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.

References:

• Bribiesca E. and Guzmán A., Shape Description and Shape Similarity Measurement for Two Dimensional Regions, Proceedings of The 4th  International Conference on Pattern Recognition, pp. 608-612, Kyoto, Japan (1978).
• Bribiesca E. and Guzman A., How to Describe Pure Form and How to Measure Differences in Shapes Using Shape Numbers, IEEE Computer Society, Conference on Pattern Recognition and Image Processing, Chicago, Illinois,U.S.A. (1979).
• Bribiesca E. and Guzmán A., Shape Description and Shape Similarity Measurement for Two dimensional Regions, Geo-Processing, Vol. 1, No. 1 pp. 129-144 (1979).
• Bribiesca E. and Guzmán A., How to Describe Pure Form and How to Measure Differences in Shape Using Shape Numbers, Pattern Recognition, Vol. 12, No. 2, pp. 101-112 (1980).
• Bribiesca E., Arithmetic Operation Among Shapes Using Shape Numbers, Pattern Recognition, Vol. 13, No. 2, pp. 123-137 (1981).
• Bribiesca E., Unsupervised and Supervised-classification on Digital Images Using Shape and Color, Advances in Information Sciences and Technology, Vol. I: Pattern Recognition and Digital Technique, Calcutta (1982).
• Bribiesca E., Shape Classification on Digital Images, Proceedings of the International Society of Photogrammetry and Remote Sensing, Commission IV, Symposium: Environmental Assessment and Resource Management, Crystal City, Virginia, U.S.A. (1982).