Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D meshes and point clouds have either relied on computationally intensive node-level tokens for large objects or resorted to resampling to standardize patch size. Moreover, these methods generally lack a geometry-aware, stable Structural Embedding (SE), often depending on simplistic absolute SEs such as 3D coordinates, which compromise isometry invariance essential for tasks like semantic segmentation. In our study, we meticulously examine the various components of a geometry-aware 3D mesh transformer, from tokenization to structural encoding, assessing the contribution of each. Initially, we introduce a spectral-preserving tokenization rooted in algebraic multigrid methods. Subsequently, we detail an approach for embedding features at the patch level, accommodating patches with variable node counts. Through comparative analyses against a baseline model employing simple point-wise Multi-Layer Perceptrons (MLP), our research highlights critical insights: 1) the importance of structural and positional embeddings facilitated by heat diffusion in general 3D mesh transformers; 2) the effectiveness of novel components such as geodesic masking and feature interaction via cross-attention in enhancing learning; and 3) the superior performance and efficiency of our proposed methods in challenging segmentation and classification tasks.

本研究解决了现有基于变换器的3D网格处理方法在处理不规则几何数据时的关键问题，如缺少规范化排序和输入大小的变化。通过引入谱保持的标记方法和补丁级特征嵌入，并加强结构和位置嵌入的学习，我们的研究证明了这些新组件在提升学习效果及处理复杂分割与分类任务中的优势。

几何感知3D网格变换器的设计方案