高斯曲率可作3D重建的几何先验，提升算法性能
Towards Understanding 3D Vision: the Role of Gaussian Curvature
- 用高斯曲率描述3D表面，具有坐标不变性且表达紧凑
- 实验显示顶尖立体匹配方法性能与低总绝对曲率正相关
- 为未来3D重建提供可分析、可迁移的几何先验
计算机视觉近年依赖数据驱动方法，虽在立体匹配和单目深度重建上取得显著成果，但缺乏可直接分析、跨模态迁移或系统修改的显式3D几何模型。本文研究高斯曲率在3D表面建模中的作用。由于其在坐标变换下保持不变，我们利用Middlebury立体数据集证明其能以稀疏紧凑的方式描述3D表面。进一步发现，当前顶级立体与单目方法的性能排名与低总绝对高斯曲率强相关。结果表明该性质可作为几何先验，用于改进未来的3D重建算法。
原文摘要 · Abstract (English)
Recent advances in computer vision have predominantly relied on data-driven approaches that leverage deep learning and large-scale datasets. Deep neural networks have achieved remarkable success in tasks such as stereo matching and monocular depth reconstruction. However, these methods lack explicit models of 3D geometry that can be directly analyzed, transferred across modalities, or systematically modified for controlled experimentation. We investigate the role of Gaussian curvature in 3D surface modeling. Besides Gaussian curvature being an invariant quantity under change of observers or coordinate systems, we demonstrate using the Middlebury stereo dataset that it offers a sparse and compact description of 3D surfaces. Furthermore, we show a strong correlation between the performance rank of top state-of-the-art stereo and monocular methods and the low total absolute Gaussian curvature. We propose that this property can serve as a geometric prior to improve future 3D reconstruction algorithms.
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