The calculation of the optical flow is one of the fundamental problems in the field of computer vision. It serves as the basis for a wide range of applications, such as: motion detection, tracking of objects and people, three-dimensional reconstruction of scenes, collision detection, medical, security and surveillance image analysis, satellite image processing, etc.

In this thesis, I explore some important ideas, such as the study of methods that exploit redundant information between non consecutive frames in order to obtain more robust and accurate solutions while applying advanced strategies to accelerate the numerical schemes that are generated. Within these strategies, we consider the use of specialized hardware for the application of our methods, such as graphics processing units (GPUs), the use of libraries for the parallelization of numerical algorithms or more advanced realizations.