Lie algebra approach for tracking and 3D motion estimation using monocular vision

The main purpose of this paper is to estimate 2D and 3D transformation parameters. All the group transformations are represented in terms of their Lie algebra elements. The Lie algebra approach assures to follow the shortest path or geodesic in the involved Lie group. For the estimation of the Lie algebra parameters, we take advantage of the theory of system identification. Two experiments are presented to show the potential of the method. First, we carry out the estimation of the affine or projective parameters related to the transformation involved in monocular region tracking. Second, we develop a monocular method to estimate 3D motion of an object in the visual space. In the latter, the six parameters of the rigid motion are estimated based on measurements of the six parameters of the affine transformation in the image.