Unbiased Estimator for Distorted Conics in Camera Calibration
This addresses a critical limitation in camera calibration for computer vision applications, enabling full exploitation of conic features without needing 3D targets, though it is incremental as it builds on existing conic-based methods.
The paper tackles the problem of using conic features for camera calibration despite distortion, by introducing an unbiased estimator based on moments that preserves the first moment under distortion, leading to significantly improved calibration with accurate sub-pixel detection of circular patterns.
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.