I had a need to classify polygon shapes into general categories such as roads and buildings, and I though it might be possible to use a "thinness" factor calculated using the area and perimeter. After fooling around with it for a while and not getting the answer, I goggled and found the following solution:Slide 11
lCircularity ratio: the ratio of the area of the shape to the area of a circle (the most compact shape) having the same perimeter. (area-perimeter ratio)
M = ( 4 * Pi * Area of Polygon) / (Perimeter of Polygon)^2
For a circle, the ratio is one; for a square, it is ð / 4; for an infinitely long and narrow shape, it is zero.
I found it at: http://ce.sharif.edu/~alamgir/
Further searches indicate that this method of classification may be relatively unknown. Does anyone have knowledge in this area?