Abstract
Variability of shapes of bidimensional closed curves is a key matter in many fields of research. A statistical order of bidimensional shape variability is introduced in this paper. For such a purpose a special class of random elements is considered. The order is defined on such a class and the main properties of the order are analyzed. Such an order involves the curvature of a special parameterization of bidimensional closed curves. The new order can be used as a basis for implementing statistical procedures, such as hypothesis testing on variability of shapes. An example is developed by means of the image analysis of cell nuclei, namely the shapes of cell nuclei in mastitis-affected cow milk and non-affected cow milk are compared.
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The authors are in debt to the Spanish Ministry of Science and Technology since this research is financed by Grants MTM2007-67884 and MTM2008-01519.
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Carleos, C., López-Díaz, M.C. & López-Díaz, M. A Stochastic Order of Shape Variability with an Application to Cell Nuclei Involved in Mastitis. J Math Imaging Vis 38, 95–107 (2010). https://doi.org/10.1007/s10851-010-0215-5
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DOI: https://doi.org/10.1007/s10851-010-0215-5