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A Brief Overview on Statistical Shape Analysis

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Permutation Tests in Shape Analysis

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST,volume 15))

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Abstract

In this chapter we introduce the basic concepts and terms that will be used throughout the book. In particular we provide a brief overview of statistical shape analysis and geometric morphometric techniques, focussing on landmark and semilandmark-based representations of shapes.Shape is described as the geometric property of an object invariant under rotation, scale, or translation. Morphometric is a new promising branch of statistics that integrates knowledge from mathematics, geometry, biometrics, computer science, and modern engineering (essential especially for complicated three-dimensional object) to study shape and size of objects, along with their covariations with other variables. In this context the shape of an object is considered as a whole, align with the interdependence of its parts and conclusions are drawn under conditions of uncertainty. Geometric morphometrics is a more recent area of morphometrics that, by means of statistical tools, analyzes geometric information of objects, focusing on exactly where points or parts of the organism are located with respect to each other. To illustrate how landmarks and semilandmarks are chosen and then classified in real applications, we propose two case studies.

“We have the duty of formulating, of summarizing, and of communicating our conclusions, in intelligible form, in recognition of the right of other free minds to utilize them in making their own decisions”.

Statistical methods and scientific induction. Journal of the Royal Statistical Society, B, 17, 69–78, 1955.

R.A. Fisher

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Authors and Affiliations

  1. CUSSB, Vita-Salute, University of San Raffaele, Milan, Italy

    Chiara Brombin

  2. Department of Management and Engineering, University of Padova, Vicenza, Italy

    Luigi Salmaso

Authors
  1. Chiara Brombin
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  2. Luigi Salmaso
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Brombin, C., Salmaso, L. (2013). A Brief Overview on Statistical Shape Analysis. In: Permutation Tests in Shape Analysis. SpringerBriefs in Statistics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8163-8_1

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