Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field

TL;DR

This paper introduces a novel smooth objective function to achieve globally consistent normal orientations in point clouds, effectively handling imperfections like sparsity, gaps, and complex geometries.

Contribution

It proposes a new regularization method based on the winding-number field that improves normal orientation consistency in challenging point cloud data.

Findings

Outperforms existing methods on sparse and noisy data

Handles complex geometries and topologies effectively

Ensures balanced and correct normal orientations

Abstract

Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal with an unoriented point cloud with various imperfections, particularly in the presence of data sparsity coupled with nearby gaps or thin-walled structures. In this paper, we propose a smooth objective function to characterize the requirements of an acceptable winding-number field, which allows one to find the globally consistent normal orientations starting from a set of completely random normals. By taking the vertices of the Voronoi diagram of the point cloud as examination points, we consider the following three requirements: (1) the winding number is either 0 or 1, (2) the occurrences of 1 and the occurrences of 0 are balanced around the point cloud, and (3) the normals align with the outside Voronoi poles as much as possible. Extensive experimental results show that our method outperforms the existing approaches, especially in handling sparse and noisy point clouds, as well as shapes with complex geometry/topology.