2CoBel: A scalable belief function representation for 2D discernment frames

This paper introduces an innovative approach for handling 2D compound hypotheses within the Belief Function framework. We propose a polygon-based generic representation which relies on polygon clipping operators, as well as on a topological ordering of the focal elements within a directed acyclic graph encoding their interconnections. This approach allows us to make the computational cost for the hypothesis representation independent of the cardinality of the discernment frame. For belief combination, canonical decomposition and decision making, we propose efficient algorithms which rely on hashes for fast lookup, and which benefit from the proposed graph representation. An implementation of the functionalities proposed in this paper is provided as an open source library. In addition to an illustrative synthetic example, quantitative experimental results on a pedestrian localization problem are reported. The experiments show that the solution is accurate and that it fully benefits from the scalability of the 2D search space granularity provided by our representation.