Optical Flow Constraints

In order to compute Optical Flow there are two assumptions/constraints:

Image moves in u(x cord) and v(y cord):

1. The brightness(grayscale)/color consistency is same between the original image I ( x, y,t),  and the image in I ( x+u, y+v,t+1).
2. The change in motion is almost zero(smooth), which means that the original I ( x+u, y+v) ≅(approximately equals) the image +  gradient of x times delta x (u) + gradient of y time delta y(v) = I ( x, y )  + ∂I/∂x*u+ ∂I/∂y*v.

Aperture problem and therefore additional constraints:

Aperture problem : The motion direction of a contour is ambiguous, because the motion component parallel to the line cannot be inferred based on the visual input.

You can only tell the motion locally in the direction perpendicular to the edge.

So we need extra constraints:

1. Nearby pixels move together. (local constraint).
2. Motion must be consistent around the entire image (not identical but consistent) such as same global direction are prefable solutions. (global soft(not strong) constraint).
3. Considering distinct regions – like corners where ambiguity of flow direction is small – interpolate flow between them (approximate flow).