Quadratic Gaussian Splatting for Efficient and Detailed Surface Reconstruction (2411.16392v1)

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.

• The paper introduces QGS, a method that leverages quadric surfaces for second-order approximation to enhance the accuracy of 3D surface reconstruction.
• It employs geodesic distances to localize Gaussian distributions, thereby achieving high-fidelity texture capture and improved depth consistency.
• Experimental results on DTU and Tanks and Temples datasets validate QGS's superior performance in generating detailed and robust 3D mesh models.

Quadratic Gaussian Splatting for Efficient and Detailed Surface Reconstruction

The paper "Quadratic Gaussian Splatting for Efficient and Detailed Surface Reconstruction" presents a novel approach aimed at improving the surface reconstruction and novel view synthesis capabilities of Gaussian splatting methods. Introduction of Quadratic Gaussian Splatting (QGS) represents a significant technical advance in terms of geometric fitting capability when reconstructing 3D scenes from multi-view RGB images.

Overview

Surface reconstruction from multi-view images is a crucial area in computer graphics and vision, primarily associated with recovering dense geometric structures and generating photorealistic views. Traditional methods like Neural Radiance Fields (NeRF) have been surpassed in recent times by Gaussian Splatting (GS) techniques, particularly 3D Gaussian Splatting (3DGS) due to its enhanced rendering speed and quality. However, limitations in accurate surface representation led to the development of 2D Gaussian Splatting (2DGS), which models scenes using disk primitives for more consistent geometry across multiple views. 2DGS, however, can result in over-smoothed geometry due to its first-order approximation of scene surfaces.

QGS addresses these limitations by replacing disk-based primitives in 2DGS with quadric surfaces, enabling second-order surface approximation. This methodological shift allows QGS to achieve finer geometric fitting and extract accurate surface meshes comprising complex textures. QGS operates in a non-Euclidean space, focusing on quadric paraboloids that encompass both convex and concave forms, providing more flexibility in geometric fitting than linear approximations.

Key Contributions

1. Second-order Surface Approximation: By defining Gaussian distributions on quadric surfaces, QGS effectively improves the fitting of scene primitives. It accurately captures spatial curvature, allowing for the rendering of detailed multi-view consistent normals and depth, mitigating the over-smoothing issues seen in previous disk-like models.
2. Application of Geodesic Distances: QGS introduces the innovative use of geodesic distances to define Gaussian distributions, thus localizing the primitive's energy on the surface for higher-fidelity texture capture.
3. Enhanced Geometric Reconstruction: Experimental verification on DTU and Tanks and Temples (TNT) datasets demonstrates QGS's superior performance compared to state-of-the-art reconstruction methods, providing precise and detail-rich mesh models.
4. Refined Depth Sorting: Adoption of improved sorting criteria from existing volumetric approaches eliminates popping artifacts in novel view synthesis and geometric reconstructions, specifically enhancing the QGS method's handling of complex intersections of quadratic surfaces.

Implications and Future Directions

The introduction of quadric surfaces in Gaussian splatting methodologies opens avenues for developing more precise 3D scene reconstructions. This advancement holds implications for applications requiring high-detail fidelity, such as virtual reality and complex scene visualization. The development also speculates on the potential for future exploration in integrating multi-view geometric techniques to further sharpen the precision of QGS.

In terms of practical implications, the capabilities of QGS in generating detailed geometric reconstructions could enhance various fields that rely on accurate 3D modeling, such as digital heritage preservation, architectural visualization, and autonomous navigation systems embedded in robotics. The theoretical exploration in geometric fitting and Gaussian distribution offers a foundation for extending this approach to various domains, potentially addressing more complex challenges within computer vision.

Overall, Quadratic Gaussian Splatting enriches surface reconstruction methodologies not by an overhauling paradigm shift but by introducing nuanced changes that significantly improve upon the granularity and accuracy achievable with existing Gaussian splatting methods. As this technique undergoes further refinement and integration within diverse applications, it can serve as a cornerstone for more comprehensive reconstructions and renderings of real-world geometric scenarios.