Single Camera Structure and Motion

A reduced order nonlinear observer is proposed for the problem of “structure and motion (SaM)” estimation of a stationary object observed by a moving calibrated camera. In comparison to existing work which requires some knowledge of the Euclidean geometry of an observed object or full knowledge of the camera motion, the developed reduced order observer only requires one camera linear velocity and corresponding acceleration to asymptotically identify the Euclidean coordinates of the feature points attached to an object (with proper scale reconstruction) and the remaining camera velocities. The unknown linear velocities are assumed to be generated using a model with unknown parameters. The unknown angular velocities are determined from a robust estimator which uses a standard Homography decomposition algorithm applied to tracked feature points. A Lyapunov analysis is provided to prove the observer asymptotically estimates the unknown states under a persistency of excitation condition.