Calibration of radially symmetric distortion based on linearity in the calibrated image

For calibration of general radially symmetric distortion of omnidirectional cameras such as fish-eye lenses, calibration parameters are usually estimated so that curved lines, which are supposed to be straight in the real-world, are mapped to straight lines in the calibrated image, which is called plumbline principle. Under the principle, the camera with radially symmetric distortion can be calibrated by at least one distorted line in a image, theoretically, and the calibrated image is equivalent to the image taken by an ideal pin-hole camera. In this paper, the method to optimize the calibration parameters by maximizing the sum of the straightness, which is invariant under translation, rotation and magnification (scaling), of distorted lines on calibrated image is proposed. The performance of the proposed method is evaluated by artificial data and a real image.