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SGCR: Spherical Gaussians for Efficient 3D Curve Reconstruction

Xinran Yang, Donghao Ji, Yuanqi Li, Jie Guo, Yanwen Guo, Junyuan Xie

TL;DR

SGCR introduces Spherical Gaussians to represent 3D edges with a geometry-first bias, learned from multi-view 2D edge maps. A two-stage pipeline first builds SGs via a view-based edge rendering loss and then extracts 3D parametric curves through SGCR's line fitting and global optimization into rational Bézier curves. Experiments across ABC-NEF, ModelNet, DTU, and Replica demonstrate state-of-the-art accuracy and notable efficiency gains in 3D edge reconstruction, outperforming methods that rely on dense 3D supervision or lengthy training. This work tightly couples 2D cues with explicit 3D curve representations, enabling robust, efficient 3D edge reconstruction from 2D supervision.

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.

SGCR: Spherical Gaussians for Efficient 3D Curve Reconstruction

TL;DR

SGCR introduces Spherical Gaussians to represent 3D edges with a geometry-first bias, learned from multi-view 2D edge maps. A two-stage pipeline first builds SGs via a view-based edge rendering loss and then extracts 3D parametric curves through SGCR's line fitting and global optimization into rational Bézier curves. Experiments across ABC-NEF, ModelNet, DTU, and Replica demonstrate state-of-the-art accuracy and notable efficiency gains in 3D edge reconstruction, outperforming methods that rely on dense 3D supervision or lengthy training. This work tightly couples 2D cues with explicit 3D curve representations, enabling robust, efficient 3D edge reconstruction from 2D supervision.

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.
Paper Structure (19 sections, 11 equations, 9 figures, 3 tables, 1 algorithm)

This paper contains 19 sections, 11 equations, 9 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Image-based 3D Representation and Rendering
  4. 3D Curve Reconstruction
  5. Method
  6. Preliminary
  7. Spherical Gaussians Generation
  8. Initialization
  9. Training Losses
  10. Training Strategy
  11. Parametric Curve Extraction from Spherical Gaussians
  12. Line Fitting
  13. Global Optimization
  14. Experiments
  15. Dataset
  16. ...and 4 more sections

Figures (9)

  • Figure 1: Visualization for optimized Gaussians. (a) Gaussians from original 3D Gaussian Splatting. (b) Our Spherical Gaussians.
  • Figure 2: Illustration for fitting Bézier curve from Spherical Gaussians. $P_1$, $P_2$, $P_3$ and $P_4$ are weighted control points of the curve.
  • Figure 3: Pipeline illustration across 2D and 3D modality. Stage1: Spherical Gaussians generation. Stage2: Parametric curves extraction.
  • Figure 4: The change on number of Gaussians during training.
  • Figure 5: Qualitative comparisons. The first two objects come from ABC-NEF dataset and the last one comes from ModelNet dataset. Ours(SG) refers to our generated Spherical Gaussian in the first stage, GT refers to the ground-truth edge.
  • ...and 4 more figures