Surface Extraction from Neural Unsigned Distance Fields

TL;DR

This paper introduces DualMesh-UDF, a novel method for extracting accurate surface meshes from neural unsigned distance functions, overcoming previous challenges related to sign ambiguity and approximation errors.

Contribution

The paper presents a new surface extraction technique from neural UDFs that estimates tangent planes and constructs surface points via local clustering and least squares, improving accuracy and robustness.

Findings

Outperforms existing methods in surface reconstruction quality.

Maintains computational efficiency comparable to prior approaches.

Effectively handles arbitrary topologies in neural UDFs.

Abstract

We propose a method, named DualMesh-UDF, to extract a surface from unsigned distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural UDFs are becoming increasingly popular for surface representation because of their versatility in presenting surfaces with arbitrary topologies, as opposed to the signed distance function that is limited to representing a closed surface. However, the applications of neural UDFs are hindered by the notorious difficulty in extracting the target surfaces they represent. Recent methods for surface extraction from a neural UDF suffer from significant geometric errors or topological artifacts due to two main difficulties: (1) A UDF does not exhibit sign changes; and (2) A neural UDF typically has substantial approximation errors. DualMesh-UDF addresses these two difficulties. Specifically, given a neural UDF encoding a target surface $\bar{S}$ to be recovered, we first estimate the tangent planes of $\bar{S}$ at a set of sample points close to $\bar{S}$. Next, we organize these sample points into local clusters, and for each local cluster, solve a linear least squares problem to determine a final surface point. These surface points are then connected to create the output mesh surface, which approximates the target surface. The robust estimation of the tangent planes of the target surface and the subsequent minimization problem constitute our core strategy, which contributes to the favorable performance of DualMesh-UDF over other competing methods. To efficiently implement this strategy, we employ an adaptive Octree. Within this framework, we estimate the location of a surface point in each of the octree cells identified as containing part of the target surface. Extensive experiments show that our method outperforms existing methods in terms of surface reconstruction quality while maintaining comparable computational efficiency.