HKMCNN: Heat Kernel Mesh-Based Convolutional Neural Networks

Abstract

Convolutional neural networks (CNN) have achieved remarkable results in various computer vision and pattern recognition applications. However, in computer graphics and geometry processing, the focus is on non-Euclidean structured meshed surfaces. Since CNNs operate based on Euclidean domains, the fundamental operations of CNNs, such as convolution and pooling, are not well defined in non-Euclidean domains. To address this issue, we propose a novel mesh representation named Heat Kernel Mesh (HKM), which utilizes the heat diffusion on the non-Euclidean domain. The HKM represents a meshed surface as a spatio-temporal graph signal, sampled on the edges of the mesh at each time interval with a Euclidean-like structure. Furthermore, we propose the Heat Kernel Mesh-Based Convolutional Neural Network (HKMCNN), where convolution, pooling, and attention mechanism are designed based on the property of our representation and operate on edges. For the fine-grained classification, we propose distance Heat Kernel Mesh (dHKM) that can identify discriminant features with the HKMCNN to represent a mesh. Extensive experiments on mesh classification and segmentation demonstrate the effectiveness and efficiency of the proposed HKMCNN.