Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Navigation and mapping in large-scale space
AI Magazine
Qualitative representation of positional information
Artificial Intelligence
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
A probabilistic method for extracting chains of collinear segments
Computer Vision and Image Understanding - Special issue on perceptual organization in computer vision
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fuzzy spatial relationships for image processing and interpretation: a review
Image and Vision Computing
On the ternary spatial relation "Between"
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
The fuzzy geometry of image subsets
Pattern Recognition Letters
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The analysis of spatial relations among objects in an image is an 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 configurations 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. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or 1D contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense.