Amplitude-Based Approach to Evidence Accumulation

We point out the need to use probability amplitudes rather than probabilities to model evidence accumulation in decision processes involving real physical sensors. Optical information processing systems are given as typical examples of systems that naturally gather evidence in this manner. We derive a new, amplitude-based generalization of the Hough transform technique used for object recognition in machine vision. We argue that one should use complex Hough accumulators and square their magnitudes to get a proper probabilistic interpretation of the likelihood that an object is present. Finally, we suggest that probability amplitudes may have natural applications in connectionist models, as well as in formulating knowledge-based reasoning problems.