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

Abstract

We introduce Topology-Aware 3D Gaussian Splatting, combining local persistent Voronoi interpolation with a persistent-homology regularizer. The method improves geometric coverage and preserves topological structure during optimization. Experiments across novel-view-synthesis benchmarks improve PSNR, SSIM, and LPIPS while maintaining efficient memory use.