Amplitude-Based Approach to Evidence Accumulation

TL;DR

This paper advocates for using probability amplitudes instead of probabilities in evidence accumulation, especially in optical systems, proposing a new amplitude-based generalization of the Hough transform for better object recognition.

Contribution

It introduces a novel amplitude-based approach to evidence accumulation and generalizes the Hough transform using complex accumulators for improved probabilistic interpretation.

Findings

Amplitude-based evidence modeling is suitable for optical systems.

Derived a complex Hough transform with magnitude squared for likelihood estimation.

Suggested applications in connectionist models and knowledge-based reasoning.

Abstract

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.