Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity
This work addresses limitations in 3D scene representation for computer vision applications, though it is incremental as it builds on existing Gaussian Splatting techniques.
The paper tackles the problem of compromised structural integrity in 3D Gaussian Splatting for novel-view synthesis by introducing topology-aware methods, resulting in improved performance on benchmarks with higher PSNR, SSIM, and LPIPS metrics while maintaining efficient memory usage.
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.