A theory of self-calibration of a moving camera

There is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement. The epipolar transformation imposes two algebraic constraints on the camera calibration. If two epipolar transformations, arising from different camera displacements, are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four. The curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces, or by a curve of degree six in the dual of the image plane. The curve in the dual plane has one singular point of order three and three singular points of order two.If three epipolar transformations are available, then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration. The two curves have a common singular point of order three.Experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation. The real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0, 2]. The intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations.