  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.
