2CoBei: An Efficient Belief Function Extension for Two-Dimensional Continuous Spaces

Abstract

This paper introduces an innovative approach for handling 2D compound hypotheses within the Belief Function Theory framework. We propose a polygon-based generic representation which relies on polygon clipping operators. This approach allows us to account in the computational cost for the precision of the representation independently of the cardinality of the discernment frame. For the BBA combination and decision making, we propose efficient algorithms which rely on hashes for fast lookup, and on a topological ordering of the focal elements within a directed acyclic graph encoding their interconnections. Additionally, an implementation of the functionalities proposed in this paper is provided as an open source library. 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.

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

“…Indeed, whereas such works propose a geometrical formulation of the basic belief assignment (BBA) itself, our focus is on the geometrical representation of 2D focal elements. This paper extends our preliminary conference work [22] and is organized as 100 follows. Section 2 presents the efficient BBA representation we adopt for the case of 2D discernment frames.…”