Shape ellipticity from Hu moment invariants

Abstract

In this paper we derive an explicit formula which uses the first two Hu moment invariants to compute a shape ellipticity measure, i.e. to evaluate how much a planar shape differs from an ellipse. The ellipticity measure computed by this formula is invariant with respect to translation, rotation and scaling transformations. Also, the highest possible value is obtained if and only if the shape considered is an ellipse. Several experiments are also provided to confirm the theoretical observations. A by product, of the derivations made in this paper, is an implicit interpretation of geometric/shape meaning of the second Hu moment invariant. A formula which connects the shape ellipticity and the first Hu moment invariant (both having a well understood behavior) and the second Hu moment invariant is derived.