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.

翻译：我们提出了一种名为DualMesh-UDF的方法，用于从由神经网络编码的无符号距离函数（UDF）或神经UDF中提取表面。神经UDF因其能够表示任意拓扑结构的表面而日益流行，这与仅限于表示闭合表面的有符号距离函数形成对比。然而，神经UDF的应用因其难以提取所代表的目标表面而受阻。近期从神经UDF中提取表面的方法由于两大难点而存在显著的几何误差或拓扑伪影：（1）UDF不呈现符号变化；（2）神经UDF通常有较大的近似误差。DualMesh-UDF解决了这两个难点。具体而言，给定一个编码待恢复目标表面$\bar{S}$的神经UDF，我们首先在接近$\bar{S}$的一组采样点上估计$\bar{S}$的切平面。接着，我们将这些采样点组织成局部簇，并对每个局部簇求解一个线性最小二乘问题以确定最终表面点。然后连接这些表面点以生成输出网格表面，其逼近目标表面。目标表面切平面的稳健估计及随后的最小化问题构成了我们的核心策略，这使DualMesh-UDF相比其他竞争方法表现出优越性能。为高效实施该策略，我们采用自适应八叉树。在此框架内，我们在每个被识别为包含目标表面部分的八叉树单元中估计表面点的位置。大量实验表明，我们的方法在保持相当计算效率的同时，在表面重建质量上优于现有方法。