Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity

2024-12-21

AI Summary

To address structural distortions and detail loss in 3D Gaussian Splatting (3D-GS) caused by incomplete initial geometric coverage and lack of topological constraints, this work introduces persistent homology into the 3D-GS optimization framework for the first time. We propose Local Persistent Voronoi Interpolation (LPVI) to enhance geometric continuity and design PersLoss—a topology-aware regularization term derived from persistent barcodes—to explicitly enforce pixel- and feature-level topological consistency. Integrated with differentiable Gaussian rendering, our topology-guided optimization achieves state-of-the-art performance on three novel-view synthesis benchmarks—Synthetic, Real Forward, and Real Backward—surpassing existing methods in PSNR, SSIM, and LPIPS while maintaining efficient memory usage. Our core contribution is the first topology-driven reconstruction paradigm for 3D-GS, significantly improving structural fidelity and visual realism.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Data transparency and provenance

Abstract

Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces Topology-Aware 3D Gaussian Splatting (Topology-GS), which addresses two key limitations in current approaches: compromised pixel-level structural integrity due to incomplete initial geometric coverage, and inadequate feature-level integrity from insufficient topological constraints during optimization. To overcome these limitations, Topology-GS incorporates a novel interpolation strategy, Local Persistent Voronoi Interpolation (LPVI), and a topology-focused regularization term based on persistent barcodes, named PersLoss. LPVI utilizes persistent homology to guide adaptive interpolation, enhancing point coverage in low-curvature areas while preserving topological structure. PersLoss aligns the visual perceptual similarity of rendered images with ground truth by constraining distances between their topological features. Comprehensive experiments on three novel-view synthesis benchmarks demonstrate that Topology-GS outperforms existing methods in terms of PSNR, SSIM, and LPIPS metrics, while maintaining efficient memory usage. This study pioneers the integration of topology with 3D-GS, laying the groundwork for future research in this area.

Problem

• 3D Graphics Processing
• Structural Stability
• Detail Preservation

Innovation

• Topology-GS
• LPVI
• PersLoss