2CoBel : An Efficient Belief Function Extension for Two-dimensional Continuous Spaces

TL;DR

This paper presents a novel polygon-based method for efficiently handling 2D hypotheses in Belief Function Theory, enabling scalable and precise reasoning in continuous spaces with practical algorithms and open-source implementation.

Contribution

It introduces a polygon clipping-based representation and algorithms for 2D belief functions, improving scalability and efficiency in continuous hypothesis spaces.

Findings

Accurate pedestrian localization results

Efficient computation independent of frame cardinality

Open-source library implementation available

Abstract

This paper introduces an innovative approach for handling 2D compound hypotheses within the Belief Function Theory framework. We propose a polygon-based generic rep- resentation 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.