On the optimization criteria used 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 points. The last one has a better statistical interpretation, but is, however, significantly slower than the first two. In this paper, I show that, given a reasonable initial guess of the epipolar geometry, 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, as shown experimentally. The first two criteria are equivalent only when the epipoles are at infinity and when the observed object/scene has the same scale in the two images. This suggests that the second criterion is sufficient in practice because of its computational efficiency. Experiments with several thousand computer simulations and four sets of real data confirm the analysis. The result is valid for both calibrated and uncalibrated images. Index Terms - Motion analysis, multiple-view geometry, 3D reconstruction, optimization criteria, algorithmic comparison, structure from motion, uncalibrated images.