Fuzzy Modeling and Evaluation of the Spatial Relation "Along"

The analysis of spatial relations among objects in an image is a important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configuration in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures, thus showing their adequation with the common sense.