Consistent Point Orientation for Manifold Surfaces via Boundary Integration

TL;DR

This paper presents a novel boundary integration method to achieve globally consistent normals for point clouds on manifold surfaces, improving robustness and accuracy over existing techniques.

Contribution

It introduces a boundary energy formulation based on the Dirichlet energy of the GWN field and optimizes it to recover consistent normals, a novel approach in point cloud processing.

Findings

Outperforms state-of-the-art methods in normal consistency

Shows robustness to noise, outliers, and complex geometries

Effectively handles thin structures and topological variations

Abstract

This paper introduces a new approach for generating globally consistent normals for point clouds sampled from manifold surfaces. Given that the generalized winding number (GWN) field generated by a point cloud with globally consistent normals is a solution to a PDE with jump boundary conditions and possesses harmonic properties, and the Dirichlet energy of the GWN field can be defined as an integral over the boundary surface, we formulate a boundary energy derived from the Dirichlet energy of the GWN. Taking as input a point cloud with randomly oriented normals, we optimize this energy to restore the global harmonicity of the GWN field, thereby recovering the globally consistent normals. Experiments show that our method outperforms state-of-the-art approaches, exhibiting enhanced robustness to noise, outliers, complex topologies, and thin structures. Our code can be found at \url{https://github.com/liuweizhou319/BIM}.