Laplacian2Mesh: Laplacian-Based Mesh Understanding
This addresses shape understanding tasks in computer graphics for researchers and practitioners, offering a novel method to handle irregular meshes, though it appears incremental in applying CNNs to this domain.
The paper tackles the problem of irregular mesh structures in geometric deep learning by introducing Laplacian2Mesh, a CNN framework that maps meshes to Laplacian-Beltrami space, enabling shape classification and segmentation without handling irregular connectivity, with extensive tests showing effectiveness and efficiency.
Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.