DocumentCode :
865788
Title :
On the ternary spatial relation "Between"
Author :
Bloch, Isabelle ; Colliot, Olivier ; Cesar, Roberto M., Jr.
Author_Institution :
Signal & Image Process. Dept., CNRS UMR, Paris, France
Volume :
36
Issue :
2
fYear :
2006
fDate :
4/1/2006 12:00:00 AM
Firstpage :
312
Lastpage :
327
Abstract :
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.
Keywords :
fuzzy set theory; mathematical morphology; object recognition; spatial reasoning; between ternary spatial relation; convex hull; convexity; mathematical morphology; morphological operators; object recognition; separation tools; spatial reasoning; structural pattern recognition; visibility fuzzy notion; Biomedical imaging; Counting circuits; Deformable models; Fuzzy reasoning; Morphology; Object recognition; Pattern recognition; Roads; Shape; Signal processing; Convex hull; fuzzy and three-dimensional (3-D) objects; mathematical morphology; relationship “between”; spatial reasoning; structural pattern recognition; visibility; Algorithms; Artificial Intelligence; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Information Storage and Retrieval; Pattern Recognition, Automated;
fLanguage :
English
Journal_Title :
Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on
Publisher :
ieee
ISSN :
1083-4419
Type :
jour
DOI :
10.1109/TSMCB.2005.857095
Filename :
1605379
Link To Document :
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