Extracting physical camera parameters from the 3x3 direct linear transformation matrix

摘要

Abstract: The projective transformation of 3D object points to 2D image points can be expressed in homogeneous coordinates by the 3 by 4 direct linear transformation (DLT) matrix. If the object points are coplanar, the transformation can be expressed by the 3 by 3 DLT matrix. This article presents non-iterative, fast and exact methods for extracting the physical camera parameters from the 3 by 3 matrix. Three parameters must be known or estimated in order to extract the remaining eight. The decomposition problem is solved under three different assumptions about known parameters. All three methods are based on solving two quadratic equations in two unknowns. The equations originate from the orthogonality constraints on the first two columns of the rotation matrix. The methods are well suited for finding initial values in point based camera calibration. They solve the coplanar perspective-n-point problem for any n $GREQ 4. !12