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3-D Motion Estimation Using a Sequence of Noisy Stereo Images: Models, Estimation, and Uniqueness Results
August 1990 (vol. 12 no. 8)
pp. 735-759

A kinematic model-based approach for the estimation of 3-D motion parameters from a sequence of noisy stereo images is discussed. The approach is based on representing the constant acceleration translational motion and constant precession rotational motion in the form of a bilinear state-space model using standard rectilinear states for translation and quaternions for rotation. Closed-form solutions of the state transition equations are obtained to propagate the quaternions. The measurements are noisy perturbations of 3-D feature points represented in an inertial coordinate system. It is assumed that the 3-D feature points are extracted from the stereo images and matched over the frames. Owing to the nonlinearity in the state model, nonlinear filters are designed for the estimation of motion parameters. Simulation results are included. The Cramer-Rao performance bounds for motion parameter estimates are computed. A constructive proof for the uniqueness of motion parameters is given. It is shown that with uniform sampling in time, three noncollinear feature points in five consecutive binocular image pairs contain all the spatial and temporal information. Both nondegenerate and degenerate motions are analyzed. A deterministic algorithm to recover motion parameters from a stereo image sequence is summarized from the constructive proof.

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Index Terms:
computer vision; nondegenerate motion; 3-D motion estimation; noisy stereo images; uniqueness; kinematic model-based approach; constant acceleration translational motion; constant precession rotational motion; bilinear state-space model; 3-D feature points; nonlinear filters; Cramer-Rao performance bounds; parameter estimates; degenerate motions; computer vision; kinematics; parameter estimation
Citation:
G.S.J. Young, R. Chellappa, "3-D Motion Estimation Using a Sequence of Noisy Stereo Images: Models, Estimation, and Uniqueness Results," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 8, pp. 735-759, Aug. 1990, doi:10.1109/34.57666
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