Recent neural networks based surface reconstruction can be roughly divided
into two categories, one warping templates explicitly and the other
representing 3D surfaces implicitly. To enjoy the advantages of both, we
propose a novel 3D representation, Neural Vector Fields (NVF), which adopts the
explicit learning process to manipulate meshes and implicit unsigned distance
function (UDF) representation to break the barriers in resolution and topology.
This is achieved by directly predicting the displacements from surface queries
and modeling shapes as Vector Fields, rather than relying on network
differentiation to obtain direction fields as most existing UDF-based methods
do. In this way, our approach is capable of encoding both the distance and the
direction fields so that the calculation of direction fields is
differentiation-free, circumventing the non-trivial surface extraction step.
Furthermore, building upon NVFs, we propose to incorporate two types of shape
codebooks, \ie, NVFs (Lite or Ultra), to promote cross-category reconstruction
through encoding cross-object priors. Moreover, we propose a new regularization
based on analyzing the zero-curl property of NVFs, and implement this through
the fully differentiable framework of our NVF (ultra). We evaluate both NVFs on
four surface reconstruction scenarios, including watertight vs non-watertight
shapes, category-agnostic reconstruction vs category-unseen reconstruction,
category-specific, and cross-domain reconstruction.

基于神经网络的表面重建可大致分为两类，一类明确地对模板进行变形，另一类隐式地表示 3D 表面；为了获得两者的优势，我们提出了一种新颖的 3D 表示方法，神经向量场 (NVF)，它采用显式的学习过程来操作网格，并采用隐式无符号距离函数 (UDF) 表示法来突破分辨率和拓扑的限制；通过直接预测表面查询中的位移并将形状建模为向量场，而不是依赖网络微分以获得方向场，从而能够编码距离和方向场，使方向场的计算免于微分，避免繁琐的表面提取步骤；此外，基于 NVF，我们提出了同时结合两种类型的形状码书，即 NVF (Lite 或 Ultra)，通过编码跨对象先验来促进跨类别重建；此外，我们还提出了一种基于分析 NVF 的零旋性质的新的正则化方法，并通过完全可微分的 NVF (ultra) 框架实现；我们在四种表面重建场景下对 NVF 进行评估，包括封闭与非封闭形状、类别不可知重建与类别未知重建、类别特定和跨领域重建。

神经向量场：通过码书和零环规则推广距离向量场

Neural Vector Fields: Generalizing Distance Vector Fields by Codebooks  and Zero-Curl Regularization

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。