GeoSplat: A Deep Dive into Geometry-Constrained Gaussian Splatting

2025-09-05

AI Summary

Existing Gaussian splatting methods rely on noise-sensitive low-order geometric priors—such as PCA-based normal estimation—leading to inaccurate initialization, training instability, and incomplete surface coverage. To address this, we propose GeoSplat, the first systematic Gaussian optimization framework that jointly incorporates first-order (surface normals) and second-order (principal curvatures) differential geometry cues. Specifically, GeoSplat pioneers the use of principal curvatures to guide Gaussian scale initialization and introduces a noise-robust, dynamically updated geometric estimator based on local manifold modeling, significantly improving gradient accuracy and densification fidelity. Evaluated on multiple standard benchmarks, GeoSplat achieves substantial gains in novel-view synthesis quality (average +1.2 dB PSNR, +0.015 SSIM), accelerates convergence by 30%, and yields more complete and detailed surface reconstructions. These results empirically validate the critical importance of high-order geometric priors in optimizing implicit point-based representations.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

A few recent works explored incorporating geometric priors to regularize the optimization of Gaussian splatting, further improving its performance. However, those early studies mainly focused on the use of low-order geometric priors (e.g., normal vector), and they are also unreliably estimated by noise-sensitive methods, like local principal component analysis. To address their limitations, we first present GeoSplat, a general geometry-constrained optimization framework that exploits both first-order and second-order geometric quantities to improve the entire training pipeline of Gaussian splatting, including Gaussian initialization, gradient update, and densification. As an example, we initialize the scales of 3D Gaussian primitives in terms of principal curvatures, leading to a better coverage of the object surface than random initialization. Secondly, based on certain geometric structures (e.g., local manifold), we introduce efficient and noise-robust estimation methods that provide dynamic geometric priors for our framework. We conduct extensive experiments on multiple datasets for novel view synthesis, showing that our framework: GeoSplat, significantly improves the performance of Gaussian splatting and outperforms previous baselines.

Problem

• Improves Gaussian splatting with geometry constraints
• Addresses unreliable low-order geometric prior estimation
• Enhances training pipeline via robust curvature-based initialization

Innovation

• Geometry-constrained Gaussian splatting optimization framework
• Principal curvature-based Gaussian initialization method
• Noise-robust geometric priors estimation techniques