Learning-based surface reconstruction based on unsigned distance functions
(UDF) has many advantages such as handling open surfaces. We propose SuperUDF,
a self-supervised UDF learning which exploits a learned geometry prior for
efficient training and a novel regularization for robustness to sparse
sampling. The core idea of SuperUDF draws inspiration from the classical
surface approximation operator of locally optimal projection (LOP). The key
insight is that if the UDF is estimated correctly, the 3D points should be
locally projected onto the underlying surface following the gradient of the
UDF. Based on that, a number of inductive biases on UDF geometry and a
pre-learned geometry prior are devised to learn UDF estimation efficiently. A
novel regularization loss is proposed to make SuperUDF robust to sparse
sampling. Furthermore, we also contribute a learning-based mesh extraction from
the estimated UDFs. Extensive evaluations demonstrate that SuperUDF outperforms
the state of the arts on several public datasets in terms of both quality and
efficiency. Code will be released after accteptance.

基于无符号距离函数（UDF）的基于学习的表面重建具有处理开放曲面等多个优势。我们提出了 SuperUDF，一种自监督的 UDF 学习方法，该方法利用了学习的几何先验进行高效训练，并采用一种新颖的正则化方法来提高对稀疏采样的鲁棒性。SuperUDF 的核心思想受到局部最优投影（LOP）经典表面逼近算子的启发，关键观点是如果 UDF 正确估计，3D 点应该沿着 UDF 梯度局部投影到基础表面。基于此，我们设计了一系列关于 UDF 几何和预先学习的几何先验的归纳偏差，以便高效地学习 UDF 估计。我们提出了一种新颖的正则化损失来使 SuperUDF 对稀疏采样具有鲁棒性。此外，我们还贡献了一种基于学习的网格提取方法来从估计的 UDF 中获取网格。广泛的评估表明，SuperUDF 在多个公共数据集上的质量和效率均优于现有技术。代码将在接受后发布。

SuperUDF: 自监督的 UDF 估计用于表面重建

SuperUDF: Self-supervised UDF Estimation for Surface Reconstruction

Latest methods represent shapes with open surfaces using unsigned distance
functions (UDFs). They train neural networks to learn UDFs and reconstruct
surfaces with the gradients around the zero level set of the UDF. However, the
differential networks struggle from learning the zero level set where the UDF
is not differentiable, which leads to large errors on unsigned distances and
gradients around the zero level set, resulting in highly fragmented and
discontinuous surfaces. To resolve this problem, we propose to learn a more
continuous zero level set in UDFs with level set projections. Our insight is to
guide the learning of zero level set using the rest non-zero level sets via a
projection procedure. Our idea is inspired from the observations that the
non-zero level sets are much smoother and more continuous than the zero level
set. We pull the non-zero level sets onto the zero level set with gradient
constraints which align gradients over different level sets and correct
unsigned distance errors on the zero level set, leading to a smoother and more
continuous unsigned distance field. We conduct comprehensive experiments in
surface reconstruction for point clouds, real scans or depth maps, and further
explore the performance in unsupervised point cloud upsampling and unsupervised
point normal estimation with the learned UDF, which demonstrate our non-trivial
improvements over the state-of-the-art methods. Code is available at
this https URL .

通过级别集投影方法来学习更连续的零级别集合，从而构造更平滑和连续的无符号距离场。

通过水平集投影学习在无符号距离场中更连续的零水平集

Learning a More Continuous Zero Level Set in Unsigned Distance Fields  through Level Set Projection

Deep neural representations of 3D shapes as implicit functions have been
shown to produce high fidelity models surpassing the resolution-memory
trade-off faced by the explicit representations using meshes and point clouds.
However, most such approaches focus on representing closed shapes. Unsigned
distance function (UDF) based approaches have been proposed recently as a
promising alternative to represent both open and closed shapes. However, since
the gradients of UDFs vanish on the surface, it is challenging to estimate
local (differential) geometric properties like the normals and tangent planes
which are needed for many downstream applications in vision and graphics. There
are additional challenges in computing these properties efficiently with a
low-memory footprint. This paper presents a novel approach that models such
surfaces using a new class of implicit representations called the closest
surface-point (CSP) representation. We show that CSP allows us to represent
complex surfaces of any topology (open or closed) with high fidelity. It also
allows for accurate and efficient computation of local geometric properties. We
further demonstrate that it leads to efficient implementation of downstream
algorithms like sphere-tracing for rendering the 3D surface as well as to
create explicit mesh-based representations. Extensive experimental evaluation
on the ShapeNet dataset validate the above contributions with results
surpassing the state-of-the-art.

本文提出了一种新的隐式表示方法，称为最接近的表面点（CSP）表示，用于表示具有任何拓扑结构的开放或封闭形状并计算本地几何属性，可以实现高保真度和有效实现外围算法，如球追踪来呈现三维表面和创建显式基于网格的表示，并在 ShapeNet 数据集上验证了超越最先进结果的贡献。