The article considers digital processing of image series using the discrete systems. The problem of displacement field calculation for image sequences is presented. The mathematical model based on discrete optimization is proposed as its solution. The model reflects the discrete nature of image series acquisition. It also takes into account the intensity change along the system trajectories. The study of integral-type functional on the trajectories ensemble of the discrete system was performed, and the optimization algorithm for displacement field construction based on its results was designed. The analytical form of functional variation is obtained and the functional gradient is derived, which allows us to use directional optimization methods to find the required parameters. The algorithm can be used in digital image processing, in particular, in nuclear medicine imaging. The method example implementation for nuclear medicine image processing is considered.