在计算机视觉中单应性矩阵的求解在摄像机标定的过程中有重要的意义,单应性矩阵中包含着摄像机的内参数矩阵,旋转向量和平移向量。
我们设3维空间有一点Q=[X Y Z 1]T(齐次坐标系表示),到成像仪上的q[x y 1]T映射,设单应性矩阵为H,s为比例系数。则Q和q之间的关系可表示为q=ShQ.
在点映射过程中,点要经过旋转和平移的物理变换,所以设物理变换坐标W=[R T],R为旋转向量,T为平移向量。然后再投射过程中,根据得到的摄像机的内参矩阵M,所以q=sMWQ,从而推算出
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