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

• URL: http://arxiv.org/abs/2412.16619v3
• Date: Sun, 02 Feb 2025 14:00:10 GMT
• Title: Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity
• Authors: Tianqi Shen, Shaohua Liu, Jiaqi Feng, Ziye Ma, Ning An,
• Abstract summary: This work introduces Topology-Aware 3D Gaussian Splatting (Topology-GS)<n>Topology-GS addresses compromised pixel-level structural integrity due to incomplete initial geometric coverage.<n>Experiments on three novel-view benchmarks demonstrate that Topology-GS outperforms existing methods in terms of PSNR, SSIM, and LPIPS metrics.
• Score: 3.792470553976718
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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