A NONLINEAR GAUSS-SEIDEL ALGORITHM FOR NONCOPLANAR AND COPLANAR CAMERA CALIBRATION WITH CONVERGENCE ANALYSIS

In this study, we discuss the nonlinear structure of the camera calibr ation problem and present new and provably convergent algorithms for n oncoplanar and coplanar cases. From the perspective of optimization th eory, we have included the following features in solving this nonlinea r problem: (1) An initialization algorithm that computes an approximat e solution as a starting value close to the global minimum. (2) A main estimation method that partitions the parameter space and uses a Gaus s-Seidel optimization procedure for block components, For the noncopla nar case, the extrinsic and lens distortion parameters are computed by linear iterations or in closed form in each iteration, Nonlinear opti mization is performed on a reduced parameter space of dimension three. For the coplanar case, the lens distortion parameters are computed by linear iterations. In both cases, the orthonormality condition of the camera vectors is satisfied. Thus, while performing nonlinear optimiz ation over all parameters, we still retain many advantages of the line ar methods, and in the process obtain an optimal solution. (3) A Lyapu nov type convergence analysis is given for the algorithms. The structu re of the objective function is analyzed in each iteration. In additio n, for the coplanar case, we discuss new methods for obtaining startin g estimates of image center and scale factor parameters. Furthermore, we consider lens distortion with radial, decentering, and thin prism d istortion models. (C) 1997 Academic Press.