Optical flow
Optical flow is an algorithm that detects the pattern of the motion of objects, or edges, between consecutive frames in a video. This motion may be caused by the motion of the object or the motion of the camera. Optical flow is a vector that depicts the motion of a point from the first frame to the second.
The optical flow algorithm works under two basic assumptions:
- The pixel intensities are almost constant between consecutive frames
- The neighboring pixels have the same motion as the anchor pixel
We can represent the intensity of a pixel in any frame by f(x,y,t). Here, the parameter t represents the frame in a video. Let's assume that, in the next dt time, the pixel moves by (dx,dy). Since we have assumed that the intensity doesn't change in consecutive frames, we can say:
f(x,y,t) = f(x + dx,y + dy,t + dt)
Now we take the Taylor series expansion of the RHS in the preceding equation:
Cancelling the common term, we get:
Where 
.
Dividing both sides of the equation by dt...
