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 fu...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 N 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.展开更多
基金Regular Paper This work was supported by the National Natural Science Foundation of China under Grant No. 60121302 and No. 60303021.
文摘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 N 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.
