Sphere-based calibration method for trinocular vision sensor

A new method to calibrate a trinocular vision sensor is proposed and two main tasks are finished in this paper, i.e. to determine the transformation matrix between each two cameras and the trifocal tensor of the trinocular vision sensor. A flexible sphere target with several spherical circles is designed. As the isotropy of a sphere, trifocal tensor of the three cameras can be determined exactly from the feature on the sphere target. Then the fundamental matrix between each two cameras can be obtained. Easily, compatible rotation matrix and translation matrix can be deduced base on the singular value decomposition of the fundamental matrix. In our proposed calibration method, image points are not requested one-to-one correspondence. When image points locates in the same feature are obtained, the transformation matrix between each two cameras with the trifocal tensor of trinocular vision sensor can be determined. Experiment results show that the proposed calibration method can obtain precise results, including measurement and matching results. The root mean square error of distance is 0.026 mm with regard to the view field of about 200×200 mm and the feature matching of three images is strict. As a sphere projection is not concerned with its orientation, the calibration method is robust and with an easy operation. Moreover, our calibration method also provides a new approach to obtain the trifocal tensor.