In mesh simplification, common requirements like accuracy, triangle quality,
and feature alignment are often considered as a trade-off. Existing algorithms
concentrate on just one or a few specific aspects of these requirements. For
example, the well-known Quadric Error Metrics (QEM) approach prioritizes
accuracy and can preserve strong feature lines/points as well but falls short
in ensuring high triangle quality and may degrade weak features that are not as
distinctive as strong ones. In this paper, we propose a smooth functional that
simultaneously considers all of these requirements. The functional comprises a
normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term,
with the variables being a set of movable points lying on the surface. The
former inherits the spirit of QEM but operates in a continuous setting, while
the latter encourages even point distribution, allowing various surface
metrics. We further introduce a decaying weight to automatically balance the
two terms. We selected 100 CAD models from the ABC dataset, along with 21
organic models, to compare the existing mesh simplification algorithms with
ours. Experimental results reveal an important observation: the introduction of
a decaying weight effectively reduces the conflict between the two terms and
enables the alignment of weak features. This distinctive feature sets our
approach apart from most existing mesh simplification methods and demonstrates
significant potential in shape understanding.

我们提出了一种新的网格简化算法，利用正态各向异性项和 Centroidal Voronoi Tessellation 能量项，通过一种逐渐减少的权重实现了同时考虑精度、三角形质量、特征对齐等要求，并证明其在形状理解方面具有重要潜力。

CWF：高质量网格简化中的弱特征整合

CWF: Consolidating Weak Features in High-quality Mesh Simplification

While surface-based view synthesis algorithms are appealing due to their low
computational requirements, they often struggle to reproduce thin structures.
In contrast, more expensive methods that model the scene's geometry as a
volumetric density field (e.g. NeRF) excel at reconstructing fine geometric
detail. However, density fields often represent geometry in a "fuzzy" manner,
which hinders exact localization of the surface. In this work, we modify
density fields to encourage them to converge towards surfaces, without
compromising their ability to reconstruct thin structures. First, we employ a
discrete opacity grid representation instead of a continuous density field,
which allows opacity values to discontinuously transition from zero to one at
the surface. Second, we anti-alias by casting multiple rays per pixel, which
allows occlusion boundaries and subpixel structures to be modelled without
using semi-transparent voxels. Third, we minimize the binary entropy of the
opacity values, which facilitates the extraction of surface geometry by
encouraging opacity values to binarize towards the end of training. Lastly, we
develop a fusion-based meshing strategy followed by mesh simplification and
appearance model fitting. The compact meshes produced by our model can be
rendered in real-time on mobile devices and achieve significantly higher view
synthesis quality compared to existing mesh-based approaches.

在这项工作中，我们修改了密度场，以鼓励它们向表面聚集，同时保持它们重建薄结构的能力。我们采用了离散不透明度网格表示，通过像素投射多条光线来抗锯齿，最小化不透明度值的二元熵，并开发了基于融合的网格化策略，最后进行网格简化和外观模型拟合。与现有的基于网格的方法相比，我们的模型产生的紧凑网格可以在移动设备上实时渲染，并实现了更高的视角合成质量。

二进制不透明网格：为基于网格的视图合成捕捉细致几何细节

Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based  View Synthesis

3D shape analysis is an important research topic in computer vision and
graphics. While existing methods have generalized image-based deep learning to
meshes using graph-based convolutions, the lack of an effective pooling
operation restricts the learning capability of their networks. In this paper,
we propose a novel pooling operation for mesh datasets with the same
connectivity but different geometry, by building a mesh hierarchy using mesh
simplification. For this purpose, we develop a modified mesh simplification
method to avoid generating highly irregularly sized triangles. Our pooling
operation effectively encodes the correspondence between coarser and finer
meshes in the hierarchy. We then present a variational auto-encoder structure
with the edge contraction pooling and graph-based convolutions, to explore
probability latent spaces of 3D surfaces. Our network requires far fewer
parameters than the original mesh VAE and thus can handle denser models thanks
to our new pooling operation and convolutional kernels. Our evaluation also
shows that our method has better generalization ability and is more reliable in
various applications, including shape generation, shape interpolation and shape
embedding.

本文提出了一种基于图卷积的网格平均池化方法，使用改进型网格简化避免产生高度不规则的三角形。在此基础上，提出了一种利用边缩减池化和图卷积的自动编码器结构，能够对 3D 表面进行概率潜空间的探索，并展示了在形态生成、形态插值和形态嵌入等各种应用中其更好的泛化能力和更可靠的性能。