The relative
position between two objects in a 2D raster image is often represented
quantitatively by a force histogram. In the general case, force
histograms are computed in O(KN√N) time: N is the number of
pixels in the image and K is the number of directions in which forces
are considered. When the objects are defined as fuzzy sets, this
complexity also depends quadratically on the number M of possible
membership degrees. In the present paper, an algorithm that runs in O(NlogN) is introduced. Computation
times are basically independent of K and M. All objects (convex,
concave, crisp, fuzzy) are handled in an equally fast manner.
Experiments validate the theoretical analysis.
