Optimization approach to the velocity field determining problem

Abstract

A reconstruction of the velocity field is of current interest for different theoretical and practical problems. In the presented work the optimization method of the velocity field construction for successive images is developed and generalized using the concepts of trajectory beam (an ensemble of trajectories), a distribution density function (brightness), and a quality functional. A new formulation of the problem is proposed with the splitting of the initial image to subsets and taking into account a temporal variation. Analytical expressions of the variation and gradient of the investigated functional are given, allowing one to construct various directed optimization methods. The proposed approach can be used for determining the velocity field within different tasks, particularly, for the problems of diagnostic image processing.