds, we distinguish between denoising [UH07] and surface extraction methods [DG04, SW09, MDD*10]. Chang et al .…”

“…Section 4 presents CSD04, JR07, DLRW09, TOZ*11, SSZCO10,KBH06]. For noisy clouds, we distinguish between denoising [UH07] and surface extraction methods [DG04, SW09, MDD*10]. Chang et al present a comprehensive comparison of the strengths and limitations of 16 surface reconstruction methods [CLK09].…”