A UNIFIED APPROACH TO THE LINEAR CAMERA CALIBRATION-PROBLEM

The camera calibration process relates camera system measurements (pixels) to known reference points in a three-dimensional world coordinate system. In this correspondence, the calibration process is viewed as consisting of two independent phases: the first is removing geometrical camera distortion so that rectangular calibration grids are straightened in the image plane, while the second is using a linear affine transformation as a map between the rectified camera coordinates and the geometrically projected coordinates on the image plane of known reference points. Phase one is camera dependent, and in some systems may not be necessary. Phase two is concerned with a generic model that includes 12 extrinsic variables and up to 5 intrinsic parameters. The generic extrinsic variables include a rotation matrix describing the orientation of the optical axis and the displacements of the camera's focal point in the world coordinate system. The intrinsic variables correct for scale, displacement of the optical axis, and skewing of the coordinate axis in the camera coordinate system. Although there are three independent rotation angles, we treat the components of the rotation matrix as nine extrinsic parameters satisfying six constraint equations. We present general methods which handle additional constraints on the intrinsic variables in a manner consistent with explicit satisfaction of all six constraints on the orthogonal rotation matrix. We describe the use of both coplanar and noncoplanar calibration points. There are fewer equations in the coplanar case; therefore, it is necessary for the user to supply up to three additional constraint equations. © 1990 IEEE