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

arXiv: https://arxiv.org/abs/2412.16619 · HTML: https://mlsanity.com/paper/2412.16619/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 21 Dec 2024.

## Builds on (most cited first, 30 of 32)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering](https://mlsanity.com/paper/2311.12775/) (2023)
- [DNGaussian: Optimizing Sparse-View 3D Gaussian Radiance Fields with Global-Local Depth Normalization](https://mlsanity.com/paper/2403.06912/) (2024)
- [BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering](https://mlsanity.com/paper/2112.05504/) (2021)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Eigen-CAM: Class Activation Map using Principal Components](https://mlsanity.com/paper/2008.00299/) (2020)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [DN-Splatter: Depth and Normal Priors for Gaussian Splatting and Meshing](https://mlsanity.com/paper/2403.17822/) (2024)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [RadSplat: Radiance Field-Informed Gaussian Splatting for Robust Real-Time Rendering with 900+ FPS](https://mlsanity.com/paper/2403.13806/) (2024)
- [Grid-guided Neural Radiance Fields for Large Urban Scenes](https://mlsanity.com/paper/2303.14001/) (2023)
- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (2023)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [SA-GS: Scale-Adaptive Gaussian Splatting for Training-Free Anti-Aliasing](https://mlsanity.com/paper/2403.19615/) (2024)
- [Geometry Helps to Compare Persistence Diagrams](https://mlsanity.com/paper/1606.03357/) (2016)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Spectrally Pruned Gaussian Fields with Neural Compensation](https://mlsanity.com/paper/2405.00676/) (2024)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [Persformer: A Transformer Architecture for Topological Machine Learning](https://mlsanity.com/paper/2112.15210/) (2021)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)

## Built on by (most cited first, 6 of 6)

- [DVP-MVS++: Synergize Depth-Normal-Edge and Harmonized Visibility Prior for Multi-View Stereo](https://mlsanity.com/paper/2506.13215/) (2025)
- [Spatiotemporal Degradation-Aware 3D Gaussian Splatting for Realistic Underwater Scene Reconstruction](https://mlsanity.com/paper/2604.23551/) (2026)
- [GSM-GS: Geometry-Constrained Single and Multi-view Gaussian Splatting for Surface Reconstruction](https://mlsanity.com/paper/2602.12796/) (2026)
- [MemRepair: Hierarchical Memory for Agentic Repository-Level Vulnerability Repair](https://mlsanity.com/paper/2605.17444/) (2026)
- [STARS-GS: Structure-Aware Regularized Gaussian Splatting for Large-Scale Aerial Surface Reconstruction](https://mlsanity.com/paper/2609.03447/) (2026)
- [SILSA: Sliding-Window Slice Latents for Topology-Preserving High-Resolution 3D Generation](https://mlsanity.com/paper/2610.02201/) (2026)

## Abstract (arXiv)

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.