Optical flow or optic flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and a scene. Optical flow can also be defined as the distribution of apparent velocities of movement of brightness pattern in an image.

The concept of optical flow was introduced by the American psychologist James J. Gibson in the 1940s to describe the visual stimulus provided to animals moving through the world. Gibson stressed the importance of optic flow for affordance perception, the ability to discern possibilities for action within the environment. Followers of Gibson and his ecological approach to psychology have further demonstrated the role of the optical flow stimulus for the perception of movement by the observer in the world; perception of the shape, distance and movement of objects in the world; and the control of locomotion.

The term optical flow is also used by roboticists, encompassing related techniques from image processing and control of navigation including motion detection, object segmentation, time-to-contact information, focus of expansion calculations, luminance, motion compensated encoding, and stereo disparity measurement.

Optical flow can be estimated in a number of ways. Broadly, optical flow estimation approaches can be divided into machine learning based models (sometimes called data-driven models), classical models (sometimes called knowledge-driven models) which do not use machine learning and hybrid models which use aspects of both learning based models and classical models.

Many classical models use the intuitive assumption of brightness constancy; that even if a point moves between frames, its brightness stays constant. To formalise this intuitive assumption, consider two consecutive frames from a video sequence, with intensity ${\displaystyle I(x,y,t)}$, where ${\displaystyle (x,y)}$ refer to pixel coordinates and ${\displaystyle t}$ refers to time. In this case, the brightness constancy constraint is

where ${\displaystyle \mathbf {w} :=(u,v)}$ is the displacement vector between a point in the first frame and the corresponding point in the second frame. By itself, the brightness constancy constraint cannot be solved for ${\displaystyle u}$ and ${\displaystyle v}$ at each pixel, since there is only one equation and two unknowns. This is known as the aperture problem. Therefore, additional constraints must be imposed to estimate the flow field.

Perhaps the most natural approach to addressing the aperture problem is to apply a smoothness constraint or a regularization constraint to the flow field. One can combine both of these constraints to formulate estimating optical flow as an optimization problem, where the goal is to minimize the cost function of the form,

where ${\displaystyle \Omega }$ is the extent of the images ${\displaystyle I(x,y)}$, ${\displaystyle \nabla }$ is the gradient operator, ${\displaystyle \alpha }$ is a constant, and ${\displaystyle \Psi ()}$ is a loss function.