This paper explores the problem of effectively compressing 3D geometry sets containing diverse categories. We make \textit{the first} attempt to tackle this fundamental and challenging problem and propose NeCGS, a neural compression paradigm, which can compress hundreds of detailed and diverse 3D mesh models (~684 MB) by about 900 times (0.76 MB) with high accuracy and preservation of detailed geometric details. Specifically, we first represent each irregular mesh model/shape in a regular representation that implicitly describes the geometry structure of the model using a 4D regular volume, called TSDF-Def volume. Such a regular representation can not only capture local surfaces more effectively but also facilitate the subsequent process. Then we construct a quantization-aware auto-decoder network architecture to regress these 4D volumes, which can summarize the similarity of local geometric structures within a model and across different models for redundancy limination, resulting in more compact representations, including an embedded feature of a smaller size associated with each model and a network parameter set shared by all models. We finally encode the resulting features and network parameters into bitstreams through entropy coding. After decompressing the features and network parameters, we can reconstruct the TSDF-Def volumes, where the 3D surfaces can be extracted through the deformable marching cubes.Extensive experiments and ablation studies demonstrate the significant advantages of our NeCGS over state-of-the-art methods both quantitatively and qualitatively.

翻译：本文探讨了如何高效压缩包含多种类别的三维几何集合这一基础性难题。我们首次尝试解决这一根本性挑战，提出了NeCGS——一种神经压缩范式，能够以约900倍的压缩率（0.76 MB）对数百个精细多样的三维网格模型（约684 MB）进行高精度压缩，同时完整保留几何细节。具体而言，我们首先将每个不规则网格模型/形状转换为基于4D规则体素（称为TSDF-Def体积）的规则化表示，该表示能隐式描述模型的几何结构。这种规则化表示不仅能更有效地捕捉局部表面特征，还为后续处理流程提供了便利。随后，我们构建了量化感知的自解码器网络架构来回归这些4D体积，该架构能够提取单个模型内部及跨模型间的局部几何结构相似性以消除冗余，从而生成更紧凑的表示形式——包括与每个模型关联的较小尺寸嵌入特征，以及所有模型共享的网络参数集。最后，我们通过熵编码将所得特征和网络参数编码为比特流。在解压缩特征和网络参数后，可重建TSDF-Def体积，进而通过可变形移动立方体算法提取三维表面。大量实验与消融研究证明，我们的NeCGS方法在定量与定性评估上均显著优于现有先进方法。