Ranking Star-Shaped Valued Mappings with Respect to Shape Variability

The study of shapes is a difficult topic, but it is becoming more and more important as computer vision techniques are already crucial in many research fields. Concretely, the variability of shapes is the basis for many criteria of symptom definition in medical diagnosis. This article introduces a stochastic order to address the variability of star-shaped sets. The main properties of the order are analyzed. An example of an application to hypothesis testing in medical diagnosis is also provided. Namely, we study if there are significant differences between healthy and diseased corneal endothelia with respect to cell shapes by means of ocular images.