HOW TO DESCRIBE PURE FORM AND HOW TO MEASURE DIFFERENCES IN SHAPES USING SHAPE NUMBERS.

The shape number of a curve is derived for two-dimensional 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.