A variational approach to problems in calibration of multiple cameras

This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed in this paper is the severe lens distortion in wide angle/inexpensive camera lenses. The camera distortion effects lead to inaccurate 3D reconstructions and geometrical measurements if not accounted for. A second problem is the color calibration problem caused by variations in camera responses which results in different color measurements and affects the algorithms that depend on these measurements. We present multi-view stereo techniques based on variational ideas to address these calibration problems. To reduce computational complexity of such algorithms, we utilize a prior knowledge on the calibration object which is used in the process, and evolve the pose, orientation, and scale parameters of such a 3D model object. We derive the evolution equations for the distortion coefficients, the color calibration parameters of the cameras, and present experimental results which demonstrate their potential use.