Sensitivity/robustness flexible ellipticity measures

Abstract

Ellipse is one of basic shapes used frequently for modeling in different domains. Fitting an ellipse to the certain data set is a well-studied problem. In addition the question how to measure the shape ellipticity has also been studied. The existing methods to estimate how much a given shape differs from a perfect ellipse are area based. Because of this, these methods are robust (e.g. with respect to noise or to image resolution applied). This is a desirable property when working with a low quality data, but there are also situations where methods sensitive to the presence of noise or to small object deformations, are more preferred. (e.g. in high precision inspection tasks.) In this paper we propose a new family of ellipticity measure. The ellipticity measures are dependent on a single parameter and by varying this parameter the sensitivity/robustness properties of the related ellipticity measures, vary as well. Independently on the parameter choice, all the new ellipticity measures are invariant with respect to the translation, scaling, and rotation transformation, they all range over (0; 1] and pick 1 if and only if the shape considered is an ellipse. New measures are theoretically well founded. Because of this their behavior in particular applications is well understood and can be predicted to some extent, which is always an advantage. Several experiments are provided illustrate the behavior and performance of the new measures.