相机标定中畸变圆锥曲线的无偏估计器
Unbiased Estimator for Distorted Conics in Camera Calibration
AI总结：
针对畸变导致圆锥曲线属性丧失、限制其在相机标定中应用的问题，提出基于一阶矩无偏估计的圆锥曲线标定方法，可亚像素检测圆形图案，显著提升标定精度，代码已开源。
摘要：
在现有文献中，点和圆锥曲线一直是相机几何标定的主要特征。尽管圆锥曲线比点特征包含更多信息，但畸变下圆锥曲线属性的丧失严重限制了圆锥曲线特征在相机标定中的应用。许多现有方法要么忽略畸变，要么引入3D球形靶标来规避这一局限，以此实现基于圆锥曲线的标定。本文提出了一种基于矩的圆锥曲线标定新公式。我们的推导基于一项数学发现：即使存在畸变，一阶矩也可以被无偏估计。这使得我们能够追踪投影和畸变过程中的矩变化，确保畸变圆锥曲线的一阶矩得以保留。借助无偏估计器，圆形图案可以在亚像素级别被精确检测，如今可在完整标定流程中得到充分利用，从而显著提升标定效果。完整代码可从https://github.com/ChaehyeonSong/discocal 获取。
英文摘要：
In the literature, points and conics have been major features for camera geometric calibration. Although conics are more informative features than points, the loss of the conic property under distortion has critically limited the utility of conic features in camera calibration. Many existing approaches addressed conic-based calibration by ignoring distortion or introducing 3D spherical targets to circumvent this limitation. In this paper, we present a novel formulation for conic-based calibration using moments. Our derivation is based on the mathematical finding that the first moment can be estimated without bias even under distortion. This allows us to track moment changes during projection and distortion, ensuring the preservation of the first moment of the distorted conic. With an unbiased estimator, the circular patterns can be accurately detected at the sub-pixel level and can now be fully exploited for an entire calibration pipeline, resulting in significantly improved calibration. The entire code is readily available from https://github.com/ChaehyeonSong/discocal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
