A General Approach to the Fuzzy Modeling of Spatial Relationships

How to satisfactorily model spatial relationships between 2D or 3D objects? If the objects are far enough from each other, they can be approximated by their centers. If they are not too far, not too close, they can be approximated by their minimum bounding rectangles or boxes. If they are close, no such simplifying approximation should be made. Two concepts are at the core of the approach described in this paper: the concept of the \(\mathcal{F}\)-histogram and that of the \(\mathcal{F}\)-template. The basis of the former was laid a decade ago; since then, it has naturally evolved and matured. The latter is much newer, and has dual characteristics. Our aim here is to present a snapshot of these concepts and of their applications. It is to highlight (and reflect on) their duality–a duality that calls for a clear distinction between the terms spatial relationship, relationship to a reference object, and relative position. Finally, it is to identify directions for future research.