Denoising Manifold and Non-Manifold Point Clouds

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.