Optimization Approach to Determining the Velocity Field in Image Processing Problems

A new approach to constructing the velocity field based on the control theory and optimization of dynamics of trajectory ensembles is considered. This approach accepts the situation in which the intensity along the motion trajectory is variable. This makes it possible to design directed optimization methods for determining optical and non-optical flows. The velocity field is specified as a function depending on a vector of arbitrary parameters found as a result of minimizing a functional defined on the ensemble of trajectories determined by this velocity field. An algorithm for reconstructing the velocity field using an analytical representation of the variation of the functional under study is developed. Results of testing the proposed algorithm, including a partitioning of the image into subregions, are presented.