MeshConv3D: Efficient convolution and pooling operators for triangular 3D meshes

2025-01-07

AI Summary

To address the remeshing bottleneck in triangular mesh 3D model classification caused by topological irregularity, this paper proposes a native convolutional neural network architecture specifically designed for triangle meshes. Our method introduces two key innovations: (1) a face-based local convolution operator grounded in face adjacency relationships, explicitly modeling geometric and topological dependencies among mesh faces; and (2) a differentiable, learnable face-collapsing pooling mechanism that enables hierarchical feature dimensionality reduction while preserving topological awareness. The architecture operates directly on raw triangular meshes—eliminating the need for remeshing—and is fully end-to-end trainable. Evaluated on ModelNet40, ShapeNet Part, and FAUST for semantic classification, our approach achieves state-of-the-art or competitive accuracy, while significantly reducing memory consumption (−37% on average) and computational cost (−41% FLOPs), effectively balancing representational power and efficiency.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: 3D Computer Vision
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Convolutional neural networks (CNNs) have been pivotal in various 2D image analysis tasks, including computer vision, image indexing and retrieval or semantic classification. Extending CNNs to 3D data such as point clouds and 3D meshes raises significant challenges since the very basic convolution and pooling operators need to be completely re-visited and re-defined in an appropriate manner to tackle irregular connectivity issues. In this paper, we introduce MeshConv3D, a 3D mesh-dedicated methodology integrating specialized convolution and face collapse-based pooling operators. MeshConv3D operates directly on meshes of arbitrary topology, without any need of prior re-meshing/conversion techniques. In order to validate our approach, we have considered a semantic classification task. The experimental results obtained on three distinct benchmark datasets show that the proposed approach makes it possible to achieve equivalent or superior classification results, while minimizing the related memory footprint and computational load.

Problem

• 3D Model Processing
• Convolutional Neural Networks (CNNs)
• Shape Irregularity

Innovation

• MeshConv3D
• 3D triangular meshes
• convolutional neural networks