%0 Journal Article
%T The Number of Independent Kruppa Constraints from N Images
%A Zhan-Yi Hu
%A Yi-Hong Wu
%A Fu-Chao Wu
%A Song-De Ma
%A <br>Zhan-Yi Hu
%A Yi-Hong Wu
%A Fu-Chao Wu
%A and Song-De Ma
%J 计算机科学技术学报
%D 2006
%I 
%X 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.
%K camera calibration
%K imaging geometry
%K stereo<br>照相机
%K 技术标准
%K 成像技术
%K 几何图象
%K 动态图象
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=F57FEF5FAEE544283F43708D560ABF1B&aid=E09C6CC1428A40445A20C2C9C160A836&yid=37904DC365DD7266&vid=659D3B06EBF534A7&iid=0B39A22176CE99FB&sid=79D2EF35F60110C2&eid=F9F74EC1AA08A7B9&journal_id=1000-9000&journal_name=计算机科学技术学报&referenced_num=0&reference_num=11