Fuzzy spatial relationships: a few tools for model-based pattern recognition in aerial images

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Abstract
We address in this paper the problem of defining fuzzy relationships between objects for pattern recognition purposes. We distinguish two kinds of spatial relationships. Some of them are well defined if the objects are crisp, like adjacency, inclusion or other set relationships. But since they are highly sensitive to errors or imprecision in segmentation, more useful measures can be obtained by fuzzifying these concepts. We define such measures using fuzzification principles or direct translation of binary equations into fuzzy ones. Other relationships are inherently vague concepts, like relative position. Fuzzy definitions of such relationships are then more consistent than crisp ones. We propose definitions of relative position between crisp or fuzzy objects, and illustrate them on buildings in aerial images.

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