article · Greater South Information System · 2006
On the ternary spatial relation "Between"
Isabelle Bloch, Olivier Colliot, Roberto M. César
Cited by 0Open access
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 A/sub 1/ not visible from an object A/sub 2/ is considered between A/sub 1/ and A/sub 2/ 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.
Cite this paper
Bloch, I., Colliot, O., & César, R. M. (2006). On the ternary spatial relation "Between". Greater South Information System. https://doi.org/10.60692/214k8-bh645
Bloch, Isabelle, et al. “On the ternary spatial relation "Between".” Greater South Information System, 2006, https://doi.org/10.60692/214k8-bh645.
Bloch, Isabelle, Olivier Colliot, and Roberto M. César. 2006. “On the ternary spatial relation "Between".” Greater South Information System. https://doi.org/10.60692/214k8-bh645.
Bloch, I., Colliot, O. and César, R.M. (2006) ‘On the ternary spatial relation "Between"’, Greater South Information System. Available at: https://doi.org/10.60692/214k8-bh645.
@article{bloch2006ternary,
title = {{On the ternary spatial relation "Between"}},
author = {Bloch, Isabelle and Colliot, Olivier and César, Roberto M.},
journal = {Greater South Information System},
year = {2006},
doi = {10.60692/214k8-bh645}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.