Tsais Camera Calibration Method Revisited （蔡的相机标定方法再现）.pdf

Tsai’s camera calibration method revisited Berthold K.P. Horn Copright © 2000 Introduction Basic camera calibration is the recovery of the principle distance f and the princi- ple point (x , y )T in the image plane — or, equivalently, recovery of the position 0 0 of the center of projection (x , y , f )T in the image coordinate system. This is 0 0 referred to as interior orientation in photogrammetry. A calibration target can be imaged to provide correspondences between points in the image and points in space. It is, however, generally impractical to position the calibration target accurately with respect to the camera coordinate system using only mechanical means. As a result, the relationship between the target coordinate system and the camera coordinate system typically also needs to be recovered from the correspondences. This is referred to as exterior orientation in photogrammetry. Since cameras often have appreciable geometric distortions, camera calibra- tion is often taken to include the recovery of power series coefficients of these distortions. Furthermore, an unknown scale factor in image sampling may also need to be recovered, because scan lines are typically resampled in the frame grabber, and so picture cells do not correspond discrete sensing elements. Note that in camera calibration we are trying to recover the transforma- tions, based on measurements of coordinates, where one more often uses known transformation to map coordinates from one coordinate system to another. Tsai’s method for camera calibration recovers the interior orientation, the exterior orientation, the power series coefficients for distortion, and an image scale factor that best fit the measured image coordinates corresponding to known target point coordinates. This is done in stages, startin