Laplacian2Mesh: Laplacian-Based Mesh Understanding.

Area of Science:

• Computer Graphics
• Geometric Deep Learning
• Computational Geometry

Background:

• Geometric deep learning is increasingly used for shape understanding tasks like classification and semantic segmentation.
• Irregular mesh structures in polygonal surfaces pose challenges for traditional deep learning methods.
• Existing approaches often struggle with the variable connectivity of mesh vertices.

Purpose of the Study:

• To introduce Laplacian2Mesh, a novel convolutional neural network (CNN) framework designed to address the challenges of irregular triangle meshes.
• To enable direct shape analysis on irregular meshes using mature CNN architectures.
• To improve the robustness and accuracy of shape understanding tasks in computer graphics.

Main Methods:

• Mapping input mesh surfaces to the multi-dimensional Laplacian-Beltrami space.
• Developing a mesh pooling operation to expand the network's receptive field while preserving vertex information.
• Incorporating a channel-wise self-attention block to learn feature importance.

Main Results:

• Laplacian2Mesh successfully decouples geometric features from mesh connectivity.
• The framework demonstrates enhanced capture of global features crucial for shape classification and segmentation.
• Extensive testing confirmed the effectiveness and efficiency of Laplacian2Mesh across various datasets, showing resilience to noise.

Conclusions:

• Laplacian2Mesh provides a flexible and effective CNN framework for analyzing irregular triangle meshes.
• The method significantly improves shape understanding tasks by leveraging spectral geometry and attention mechanisms.
• Laplacian2Mesh offers a robust solution for noise-vulnerable learning tasks in 3D shape analysis.