用最优传输方法解决稀疏立体匹配难题，无需标注数据。
HOT-POT: Optimal Transport for Sparse Stereo Matching
- 从最优传输视角建模相机几何约束，将特征点匹配转为可解分配问题。
- 引入视差与3D射线距离作为代价函数，在人脸分析中实现高精度匹配。
- 适用于无监督场景，尤其适合不同地标定义间的人脸特征对齐。
图像间的立体视觉面临遮挡、运动和相机畸变等挑战，广泛应用于自动驾驶、机器人和人脸识别。由于参数敏感性，稀疏特征（如面部关键点）的立体匹配更加困难。为克服这一不适定问题并实现无监督稀疏匹配，本文从最优传输（OT）角度出发，利用相机几何的直线约束，将投影点视为（半）直线，提出以经典对极距离和3D射线距离作为匹配质量的度量。将这些距离作为（部分）OT问题的代价函数，得到可高效求解的分配问题。此外，通过层次化OT模型扩展至无监督目标匹配。实验表明，该算法在数值上实现了高效的特征与物体匹配，重点应用于人脸识别领域，旨在对齐不同的地标标注规范。
原文摘要 · Abstract (English)
Stereo vision between images faces a range of challenges, including occlusions, motion, and camera distortions, across applications in autonomous driving, robotics, and face analysis. Due to parameter sensitivity, further complications arise for stereo matching with sparse features, such as facial landmarks. To overcome this ill-posedness and enable unsupervised sparse matching, we consider line constraints of the camera geometry from an optimal transport (OT) viewpoint. Formulating camera-projected points as (half)lines, we propose the use of the classical epipolar distance as well as a 3D ray distance to quantify matching quality. Employing these distances as a cost function of a (partial) OT problem, we arrive at efficiently solvable assignment problems. Moreover, we extend our approach to unsupervised object matching by formulating it as a hierarchical OT problem. The resulting algorithms allow for efficient feature and object matching, as demonstrated in our numerical experiments. Here, we focus on applications in facial analysis, where we aim to match distinct landmarking conventions.
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