An Experimental Investigation of Estimation Approaches for Optical Flow Fields

The halftone image of a scene can be described by giving the gray value as a function of the image plane coordinate vector x, i.e., the picture function g(x). In the case of relative motion between the camera and the depicted scene, the picture function will depend not only on the image plane coordinate vector x, but in addition on the time t. During a short enough time interval, △t, the resulting temporal change of the picture function can be approximated by a local shift of spatial gray value structures. This apparent shift can be described by an optical flow vector field, u(x,t). It maps the gray value g(x–u△t,t) recorded at time t at the image plane location x–u△t into the gray value g(x,t + △t) recorded at location x at time t + △t. In most cases, this optical flow field is a good approximation to the temporal displacement of the image of a depicted surface element between time t and time t + △t.