The fuzzy line between among and surround

Spatial relationships among image objects play a vital role in countless domains of computer vision (e.g., pattern recognition, image understanding, scene description). Some have received considerable attention the last few years (e.g., "to the right of," "above," "to the left of" and "below"), but others have not been the subject of as much investigation. In this paper, we design consistent fuzzy models of three important spatial relationships: "surrounded by," "between" and "among." These models are based on the histogram of forces, which represents the relative position between two objects. Here, force histograms are assimilated to fuzzy sets and processed through their α-cuts. Our goal is to extend the capabilities of a fuzzy system for linguistic scene description introduced in an earlier paper