TopoDDPM: Diffusion probabilistic model using persistent homology for 3D point cloud generation.

Area of Science:

• Computer Vision
• Machine Learning
• Computational Geometry

Background:

• Diffusion models are effective for 3D point cloud generation.
• Existing methods often overlook global topological features, leading to incomplete structures.
• Structural fidelity in 3D generation requires both geometric and topological information.

Purpose of the Study:

• To propose TopoDDPM, a novel diffusion probabilistic model for 3D point cloud generation.
• To enhance structural quality by integrating persistent homology for topological feature extraction.
• To improve the fidelity and diversity of generated 3D point clouds.

Main Methods:

• Developed TopoDDPM, a diffusion model incorporating persistent homology.
• Introduced a topology latent and a shape latent for conditional denoising.
• Implemented a topological loss function to ensure structural consistency.
• Utilized normalizing flows to parameterize the shape latent.

Main Results:

• TopoDDPM outperforms existing methods in fidelity and diversity on the ShapeNet dataset.
• The model demonstrates improved training efficiency and topological integrity preservation.
• Explicit integration of topological information significantly enhances 3D point cloud generation.

Conclusions:

• TopoDDPM effectively generates high-quality 3D point clouds by leveraging both geometric and topological features.
• Persistent homology is crucial for capturing global structural information in generative models.
• The proposed method offers a promising direction for advanced 3D shape generation.