Although polygon meshes have been a standard representation in geometry
processing, their irregular and combinatorial nature hinders their suitability
for learning-based applications. In this work, we introduce a novel learnable
mesh representation through a set of local 3D sample Points and their
associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape,
which we denote PoNQ. A global mesh is directly derived from PoNQ by
efficiently leveraging the knowledge of the local quadric errors. Besides
marking the first use of QEM within a neural shape representation, our
contribution guarantees both topological and geometrical properties by ensuring
that a PoNQ mesh does not self-intersect and is always the boundary of a
volume. Notably, our representation does not rely on a regular grid, is
supervised directly by the target surface alone, and also handles open surfaces
with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ
through a learning-based mesh prediction from SDF grids and show that our
method surpasses recent state-of-the-art techniques in terms of both surface
and edge-based metrics.

通过本文，我们引入了一种新型的可学习网格表示方法，通过一组局部三维样本点、法线和二次误差度量（QEM）相对于底层形状的获取，我们将其称为 PoNQ。我们通过高效地利用局部二次误差的知识，直接从 PoNQ 中获取全局网格，并确保了拓扑和几何特性，使 PoNQ 网格不自相交且始终是一个边界体积。值得注意的是，我们的表示方法不依赖于正规网格，仅由目标表面进行监督，并且还能处理具有边界和 / 或锐利特征的开放表面。通过从 SDF 网格进行基于学习的网格预测，我们展示了 PoNQ 的有效性，并且在表面和边缘相关指标上超过了最近研究中的先进技术。

PoNQ: 基于神经量化嵌网的网格表示

PoNQ: a Neural QEM-based Mesh Representation

Neural shape representation generally refers to representing 3D geometry
using neural networks, e.g., to compute a signed distance or occupancy value at
a specific spatial position. Previous methods tend to rely on the auto-decoder
paradigm, which often requires densely-sampled and accurate signed distances to
be known during training and testing, as well as an additional optimization
loop during inference. This introduces a lot of computational overhead, in
addition to having to compute signed distances analytically, even during
testing. In this paper, we present a novel encoder-decoder neural network for
embedding 3D shapes in a single forward pass. Our architecture is based on a
multi-scale hybrid system incorporating graph-based and voxel-based components,
as well as a continuously differentiable decoder. Furthermore, the network is
trained to solve the Eikonal equation and only requires knowledge of the
zero-level set for training and inference. Additional volumetric samples can be
generated on-the-fly, and incorporated in an unsupervised manner. This means
that in contrast to most previous work, our network is able to output valid
signed distance fields without explicit prior knowledge of non-zero distance
values or shape occupancy. In other words, our network computes approximate
solutions to the boundary-valued Eikonal equation. It also requires only a
single forward pass during inference, instead of the common latent code
optimization. We further propose a modification of the loss function in case
that surface normals are not well defined, e.g., in the context of
non-watertight surface-meshes and non-manifold geometry. We finally demonstrate
the efficacy, generalizability and scalability of our method on datasets
consisting of deforming 3D shapes, single class encoding and multiclass
encoding, showcasing a wide range of possible applications.

使用神经网络进行神经形状表示，通过单次前向传递嵌入 3D 形状，无需明确的先验知识，有效地计算边界值 Eikonal 方程的近似解并展示了广泛的应用领域。

神经距离场的零级集编码器

Zero-Level-Set Encoder for Neural Distance Fields

This paper presents a simple and effective solution to the longstanding
classical multi-view photometric stereo (MVPS) problem. It is well-known that
photometric stereo (PS) is excellent at recovering high-frequency surface
details, whereas multi-view stereo (MVS) can help remove the low-frequency
distortion due to PS and retain the global geometry of the shape. This paper
proposes an approach that can effectively utilize such complementary strengths
of PS and MVS. Our key idea is to combine them suitably while considering the
per-pixel uncertainty of their estimates. To this end, we estimate per-pixel
surface normals and depth using an uncertainty-aware deep-PS network and
deep-MVS network, respectively. Uncertainty modeling helps select reliable
surface normal and depth estimates at each pixel which then act as a true
representative of the dense surface geometry. At each pixel, our approach
either selects or discards deep-PS and deep-MVS network prediction depending on
the prediction uncertainty measure. For dense, detailed, and precise inference
of the object's surface profile, we propose to learn the implicit neural shape
representation via a multilayer perceptron (MLP). Our approach encourages the
MLP to converge to a natural zero-level set surface using the confident
prediction from deep-PS and deep-MVS networks, providing superior dense surface
reconstruction. Extensive experiments on the DiLiGenT-MV benchmark dataset show
that our method provides high-quality shape recovery with a much lower memory
footprint while outperforming almost all of the existing approaches.

本文提出一种有效的解决方案，利用光度立体测量和多视角立体测量的互补优势，通过基于不确定性感知的深光度立体网络和深多视角立体网络估计每像素表面法线和深度，从而实现密集、详细和精确的物体表面轮廓重建。