Understanding the relationship between the optimization criteria in two-view motion analysis

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 paints. 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 result is valid for both calibrated and uncalibrated images.