Partial Calibration and Mirror Shape Recovery for Non-Central Catadioptric Systems

In this paper we present a method for mirror shape recovery and partial calibration for non-central catadioptric systems. This method is based on an existing algorithm for calibration of general vision systems. In addition only two images are required for both mirror shape recovery and partial calibration instead of three as in the original algorithm. On the other hand the knowledge of the parameters of the primary vision system is required. In this paper collinearity is used to constrain the position of three points in each ray. Transformation matrices convert the local coordinates (known) into world coordinates or equivalently, estimate the motion of the calibration object between the two positions. The third point is defined as the intersection between the incident and reflected rays. In order for three points being collinear four tensor equations must be satisfied. These tensor equations depend on the motion parameters. Once the motion parameters are computed, the ray in space corresponding to each pixel can be estimated. Its intersection with the camera ray yields the coordinates of a mirror point. Simulations and real experiments showed that the solution is possible and accurate, although very sensitive to errors.