A Logical Interpretation of Dempster-Shafer Theory, with Application to Visual Recognition
This provides a logical framework for uncertainty handling in visual recognition, though it is incremental as it builds on existing ATMS and Dempster-Shafer methods.
The paper tackles the problem of formalizing Dempster-Shafer theory in propositional logic to enable optimal visual interpretations in recognition systems, resulting in the extension of the VICTORS system to compute best interpretations while maintaining logical semantics.
We formulate Dempster Shafer Belief functions in terms of Propositional Logic using the implicit notion of provability underlying Dempster Shafer Theory. Given a set of propositional clauses, assigning weights to certain propositional literals enables the Belief functions to be explicitly computed using Network Reliability techniques. Also, the logical procedure corresponding to updating Belief functions using Dempster's Rule of Combination is shown. This analysis formalizes the implementation of Belief functions within an Assumption-based Truth Maintenance System (ATMS). We describe the extension of an ATMS-based visual recognition system, VICTORS, with this logical formulation of Dempster Shafer theory. Without Dempster Shafer theory, VICTORS computes all possible visual interpretations (i.e. all logical models) without determining the best interpretation(s). Incorporating Dempster Shafer theory enables optimal visual interpretations to be computed and a logical semantics to be maintained.