Estimating the optical flow

When a scene is observed by a camera, the observed brightness pattern is projected on the image sensor and thus forms an image. In a video sequence, we are often interested in capturing the motion pattern, that is the projection of the 3D motion of the different scene elements on an image plane. This image of projected 3D motion vectors is called the motion field. However, it is not possible to directly measure the 3D motion of scene points from a camera sensor. All we observe is a brightness pattern that is in motion from frame to frame. This apparent motion of the brightness pattern is called the optical flow. One might think that the motion field and optical flow should be equal, but this is not always true. An obvious case would be the observation of a uniform object; for example, if a camera moves in front of a white wall, then no optical flow is generated. 

Another classical example is the illusion produced by a rotating barber pole:

In this case,...