$p$-Poisson surface reconstruction in curl-free flow from point clouds

TL;DR

This paper introduces a novel method for surface reconstruction from point clouds using a $p$-Poisson equation within implicit neural representations, emphasizing curl-free properties to improve robustness and quality without relying on ground truth normals.

Contribution

It proposes a $p$-Poisson based INR approach with a variable splitting structure and curl-free constraints, enhancing surface reconstruction from point clouds without needing additional normal information.

Findings

Outperforms existing methods on benchmark datasets

Provides robust and high-quality surface reconstructions

Eliminates dependence on ground truth normal vectors

Abstract

The aim of this paper is the reconstruction of a smooth surface from an unorganized point cloud sampled by a closed surface, with the preservation of geometric shapes, without any further information other than the point cloud. Implicit neural representations (INRs) have recently emerged as a promising approach to surface reconstruction. However, the reconstruction quality of existing methods relies on ground truth implicit function values or surface normal vectors. In this paper, we show that proper supervision of partial differential equations and fundamental properties of differential vector fields are sufficient to robustly reconstruct high-quality surfaces. We cast the $p$-Poisson equation to learn a signed distance function (SDF) and the reconstructed surface is implicitly represented by the zero-level set of the SDF. For efficient training, we develop a variable splitting structure by introducing a gradient of the SDF as an auxiliary variable and impose the $p$-Poisson equation directly on the auxiliary variable as a hard constraint. Based on the curl-free property of the gradient field, we impose a curl-free constraint on the auxiliary variable, which leads to a more faithful reconstruction. Experiments on standard benchmark datasets show that the proposed INR provides a superior and robust reconstruction. The code is available at \url{https://github.com/Yebbi/PINC}.