MDSSN: An end-to-end deep network on triangle mesh parameterization

Mesh data plays a crucial role in a wide range of applications worldwide within the field of 3D computer vision. In contrast to traditional Euclidean space arrangements, meshes encompass spatial information, including edges, faces, angles, and graph structures that embed face information within the mesh data. Nevertheless, conventional deep learning frameworks such as convolutional neural networks (CNNs) have struggled to achieve significant advancements in handling meshes. This paper proposes a simple mesh computation framework called Mesh Decomposition Second-order Sobolev Network (MDSSN) to model triangle meshes and represent their shape. The construction of face-based Riemannian and edge-based Riemannian graphs is motivated by the remarkable representation capabilities of edges and faces in mesh data, achieved through a graph composition mechanism. Furthermore, we design end-to-end operators, including the Sobolev-filter block, pooling, and unpooling blocks, which draw inspiration from traditional deep learning frameworks for modeling the mesh structure. Importantly, the design of the mesh-filter block incorporates the second-order Sobolev metric. To address common challenges in mesh classification and segmentation tasks, we have designed dedicated classification and segmentation modules. We utilize a joint loss function that integrates losses from adjacent faces and categories. We evaluate the performance of the MDSSN in mesh classification and segmentation tasks, focusing on its ability to represent 3D shapes. Experimental results demonstrate that MDSSN achieves superior performance compared to other state-of-the-art approaches. © 2023 Elsevier B.V.