Abstract It is well known that without any priori knowledge on the scene, camera motion and camera intrinsic parameters; the only constraint between a pair of images is the so-called epipolar constraint, or equivalently its fundamental matrix. For each fundamental matrix, at most two independent constraints on the cameras' intrinsic parameters are available via the Kruppa equations. Given N images, N(N - 1)/2 fundamental matrices appear, and N(N - 1) Kruppa constraints are available. However, to our knowledge, a formal proof of how many independent Kruppa constraints exist out of these N(N - 1) ones is unavailable in the literature. In this paper, we prove that given AT images captured by a pinhole camera with varying parameters and under general motion, the number of independent Kruppa constraints is (5N - 9) (N > 2), and it is less than that of independent constraints from the absolute quadric by only one. This one-constraint-less property of the Kruppa equations is their inherent deficiency and is independent of camera motion. This deficiency is due to their failure of automatic enforcement of the rank-three-ness on the absolute quadric.
GB/T 7714 Hu, ZY,Wu, YH,Wu, FC,et al. The number of independent Kruppa constraints from N images[J]. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY,2006,21(2):209-217.
APA Hu, ZY,Wu, YH,Wu, FC,&De Ma, S.(2006).The number of independent Kruppa constraints from N images.JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY,21(2),209-217.
MLA Hu, ZY,et al."The number of independent Kruppa constraints from N images".JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY 21.2(2006):209-217.