Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
Understanding the Behavior of SFM Algorithms: A Geometric Approach
International Journal of Computer Vision
Exact Two-Image Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
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The three best known criteria in two-view motion analysis are based, respectively, on the distances between points and their corresponding epipolar lines, on the gradient-weighted epipolar errors, and on the distances between points and the reprojections of their reconstructed points. The last one has a better statistical interpretation, but is, however, much slower than the first two. In this paper, we show that the last two criteria are equivalent when the epipoles are at infinity, and differ from each other only a little even when the epipoles are in the image. The first two criteria are equivalent only when the epipoles are at infinity and when the observed object has the same scale in the two images. This suggests that the second criterion is sufficient in practice because of its computational efficiency. The resultis valid for both calibrated and uncalibrated images.