平面单应矩阵对摄像机内参数约束的一些性质

Some Properties about the Constraints on the Camera's Intrinsic Parameters from a Homography

空间x-y坐标平面与图像平面之间的单应矩阵可以提供关于摄像机内参数的2个线性约束.文中研究表明:给定一个一般空间平面与图像平面之间的单应矩阵,如果空间平面在世界坐标系的坐标已知,则该单应矩阵同样可以提供关于摄像机内参数的2个线性约束;如果空间平面在世界坐标系的坐标未知,则该单应矩阵不能构成对摄像机内参数的任何约束.另外,仅仅知道某一个场景中的2幅图像间的单应矩阵不能对摄像机内参数构成任何约束.该结果对从事摄像机标定和三维重建的研究人员有一定的参考作用.

It has been proved in the literature that the homography from the x-y plane of the world coordinate system to the image plane can give rise two linear constraints on the camera＇s intrinsic parameters. We show in this work that given a homography from an arbitrary space plane to the image plane, if the plane＇s coordinates are known in the world system, the homography can similarly provide two linear constraints on the camera＇s intrinsic parameters. However, if the plane＇s coordinates are unknown in the world system, the homography cannot bring any constraints on the intrinsic parameters. Besides, we show that given a homography induced by an unknown space plane between two images, it cannot bring any constraints on the intrinsic parameters either. These results could be of interests or reference to those people who work in camera calibration and 3D reconstruction.