An algorithm to estimate motion from satellite imagery is presented. Dense displacement fields are computed from time-separated images of of significant convective activity using a Bayesian formulati on of the motion estimation problem. Ordinarily this motion estimation problem is ill-posed; there are far too many degrees of freedom than necessary to represent the motion. Therefore, some form of regularization becomes necessary and by imposing smoothness and non-divergence as desirable properties of the estimated displacement vector field, excellent solutions are obtained. Our approach provides a marked improvement over other methods in conventional � This material is supported in part by NSF ITR 0121182 and DDDAS 0540259.
@cite_1: A local approach for interframe displacement estimates is developed by minimization of the squared differences between a second-order Taylor expansion of gray values from one frame and the observed gray values within the same window from the next frame. If the second-order terms in the Taylor expansion are significant, a system of two coupled nonlinear equations for the two unknown components of the displacement vector can be derived. In the special case of “gray value corners,” these equations can be simplified to facilitate a closed form solution. An iterative refinement procedure is developed to extend these estimates for image regions which do not exhibit exactly the properties of “gray value corners.” The minimization approach is generalized in such a way that the approach of Horn and Schanck ( Artif. Intell. 17, 1981, 185–203) can be recognized as a special case of this generalized form which should be applicable even across occluding edges. It thus appears to be an interesting model for the local computation of optical flow.
Here @math is the brightness or intensity scalar field and @math a displacement vector-field. Solutions to the optic flow equation can be formulated using the well-known method by @cite_1 , which can be stated as a solution to the following system of equations: