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).