Notes on shape based tools for treating the objects ellipticity issues.

In this paper we put under the same umbrella several well known results and establish several new results related to the shape based tools which treat the objects ellipticity issues. We start with a derivation of an explicit and closed formula for the computation of the ellipticity measures, from an infinite family, introduced recently. The new formula enables a fast computation of such measures, since it does not require any optimizing procedure for the computation, as it was the case before. In addition, the established formula enables an easy theoretical manipulation. As a result, we have discovered new shape features, as they are: (i) The average shape ellipticity measure , which might be interpreted as an average value of the estimated similarities between the shape considered and all the ellipses whose axes length ratio belongs to a certain, predefined, interval; (ii) The maximal shape ellipticity measure , which might be understood as the maximal possible similarity estimate between a given shape and an ellipses. Some of the other results obtained relate strongly to the well-known measures and methods broadly used in shape based object analysis tasks. [ABSTRACT FROM AUTHOR]