Typical computational models for recovering optical flow assume that there is a unique velocity vector at each point in the retinal image. This unique vector corresponds to the image projection image of a 3D scene point. These computational models usually assume, moreover, that the vectors vary continuously almost everywhere across the image. Such an assumption makes sense provided that the visual field has few depth discontinuities, for example, if there is a single ground plane and only a few objects.

For cluttered 3-D scenes, however, the above assumptions made by optical flow models fail miserably. The reason is that depth discontinuities occur nearly everywhere in a cluttered scene. An extreme case is a scene during a snowfall. Since the image velocity of each snowflake varies inversely with the distance between the eye and the flake, and since each patch of the retinal image contains snowflakes at a range of distances, each image patch must contain a range of velocities rather than a unique velocity. A less extreme version of this problem in which the failures are still dramatic occurs in cluttered scenes such as a forest or a crowd. Image occlusion relationships vary rapidly as the observer moves through such scenes and, as a result, classical optical flow methods fail. We call such image motions "optical snow," and we are currently addressing the computational problem of how to recover their motion properties.

Our main findings thus far are as follows. Optical snow gives rise to a "bow tie" signature of power in the 3D spatio-temporal frequency domain. We will show how this fact follows directly from the result of (Watson and Ahumada, JOSA 1985) that pure translation optical flow produces a plane in the spatio-temporal frequency domain. Using the bow tie signature, we will show how to recover parameters of the optical flow, in two stages. First, we determine the direction of the optical snow; second, we determine the range of speeds. A more complete description of our results can be found in (M.S. Langer and R. Mann, Eighth International Conference on Computer Vision, Vancouver, Canada. July, 2001). That paper can be downloaded from

http://www.cim.mcgill.ca/~langer/pubs.html.