We introduce Explicit Neural Surfaces (ENS), an efficient surface
reconstruction method that learns an explicitly defined continuous surface from
multiple views. We use a series of neural deformation fields to progressively
transform a continuous input surface to a target shape. By sampling meshes as
discrete surface proxies, we train the deformation fields through efficient
differentiable rasterization, and attain a mesh-independent and smooth surface
representation. By using Laplace-Beltrami eigenfunctions as an intrinsic
positional encoding alongside standard extrinsic Fourier features, our approach
can capture fine surface details. ENS trains 1 to 2 orders of magnitude faster
and can extract meshes of higher quality compared to implicit representations,
whilst maintaining competitive surface reconstruction performance and real-time
capabilities. Finally, we apply our approach to learn a collection of objects
in a single model, and achieve disentangled interpolations between different
shapes, their surface details, and textures.

本篇研究提出了一种名为 ENS 的表面重构方法，使用一系列神经形变场逐步将连续输入表面转换到目标形状，通过 Laplace-Beltrami 本征函数和标准外部傅里叶特征进行表征，具有实时性能和高质量的网格抽取能力。

显式神经表面：利用形变场学习连续几何

Explicit Neural Surfaces: Learning Continuous Geometry With Deformation  Fields

In this paper, we propose a method for computing partial functional
correspondence between non-rigid shapes. We use perturbation analysis to show
how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and
exploit it as a prior on the spectral representation of the correspondence.
Corresponding parts are optimization variables in our problem and are used to
weight the functional correspondence; we are looking for the largest and most
regular (in the Mumford-Shah sense) parts that minimize correspondence
distortion. We show that our approach can cope with very challenging
correspondence settings.

本文提出了一种计算非刚性形状之间部分函数对应的方法，利用摄动分析展示了何以通过去除形状部件改变 Laplace-Beltrami 特征函数，进而将其作为先验应用到对应的谱表示中，匹配的部分是问题中的优化变量，用于加权函数对应；找到最小化对应失真的最大和最规则（在 Mumford-Shah 意义下）的部分。我们证明了我们的方法可以处理非常具有挑战性的对应设置。