Supervertex Sampling Network: A Geodesic Differential SLIC Approach for 3D Mesh

Area of Science:

• Computer Graphics
• Deep Learning
• Computational Geometry

Background:

• Deep learning for 3D mesh analysis is growing.
• Hierarchical mesh representation is crucial for multiscale analysis.
• Current methods are non-differentiable, limiting integration with trainable networks.

Purpose of the Study:

• To propose a novel differentiable chart-based segmentation method for 3D meshes.
• To enable seamless integration of mesh hierarchy construction into deep learning frameworks.
• To overcome limitations of existing non-differentiable mesh processing techniques.

Main Methods:

• Proposed Geodesic Differential Supervertex (GDSV), a differentiable chart-based segmentation method.
• Ensured differentiability of geodesic position updates while maintaining supervertices on the manifold.
• Utilized differential SLIC clustering and the Gumbel-Softmax trick for supervertex updates.

Main Results:

• The GDSV method ensures differentiable geodesic position updates.
• The method converts geodesic position updates into a linear matrix multiplication problem.
• Experimental results demonstrate excellent performance across various datasets.

Conclusions:

• GDSV offers a differentiable and integrable approach to 3D mesh segmentation.
• The method can be used as a standalone module or a plug-in component in deep learning pipelines.
• GDSV facilitates advanced 3D tasks like shape classification, part segmentation, and scene understanding.