A Brief Overview on Statistical Shape Analysis

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.

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