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.

翻译：计算机视觉领域的最新进展主要依赖于数据驱动方法，这些方法利用深度学习和大规模数据集。深度神经网络在立体匹配和单目深度重建等任务中取得了显著成功。然而，这些方法缺乏可直接分析、跨模态迁移或为受控实验系统修改的显式三维几何模型。我们研究了高斯曲率在三维表面建模中的作用。除了高斯曲率在观察者或坐标系变换下具有不变性外，我们利用Middlebury立体数据集证明，它提供了三维表面的稀疏且紧凑的描述。此外，我们发现顶尖立体视觉与单目方法的性能排名与低总绝对高斯曲率之间存在强相关性。我们提出，这一特性可作为几何先验，以改进未来的三维重建算法。