The problem of estimating motion and shape of a moving object has been considered from a time series of image data obtained via perspective projection. First of all, we analyze motion and shape dynamics of a planar surface undergoing rigid motion. It is shown that, for a class of motion parameters, the shape parameters are asymptotically decoupled from the optical flow dynamics, hence, become unobservable, asymptotically. For other choices of motion parameters, shape parameters remain asymptotically observable. We present a numerical study and compare a recursive algorithm using an extended Kalman filter with a nonrecursive algebraic method, for estimating motion and planar surface parameters. The conclusion of the paper is that recursive methods yield robust estimates whenever they are applicable. Algebraic estimation schemes, on the other hand, are always susceptible to noise.
- Optical flow
- Rigid motion