Shape Numbers


The theory of shape numbers was proposed by E. Bribiesca and A. Guzman in 1978. The shape number of a curve is derived for two-dimensional (2D) non-intersecting closed curves that are the boundary of simply connected regions. This description is independent of their size, orientation and position, but it depends on their shape. Each curve carries “within it” its own shape number. The order of the shape number indicates the precision with which that number describes the shape of the curve. For a curve, the order of its shape number is the length of the perimeter of a “discrete shape” (a closed curve formed by vertical and horizontal segments, all of equal length) closely corresponding to the curve. A procedure is given that deduces, without table look-up, string matching or correlations , the shape number of any order for an arbitrary curve. To find out how close in shape two curves are, the degree of similarity between them is introduced. Informally speaking, the degree of similarity between the shapes of two curves tells how deep it is necessary to descend into a list of shapes, before being able to differentiate  between the shape of those two curves.