2-d Analogues of Allen Interval Algebra for Image Analysis: towards Justification

In reasoning about time and duration, researchers often use Allen’s Interval Algebra. This algebra describes possible relations between 1-D intervals. An interval can precede the other one, follow the other one, start the other one, etc. This algebra describes the relationship between different intervals in terms of words from natural language. To give a natural language description of 2D images, it is desirable to develop a similar approach for describing the relationship between 2-D objects in a picture. In their recent papers, Jim Keller and his collaborators proposed a new approach based on a simulation of a “force” between these objects. In this paper, we show that their force formula is theoretically optimal.