Robust estimation of camera location and orientation from noisy data having outliers

A solution and mathematical analysis are described for the problem of estimating camera location and orientation from a set of recognized landmarks (3D lines) appearing in the image under perspective projection. Given correspondences between these 3D lines and 2D lines found in the image, the goal is to find rotation (R) and transition (T) which map a world coordinate system to the camera coordinate system. Three algorithms are developed: R-then-T, R-and-T, and Med-R-and-T. Algorithms R-then-T and R-and-T are least square algorithms. Algorithm R-then-T solves for rotation first and uses the result to solve for translation. The second algorithm R-and-T solves for both rotation and translation simultaneously. The results from the second algorithm are much better. Some of the correspondences may be wrong. Algorithm Med-R-and-T can handle up to 49.9% outliers or gross errors in the date. It minimizes the median of the square of the same error measure used by the R-and-T algorithm. A closed-form expression function is developed for the uncertainty in the output parameters as a function of the variance of the noise in the input parameters