Quadratic Gaussian Splatting for Efficient and Detailed Surface Reconstruction

2024-11-25

arXiv.org

AI Summary

To address the weak geometric expressiveness of 3D Gaussian splatting and the density-geometry inconsistency arising from Euclidean distance modeling, this paper proposes Quadratic Gaussian Splatting (QGS). QGS replaces conventional disk-shaped primitives with deformable quadric surfaces (e.g., ellipsoids, paraboloids) as scene primitives, enabling high-fidelity geometric fitting and curvature-aware modeling. It defines Gaussian distributions on surface embeddings within a non-Euclidean space to enhance texture representation, and introduces a curvature-guided normal consistency constraint to suppress over-smoothing. The method integrates quadric surface parameterization, non-Euclidean Gaussian modeling, curvature-aware optimization, and joint geometry-appearance training. Extensive experiments on DTU and TNT benchmarks demonstrate significant improvements over state-of-the-art methods, yielding reconstructions with finer geometric detail and more consistent surface normals. The source code will be made publicly available.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Recently, 3D Gaussian Splatting (3DGS) has attracted attention for its superior rendering quality and speed over Neural Radiance Fields (NeRF). To address 3DGS's limitations in surface representation, 2D Gaussian Splatting (2DGS) introduced disks as scene primitives to model and reconstruct geometries from multi-view images, offering view-consistent geometry. However, the disk's first-order linear approximation often leads to over-smoothed results. We propose Quadratic Gaussian Splatting (QGS), a novel method that replaces disks with quadric surfaces, enhancing geometric fitting, whose code will be open-sourced. QGS defines Gaussian distributions in non-Euclidean space, allowing primitives to capture more complex textures. As a second-order surface approximation, QGS also renders spatial curvature to guide the normal consistency term, to effectively reduce over-smoothing. Moreover, QGS is a generalized version of 2DGS that achieves more accurate and detailed reconstructions, as verified by experiments on DTU and TNT, demonstrating its effectiveness in surpassing current state-of-the-art methods in geometry reconstruction. Our code willbe released as open source.

Problem

• Improves surface reconstruction using deformable quadric surfaces
• Introduces geodesic distance-based density for consistent shape changes
• Reduces memory usage while maintaining high rendering efficiency

Innovation

• Deformable quadric surfaces replace static primitives
• Geodesic distance-based density ensures curvature adaptation
• Fast ray-quadric intersection enables efficient rendering