In this study, we present a complete camera calibration algorithm for the solution of all extrinsic and intrinsic param~etersf or both noncoplanar and coplanar distribution of object points. The complete algorithm consists of: (a) new methods of computing image center and scale factor parameters inclluding the coplanar case, (b) compllete lens distortion algorithms with general radial and first order tangential distortion models, and (c) computation of calibration parameters within necessary constraints such as orthonormality of the camera vectors. In addition, we demonstrate the effectiveness of higher order models and of higher iterations of the lens distortional gorithms. For accuate calibration, all extrinsic parameters are updated every time the lens distortion pmneters are computed. A unique feature of all our algorithms is that parameters are solved efficiently by linear equations only. Whenever iterative methods are applied, complete proofs of convergence are provided and corroborated experimentally. Furthermore, we demonstrate analytically ttie robustness of the least squares estimates of extrinsic parameters by showing that image and world coordinate computation are insensitive to the image center and scale factor parameters if the camera is calibrated with uncompensated (not corrected for itrlage center and scale factor) image data (ignoring lens distortion). A unique formalism for error analysis is considered to study the sensitivity of the computed image and world coordinates under constant and random noise. Extensive experiments on a coplanar set of calibration points are conducted to support our analyses.

Date of this Version

November 1993