A Variational Approach to Problems in Calibration of Multiple Cameras

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Abstract
This paper addresses the problem of calibrating camera parameters using variational methods. One problem addressed is the severe lens distortion in low-cost cameras. For many computer vision algorithms aiming at reconstructing reliable representations of 3D scenes, the camera distortion effects will 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 that result in different color measurements and affects the algorithms that depend on these measurements. We also address the extrinsic camera calibration that estimates relative poses and orientations of multiple cameras in the system and the intrinsic camera calibration that estimates focal lengths and the skew parameters of the cameras. To address these calibration problems, we present multiview stereo techniques based on variational methods that utilize partial and ordinary differential equations. Our approach can also be considered as a coordinated refinement of camera calibration parameters. To reduce computational complexity of such algorithms, we utilize prior knowledge on the calibration object, making a piecewise smooth surface assumption, and evolve the pose, orientation, and scale parameters of such a 3D model object without requiring a 2D feature extraction from camera views. We derive the evolution equations for the distortion coefficients, the color calibration parameters, the extrinsic and intrinsic parameters of the cameras, and present experimental results.

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