A method based on the spatial-temporal Hadamard transform is proposed to estimate 3-D translational motion parameters. In addition to the advantages of fast computation and easy implementation, this method has no restriction on the magnitude of displacement. For an image of size 2n×2n, only 2n+1 coefficients need to be computed for translational parameters. Moreover, this method can be extended to the time-varying space-invariant (TVSI) illumination case. As a byproduct, the para- meters of rotation about the optical axis can also be estimated by the modified algorithm.
Furthermore, a modified version of Pentland's depth recovery algorithm can be incorporated into previous analysis to obtain the real-world translational motion under the constraint that only one camera is used. Finally, experimental results of this method and its comparison with the Fourier method are also illustrated.