Shape ellipticity based on the first Hu moment invariant

• A new ellipticity measure, for planar shapes, is derived.
• A fast computation is enabled by using the moments up to the second order.
• New ellipticity measure is invariant with respect to similarity transformations.
• The highest ellipticity value is obtained for the ellipses only.

In this paper we use the first Hu moment invariant to define a new ellipticity measure. The new ellipticity measure ranges over the interval (0,1](0,1] and picks the value 1 if and only if the measured shape is an ellipse. The measure is invariant with respect to translation, rotation and scaling transformations. It is straightforward and fast to compute.