F-Histograms and Fuzzy Directional Spatial Relations

The fuzzy qualitative assessment (or quantitative assessment) of directional spatial relationships (such as "to the right of", "above", "south of"...) between two plane objects often relies on the computation of a histogram of angles, which provides a representation of the relative position of the objects. In a recent paper, the notion of the F-histogram was introduced. Here, we show that this powerful tool of representation lends itself, with great flexibility, to the definition of fuzzy directional relations. Indeed, any family of directional relations that relies on the construction of angle histograms can be advantageously redefined using F-histograms. Moreover, the notion of the F-histogram enables radically new families of directional relations to be conceived: definitions which correspond to a coherent and rational perception of the world, but non-realizable by previous methods.