Geometric calibration of digital cameras through multi-view rectification

This paper introduces a new and very effective method for high-precision geometric calibration of digital cameras. The internal and external geometry are estimated: (1) by extracting features with subpixel accuracy from various views of a planar calibration plate; and (2) by mapping these feature sets into the corresponding points of the undistorted and rectified image that would be generated by an ideal pinhole digital camera with the same focal length as the camera to calibrate but devoid of lens distortion and perspective warp. The rectification of the views is formulated as a nonlinear least-squares optimization problem where a quadratic cost function expressing the residual registration error has to be minimized. The views are first prealigned with the reference image by means of a simplified mathematical model. This initialization, together with the closed-form computation of the gradient of the cost function, allows the Levenberg-Marquardt algorithm employed to find its minimum to rapidly converge to the optimal solution. The performance of the new calibration algorithm is tested with a set of real images available on the Internet and discussed in the paper. Also, its accuracy is assessed by means of synthetic versions of the actual images generated with the estimated parameters.