Fuzzy spatial relation ontology for image interpretation
Fuzzy Sets and Systems
Fuzzy skeleton by influence zones---Application to interpolation between fuzzy sets
Fuzzy Sets and Systems
Fuzzy and Bipolar Mathematical Morphology, Applications in Spatial Reasoning
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Approximate Parallelism between Fuzzy Objects: Some Definitions
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Information Sciences: an International Journal
Modelling English spatial preposition detectors
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Directional relations and frames of reference
Geoinformatica
Hi-index | 0.00 |
The spatial relation "between" is a notion which is intrinsically both fuzzy and contextual, and depends, in particular, on the shape of the objects. The literature is quite poor on this and the few existing definitions do not take into account these aspects. In particular, an object B that is in a concavity of an object A1 not visible from an object A2 is considered between A1 and A2 for most definitions, which is counter intuitive. Also, none of the definitions deal with cases where one object is much more elongated than the other. Here, we propose definitions which are based on convexity, morphological operators, and separation tools, and a fuzzy notion of visibility. They correspond to the main intuitive exceptions of the relation. We distinguish between cases where objects have similar spatial extensions and cases where one object is much more extended than the other. Extensions to cases where objects, themselves, are fuzzy and to three-dimensional space are proposed as well. The original work proposed in this paper covers the main classes of situations and overcomes the limits of existing approaches, particularly concerning nonvisible concavities and extended objects. Moreover, the definitions capture the intrinsic imprecision attached to this relation. The main proposed definitions are illustrated on real data from medical images.