Multiscale Optic Flow

Abstract

In the previous chapters we have established two definitions of spatiotemporal images with fundamentally different temporal aspects. The first one does not account for temporal causality. All time instances are treated on equal foot. As such it is useful for off-line image processing on pre-recorded data. The second definition does incorporate causality, and is therefore appropriate for on-line image processing of real-time acquisition data. Both definitions reflect the symmetries that pertain to the classical picture of space and time. However, both models could be called “pseudo-static” in the sense that none of them explicitly accounts for a kinematic relation between local image samples. Such relations naturally arise as a consequence of apparent conservation laws. For this reason we will define a kinematic concept known as optic flow, again—of course—in terms of its actual computation.

If a point moves in a figure which is divided into two parts, and if it belongs at the beginning of the motion to one part and at the end of the motion to the other part, it must during the motion arrive at the boundary between the two parts.

—Wilhelm K. J. Killing