SHAPE DESCRIPTION AND SHAPE SIMILARITY MEASUREMENT FOR TWO-DIMENSIONAL REGIONS.

An analysis is made of the forms or shapes of flat regions limited by simply connected curves. A procedure is given that deduces from every region a unique number (its shape number) independent of translation, rotation and scaling. The precision in the representation of the shape of a region by one of its shape numbers is indicated by the order of that shape number; high orders are more accurate for shape description. Informally, the number of ternary digits of a shape number will tell its order. The degree of similarity between the shapes of two regions is introduced and an algorithm is given for computing it from the corresponding shape numbers. Two regions with shapes that look alike will have a high degree of similarity. No string matching or grammatical parsing is necessary to find out how close in shape two regions are. A related theory ″B″ of shapes is presented that disregards the eccentricity of a region and offers additional advantages for shape comparison.