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Ranking Star-Shaped Valued Mappings with Respect to Shape Variability

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Dpto. de Estadística e I.O. y D.M. Facultad de Ciencias, Universidad de Oviedo, c/ Calvo Sotelo, s/n., 33007, Oviedo, Spain

    Carlos Carleos & Miguel López-Díaz

  2. Dpto. de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, c/ Calvo Sotelo, s/n., 33007, Oviedo, Spain

    María Concepción López-Díaz

Authors
  1. Carlos Carleos
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  2. María Concepción López-Díaz
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  3. Miguel López-Díaz
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Corresponding author

Correspondence to María Concepción López-Díaz.

Additional information

The authors are in debt to the Spanish Ministry of Science and Technology since this research is financed by Grants MTM2010-18370, MTM2011-22993.

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Carleos, C., López-Díaz, M.C. & López-Díaz, M. Ranking Star-Shaped Valued Mappings with Respect to Shape Variability. J Math Imaging Vis 48, 1–12 (2014). https://doi.org/10.1007/s10851-012-0381-8

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