Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity
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.
高斯点绘（Gaussian Splatting, GS）已成为表示离散体积辐射场的重要技术，它通过独特的参数化方法降低场景优化中的计算需求。本文提出了拓扑感知3D高斯点绘（Topology-GS），以解决当前方法的两个关键限制：由于初始几何覆盖不完全导致的像素级结构完整性受损，以及由于优化过程中缺乏足够的拓扑约束导致的特征级完整性不足。 为克服这些限制，Topology-GS 引入了一种新颖的插值策略 局部持久Voronoi插值（Local Persistent Voronoi Interpolation, LPVI），以及基于持久条形码的拓扑聚焦正则项 PersLoss。LPVI 利用持久同调（persistent homology）引导自适应插值，在低曲率区域增强点覆盖，同时保留拓扑结构。PersLoss 通过约束渲染图像与真实图像的拓扑特征之间的距离，将视觉感知相似性与真实场景对齐。 在三个新视角合成基准数据集上的全面实验表明，Topology-GS 在 PSNR、SSIM 和 LPIPS 指标上均优于现有方法，同时保持高效的内存使用。该研究开创性地将拓扑与3D-GS相结合，为该领域未来的研究奠定了基础。