Linguistic Description of Relative Positions in Images

In TSMC2001, we introduce new families of fuzzy directional relations that rely on the computation of histograms of forces. These families provide inputs to a fuzzy rule base that produces logical linguistic descriptions along with assessments as to the validity of the descriptions. Each linguistic output uses hedges from a dictionary of about thirty adverbs and other terms that can be tailored to individual users. Many results on synthetic data are presented in the paper. All these data are part of an animation that we built to evaluate our system. Structured round thirty-five key configurations, it is made up of more than two thousand images, and lasts about three and a half minutes. Six short movies supplement the electronic version of the paper and cover a large part of the animation. The associated caption is at the end of this page.

MOVIE 1 (zip file, 178KB)

MOVIE 2 (zip file, 193KB)

MOVIE 3 (zip file, 604KB)

MOVIE 4 (zip file, 466KB)

MOVIE 5 (zip file, 155KB)

MOVIE 6 (zip file, 454KB)

Each frame represents:

1.   Two objects A and B  (A appears in orange and B in blue).

2.   The histogram of constant forces and the histogram of gravitational forces associated with (A,B).  Four values are extracted from the analysis of each histogram: the degrees of truth (in tenths) of "A is to the right of B", "A is above B", "A is to the left of B" and "A is below B". Values equal to zero are not displayed. The direction d that makes the degree of truth of "A is in direction d of B" maximum is also shown.

3.   The linguistic expression that describes the relative position of A with regard to B.  The description produced by the system relies on the sole primitive directional relationships: "to the right of", "above", "to the left of" and "below". It assesses itself: it appears in green if the self-assessment is "satisfactory", in orange if the self-assessment is "rather satisfactory", and in red if it is "unsatisfactory". In other words, the color indicates to what extent the four primitive directional relationships are suited to describing the relative position of the objects. It indicates to what extent it is necessary to turn or not to other spatial relations (e.g., "surrounds"). If no pertinent linguistic description relying on the sole directional relationships can be given, then the system produces the message "???????".