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Dimensional analysis of image motion

Studies of image motion typically address motion categories on a case-by-case basis. Examples include a moving point, a moving contour, or a 2D optical flow field. The typical assumption made in these studies is that there is a unique velocity at each moving point in the image. In this paper we relax this assumption. We introduce a broader set of motion categories in which the set of motions at a moving point can be 0-D, 1-D, or 2-D. We consider one new motion category in detail, which we call optical snow. This motion category occurs, for example, when an observer translates relative to a massively cluttered scene. Examples include the motion seen by an observer moving through bushes, or falling snow seen by a stationary observer. Optical snow is characterized by a 1-D set of velocities at each moving point and as such, it cannot be analyzed using a classical computational method such as optical flow. We introduce a technique for analyzing optical snow which is based on a bow tie signature of the motion in the frequency domain. We demonstrate the effectiveness of the technique using both synthetic and real image sequences.