Calibration routine for a telecentric stereo vision system considering affine mirror ambiguity

Abstract

A robust calibration approach for a telecentric stereo camera system for three-dimensional (3-D) surface measurements is presented, considering the effect of affine mirror ambiguity. By optimizing the parameters of a rigid body transformation between two marker planes and transforming the two-dimensional (2-D) data into one coordinate frame, a 3-D calibration object is obtained, avoiding high manufacturing costs. Based on the recent contributions in the literature, the calibration routine consists of an initial parameter estimation by affine reconstruction to provide good start values for a subsequent nonlinear stereo refinement based on a Levenberg–Marquardt optimization. To this end, the coordinates of the calibration target are reconstructed in 3-D using the Tomasi–Kanade factorization algorithm for affine cameras with Euclidean upgrade. The reconstructed result is not properly scaled and not unique due to affine ambiguity. In order to correct the erroneous scaling, the similarity transformation between one of the 2-D calibration plane points and the corresponding 3-D points is estimated. The resulting scaling factor is used to rescale the 3-D point data, which then allows in combination with the 2-D calibration plane data for a determination of the start values for the subsequent nonlinear stereo refinement. As the rigid body transformation between the 2-D calibration planes is also obtained, a possible affine mirror ambiguity in the affine reconstruction result can be robustly corrected. The calibration routine is validated by an experimental calibration and various plausibility tests. Due to the usage of a calibration object with metric information, the determined camera projection matrices allow for a triangulation of correctly scaled metric 3-D points without the need for an individual camera magnification determination.