Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
On ordered weighted averaging aggregation operators in multicriteria decisionmaking
IEEE Transactions on Systems, Man and Cybernetics
On the description of the relative position of fuzzy patterns
Pattern Recognition Letters
Basic meanings of spatial relations: computation and evaluation in 3D space
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Fuzzy Relative Position Between Objects in Image Processing: A Morphological Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Capturing approximate relationships using fuzzy set dominance relations
ICCOMP'05 Proceedings of the 9th WSEAS International Conference on Computers
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Spatial relationships between regions in an image play an important role in scene understanding. Humans are able to quickly ascertain the relationship between two objects, for example "B is to the right of A," or "B is in front of A," but this has turned out to be a somewhat illusive task for automation. When the objects in a scene are represented by crisp sets, the all-or-nothing definitions of the subsets actually add to the problem of generating such relational descriptions. It is our belief that definitions of spatial relationships based on fuzzy set theory, coupled with a fuzzy segmentation will yield realistic results. This chapter presents an approach at defining spatial relationships among fuzzy subsets of an image plane. The idea is to project the fuzzy subsets onto two orthogonal coordinate axes and to utilize fuzzy set theoretic dominance relations to capture the approximate relationships. Simulation results are provided to corroborate the theory.