Journal of Mathematical Imaging and Vision

, Volume 48, Issue 1, pp 1–12 | Cite as

Ranking Star-Shaped Valued Mappings with Respect to Shape Variability

  • Carlos Carleos
  • María Concepción López-Díaz
  • Miguel López-Díaz


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.


Star-shaped set Shape variability order Radial function Corneal endothelia cells 



We would like to thank Guillermo Ayala (Universidad de Valencia) and Lucía Martínez-Costa (Hospital Dr. Peset, Servicio de Oftalmología, Valencia) for helping us in obtaining data for application and for suggesting the idea of shape variability stochastic order.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Carlos Carleos
    • 1
  • María Concepción López-Díaz
    • 2
  • Miguel López-Díaz
    • 1
  1. 1.Dpto. de Estadística e I.O. y D.M. Facultad de CienciasUniversidad de OviedoOviedoSpain
  2. 2.Dpto. de Matemáticas, Facultad de CienciasUniversidad de OviedoOviedoSpain

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