Motion Analysis - Background

Background

A video camera can be seen as an approximation of a pinhole camera, which means that each point in the image is illuminated by some (normally one) point in the scene in front of the camera, usually by means of light that the scene point reflects from a light source. Each visible point in the scene is projected along a straight line that passes through the camera aperture and intersects the image plane. This means that at a specific point in time, each point in the image refers to a specific point in the scene. This scene point has a position relative to the camera, and if this relative position changes, it corresponds to a relative motion in 3D. It is a relative motion since it does not matter if it is the scene point, or the camera, or both, that are moving. It is only when there is a change in the relative position that the camera is able to detect that some motion has happened. By projecting the relative 3D motion of all visible points back into the image, the result is the motion field, describing the apparent motion of each image point in terms of a magnitude and direction of velocity of that point in the image plane. A consequence of this observation is that if the relative 3D motion of some scene points are along their projection lines, the corresponding apparent motion is zero.

The camera measures the intensity of light at each image point, a light field. In practice, a digital camera measures this light field at discrete points, pixels, but given that the pixels are sufficiently dense, the pixel intensities can be used to represent most characteristics of the light field that falls onto the image plane. A common assumption of motion analysis is that the light reflected from the scene points does not vary over time. As a consequence, if an intensity I has been observed at some point in the image, at some point in time, the same intensity I will be observed at a position that is displaced relative to the first one as a consequence of the apparent motion. Another common assumption is that there is a fair amount of variation in the detected intensity over the pixels in an image. A consequence of this assumption is that if the scene point that corresponds to a certain pixel in the image has a relative 3D motion, then the pixel intensity is likely to change over time.