ON THE MATHEMATICAL STRUCTURE OF DIRECTION AND MOTION ESTIMATION

The natural characteristics of the considered signals and the statistics of the measurement noise are decisive for designing any kind of optimal estimation methods in signal processing. Astonishingly, this principle has so far only partially found its way into the field of motion estimation for image (or video) data, be it in the case of video communication or in physical precision metrology. We show that the traditional dominance of derivative operators in the context of motion or orientation estimation is little more than an epiphenomenon of using a steerable filter bank for orientation analysis. Furthermore, we sketch generalized schemes for orientation analysis that are computationally more expensive than conventional schemes, but offer the potential of analyzing even complex motion patterns in a way that directly considers the individual characteristics of the given data material (which may be quite different in various settings).

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