Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D surfaces implicitly as signed or unsigned distance functions. Taking advantage of both advanced explicit learning process and powerful representation ability of implicit functions, we propose a novel 3D representation method, Neural Vector Fields (NVF). It not only adopts the explicit learning process to manipulate meshes directly, but also leverages the implicit representation of unsigned distance functions (UDFs) to break the barriers in resolution and topology. Specifically, our method first predicts the displacements from queries towards the surface and models the shapes as \textit{Vector Fields}. Rather than relying on network differentiation to obtain direction fields as most existing UDF-based methods, the produced vector fields encode the distance and direction fields both and mitigate the ambiguity at "ridge" points, such that the calculation of direction fields is straightforward and differentiation-free. The differentiation-free characteristic enables us to further learn a shape codebook via Vector Quantization, which encodes the cross-object priors, accelerates the training procedure, and boosts model generalization on cross-category reconstruction. The extensive experiments on surface reconstruction benchmarks indicate that our method outperforms those state-of-the-art methods in different evaluation scenarios including watertight vs non-watertight shapes, category-specific vs category-agnostic reconstruction, category-unseen reconstruction, and cross-domain reconstruction. Our code will be publicly released.

翻译：深度神经网络（DNNs）广泛应用于现今的三维表面重建任务。此类方法可进一步分为两类：一类通过移动顶点显式地扭曲模板，另一类则通过有符号或无符号距离函数隐式地表示三维表面。结合显式学习过程的优势与隐式函数的强大表示能力，我们提出了一种新颖的三维表示方法——神经向量场（Neural Vector Fields, NVF）。该方法不仅采用显式学习过程直接操控网格，还利用无符号距离函数（UDFs）的隐式表示突破分辨率与拓扑结构的限制。具体而言，我们的方法首先预测从查询点到表面的位移，并将形状建模为**向量场**。与现有大多数基于UDF的方法依赖网络微分获取方向场不同，所生成的向量场同时编码距离场与方向场，并缓解了“脊点”处的模糊性，使得方向场的计算直接且无需微分。无需微分的特性使我们能进一步通过向量量化（Vector Quantization）学习形状码本，该码本编码了跨对象先验知识，加速了训练过程，并提升了模型在跨类别重建中的泛化能力。在表面重建基准上的大量实验表明，我们的方法在多种评估场景中均优于现有最先进方法，包括水密与非水密形状、类别特定与类别无关重建、未见类别重建以及跨域重建。我们的代码将公开发布。