1D camera geometry and Its application to circular motion estimation

Abstract

This paper describes a new and robust method for estimating circular motion geometry from an uncalibrated image sequence. Under circular motion, all the camera centers lie on a circle, and the mapping of the plane containing this circle to the horizon line in the image can be modelled as a 1D projection. A 2×2 homography is introduced in this paper to relate the projections of the camera centers in two 1D views. It is shown that the two imaged circular points and the rotation angle between the two views can be derived directly from the eigenvectors and eigenvalues of such a homography respectively. The proposed 1D geometry can be nicely applied to circular motion estimation using either point correspondences or silhouettes. The method introduced here is intrinsically a multiple view approach as all the sequence geometry embedded in the epipoles is exploited in the computation of the homography for a view pair. This results in a robust method which gives accurate estimated rotation angles and imaged circular points. Experimental results are presented to demonstrate the simplicity and applicability of the new method.