Circuits,signals,and systems
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Measurement of Visual Motion
A Theory of Networks for Approximation and Learning
A Theory of Networks for Approximation and Learning
Analyzing Looming Motion Components From Their Spatiotemporal Spectral Signature
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Describes how, in the process of extracting the optical flow through space-time filtering, one has to consider the constraints associated with the motion uncertainty, as well as the spatial and temporal sampling rates of the sequence of images. The motion uncertainty satisfies the Cramer-Rao (CR) inequality, which is shown to be a function of the filter parameters. On the other hand, the spatial and temporal sampling rates have lower bounds, which depend on the motion uncertainty, the maximum support in the frequency domain, and the optical flow. These lower bounds on the sampling rates and on the motion uncertainty are constraints that constitute an intrinsic part of the computational structure of space-time filtering. The author shows that if he uses these constraints simultaneously, the filter parameters cannot be arbitrarily determined but instead have to satisfy consistency constraints. By using explicit representations of uncertainties in extracting visual attributes, one can constrain the range of values assumed by the filter parameters.