Relative Position-Based Spatial Relationships using Mathematical Morphology

Spatial information is a crucial aspect of image understanding for modeling context as well as resolving the uncertainties caused by the ambiguities in low-level features. We describe intuitive, flexible and efficient methods for modeling pairwise directional spatial relationships and the ternary between relation using fuzzy mathematical morphology. First, a fuzzy landscape is constructed where each point is assigned a value that quantifies its relative position according to the reference object(s) and the type of the relationship. Then, the degree of satisfaction of this relation by a target object is computed by integrating the corresponding landscape over the support of the target region. Our models support sensitivity to visibility to handle areas that are partially enclosed by objects and are not visible from image points along the direction of interest. They can also cope with the cases where one object is significantly spatially extended relative to others. Experiments using synthetic and real images show that our models produce more intuitive results than other techniques.


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Spatial information plays a very important role in image understanding. Fuzzy mathematical morphology provides an effective basis for extracting binary and ternary spatial relationships by creating a fuzzy landscape where the value at each point corresponds to the relationship degree according to its position with respect to the reference object(s). We improve existing morphological approaches in terms of flexibility and efficiency while also obtaining more intuitive results. Our morphological definitions a...
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Citation Formats
R. G. Cinbiş, “Relative Position-Based Spatial Relationships using Mathematical Morphology,” 2007, Accessed: 00, 2020. [Online]. Available: