The problem of digital image processing based on discrete systems is considered in the article. An optimization algorithm for constructing the displacement field based on the study of the integral functional on the ensemble of trajectories is proposed. The analytical form of functional variation is presented and the representation of the functional gradient is given, which allows using directed optimization methods to find the desired parameters. This algorithm can be used for processing of various digital images, in particular, for radionuclide images for the purpose of motion correction.