Three-dimensional trajectory estimation from image position and velocity

Recovering the 3-D motion and structure of a rigid object from image sequences is a fundamental in applications such as target recognition, issance, vision-based servoing, and computer . The main approaches to 3-D trajectory estimation have usually exploited either point features [2] or optical flow [3] independently. In feature-based approaches, 3-D motion and structure are estimated by observing the 2-D positions of a set of relatively sparse set of image features (corners, lines, regions, etc.) over two or more time-sequential images. In contrast, optical-flow-based techniques estimate instantaneous 3-D motion from dense image plane velocity data. Feature-based estimation can be subdivided into recursive [ l , 4, 51 and batch [6, 71 formulations. This paper focuses on recursive estimation, which is better suited for on-line applications. In [l] , a nonlinear dynamical system is formulated, and linearized using an iterated extended Kalman filter (IEKF). Wu, et al. [8] adopt a similar approach, except assume a priori knowledge about object structure, i.e., the configuration of the feature points within an object-centered system, resulting in a simplified measurement function compared with [l]. The formulation in [4] is also simpler than in [l], except it assumed that the center of rotation is always visible, which appears difficult in practice to achieve. Silvkn and Rep0 [9] have recently developed an integrated monocular visual tracking system, with an emphasis on real-time operation. Finally, Chandrashekhar and Chellappa [ 101 use known navigational landmarks in their state estimation formulation, and interleave motion estimation and feature correspondence. Salient features of these recursive algorithms are compared in Table I. In contrast, optical-flow-based motion and structure estimation requires computation of an optical flow field {u(x,y) = [u(x,y) v(x,y>lT}. The optical flow at coordinates (x,y) on the image plane, in terms of 3-D translational velocity [T, Ty ?IT, the depth Z of 3-D point [ X Y ZIT, and rotational velocity [wx w, wZlT can be expressed as [l 11