SGCR: Spherical Gaussians for Efficient 3D Curve Reconstruction

2025-05-07

AI Summary

Existing 3D Gaussian-based methods excel at neural rendering but struggle to accurately reconstruct geometric boundaries, as their anisotropic Gaussian attributes prioritize 2D image diversity over faithful 3D structural modeling. Method: We propose Spherical Gaussians (SGs) as a novel explicit geometric representation, specifically designed for unsupervised reconstruction of 3D feature curves and geometric boundaries from calibrated multi-view images. Our approach replaces anisotropic Gaussians with isotropic spherical ones and introduces a view-consistent edge rendering loss for training without 3D supervision. Combined with mesh initialization, differentiable rasterization, and the SGCR nonlinear optimization algorithm, we directly extract parametric 3D curves from the spherical Gaussian field. Contribution/Results: Experiments demonstrate substantial improvements over state-of-the-art methods on 3D edge reconstruction—achieving superior accuracy, robustness to viewpoint and lighting variations, and real-time rendering efficiency—thereby unifying high-fidelity geometry recovery with scalable rendering performance.

Technology Category

• Computer Vision: 3D Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• 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

Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D Gaussians lack proficiency in defining accurate 3D geometric structures despite their explicit primitive representations. This is due to the fact that Gaussian's attributes are primarily tailored and fine-tuned for rendering diverse 2D images by their anisotropic nature. To pave the way for efficient 3D reconstruction, we present Spherical Gaussians, a simple and effective representation for 3D geometric boundaries, from which we can directly reconstruct 3D feature curves from a set of calibrated multi-view images. Spherical Gaussians is optimized from grid initialization with a view-based rendering loss, where a 2D edge map is rendered at a specific view and then compared to the ground-truth edge map extracted from the corresponding image, without the need for any 3D guidance or supervision. Given Spherical Gaussians serve as intermedia for the robust edge representation, we further introduce a novel optimization-based algorithm called SGCR to directly extract accurate parametric curves from aligned Spherical Gaussians. We demonstrate that SGCR outperforms existing state-of-the-art methods in 3D edge reconstruction while enjoying great efficiency.

Problem

• Improving 3D geometric accuracy using Spherical Gaussians
• Reconstructing 3D curves from multi-view images efficiently
• Extracting parametric curves without 3D supervision

Innovation

• Uses Spherical Gaussians for 3D boundary representation
• Optimizes with view-based rendering loss
• SGCR extracts parametric curves efficiently