摘要:
用代数方法系统地讨论了多平面多视点下单应矩阵间的约束关系.主要结论有(A)如
果视点间摄像机的运动为纯平移运动,则1)对于所有平面关于两视点间的单应矩阵的集合,或
单个平面关于所有视点的单应矩阵的集合的秩均等于4,2)对于多平面多视点的标准单应矩阵
的集合其秩仍等于4,3)根据以上结论可推出现有文献中关于"相对单应矩阵"约束的所有结
果;(B)如果视点间摄像机的运动为一般运动,则1)对于所有平面关于两个视点间的单应矩阵
集合的秩等于4的结论仍成立,2)对于其它情况其秩不再等于4而是等于9.
Abstract:
Homography estimation is widely used for 3D motion analysis, mosaicing,
camera calibration and more. This paper is concentrated on the investigation on multiview
and multi-plane constraints on homographies. The main results are: A. when
the camera is under a pure translation, then, 1) both the homographies of all planes
between two view points, and the homographies of a plane for all view points are of
rank 4, 2) the standard homographies in multi view and multi-plane case are still of
rank 4, 3) the above two results keep true for the relative homographies in the case of
general camera motion; B. when the camera is under a general motion, 1) the homographies
of all planes between two view points are also of rank 4, 2) however, the
rank should be 9 rather than 4 in other cases.
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