the corresponding directions. , and can be written for the derivatives in the following. Thus: or This is an equation in two unknowns and cannot be solved as such. This is known as the aperture problem of the optical flow algorithms. To find the optical flow another set of equations is needed, given by some additional constraint. All optical flow methods introduce additional conditions for estimating the actual flow. Methods for determination Phase correlation – inverse of normalized cross-power spectrum Block-based methods – minimizing sum of squared differences or sum of absolute differences, or maximizing normalized cross-correlation Differential methods of estimating optical flow, based on partial derivatives of the image signal and/or the sought flow field and higher-order partial derivatives, such as: Lucas–Kanade method – regarding image patches and an affine model for the flow field Horn–Schunck method – optimizing a functional based on residuals from the brightness constancy constraint, and a particular regularization term expressing the expected smoothness of the flow field Buxton–Buxton method – based on a model of the motion of edges in image sequences Black–Jepson method – coarse optical flow via correlation General variational methods – a range of modifications/extensions of Horn–Schunck, using other data terms and other smoothness terms. Discrete optimization methods – the search space is quantized, and then image matching is addressed through label assignment at every pixel, such that the corresponding deformation minimizes the distance between the source and the target image. The optimal solution is often recovered through Max-flow min-cut theorem algorithms, linear programming or belief propagation methods. Many of these, in addition to the current state-of-the-art algorithms are evaluated on the Middlebury Benchmark Dataset. Other popular benchmark datasets are KITTI and Sintel. Uses Motion estimation and video compression have developed as a major aspect of optical flow research. While the optical flow field is superficially similar to a dense motion field derived from the techniques of motion estimation, optical flow is the study of not only the determination of the optical flow field itself, but also of its use in estimating the three-dimensional nature and structure of the scene, as well as the 3D motion of objects and the observer relative to the scene, most of them using the image Jacobian. Optical flow was used by robotics researchers in many areas such as: object detection and tracking, image dominant plane extraction, movement detection, robot navigation and visual odometry. Optical flow