Geometry-Grounded Gaussian Splatting

2026-01-25

AI Summary

This work addresses the limitations of existing Gaussian splatting methods, which often suffer from multi-view inconsistencies and floating-point artifacts that hinder high-quality geometric reconstruction. To overcome these issues, the paper introduces a novel approach that rigorously models Gaussian primitives as stochastic entities and leverages their volumetric properties to construct an explicit geometric representation. This formulation enables high-fidelity depth map rendering and accurate extraction of fine-scale geometry. By establishing a geometrically interpretable theoretical foundation for Gaussian splatting and integrating multi-view geometric optimization, the proposed method achieves state-of-the-art performance in shape reconstruction accuracy and consistency, significantly outperforming existing approaches on public benchmarks.

Technology Category

• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation, existing shape reconstruction methods suffer from poor multi-view consistency and are sensitive to floaters. In this paper, we present a rigorous theoretical derivation that establishes Gaussian primitives as a specific type of stochastic solids. This theoretical framework provides a principled foundation for Geometry-Grounded Gaussian Splatting by enabling the direct treatment of Gaussian primitives as explicit geometric representations. Using the volumetric nature of stochastic solids, our method efficiently renders high-quality depth maps for fine-grained geometry extraction. Experiments show that our method achieves the best shape reconstruction results among all Gaussian Splatting-based methods on public datasets.

Problem

• Gaussian Splatting
• shape extraction
• geometry reconstruction
• multi-view consistency
• floaters

Innovation

• Gaussian Splatting
• stochastic solids
• geometry reconstruction
• depth rendering
• novel view synthesis