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.

本文提出了一种新的 3D 表示方法，神经向量场（NVF），该方法充分利用了显式学习过程和隐式函数表示的强大表示能力，通过从查询向表面预测位移并使用矢量场对形状进行建模来打破分辨率和拓扑中的障碍，进而提出了一个基于矢量量化的形状代码本学习方法，最终实现了在不同的评价场景下优于最先进方法的结果，包括完整及非完整形状的构建、类别特定和类别不可知构建、类别未知构建和跨域构建。