3D models are commonly used in computer vision and graphics. With the wider
availability of mesh data, an efficient and intrinsic deep learning approach to
processing 3D meshes is in great need. Unlike images, 3D meshes have irregular
connectivity, requiring careful design to capture relations in the data. To
utilize the topology information while staying robust under different
triangulation, we propose to encode mesh connectivity using Laplacian spectral
analysis, along with Mesh Pooling Blocks (MPBs) that can split the surface
domain into local pooling patches and aggregate global information among them.
We build a mesh hierarchy from fine to coarse using Laplacian spectral
clustering, which is flexible under isometric transformation. Inside the MPBs
there are pooling layers to collect local information and multi-layer
perceptrons to compute vertex features with increasing complexity. To obtain
the relationships among different clusters, we introduce a Correlation Net to
compute a correlation matrix, which can aggregate the features globally by
matrix multiplication with cluster features. Our network architecture is
flexible enough to be used on meshes with different numbers of vertices. We
conduct several experiments including shape segmentation and classification,
and our LaplacianNet outperforms state-of-the-art algorithms for these tasks on
ShapeNet and COSEG datasets.

在处理 3D meshes 方面，Laplacian spectral analysis 和 Mesh Pooling Blocks（MPBs）的结合可以更好地处理表面的局部池化和全局信息聚合，并使用 Correlation Net 计算相关矩阵来进行形状分割和分类，模型表现优良。