Abstract
The shape of an object is the geometrical information remaining after the effects of changes in location, scale and orientation have been removed. Information about the objects may come in different forms, for example as a set of landmarks or as a continuous outline. In this chapter we consider landmark based representations of shapes of two-dimensional objects. A common problem here is estimating a mean shape of the group of objects, describing their differences, or assessing the variability within each group.
One way to work with the shapes of different objects is to first register the landmark data on some common coordinate system. Bookstein (Stat Sci 1:181–242, 1986) and Kendall (Bull Lond Math Soc 16:81–121, 1984), each developed coordinate systems for removing the similarity transformations. Alternatively, Procrustes methods (Goodall, J R Stat Soc Ser B 53:285–339, 1991) may be used to remove the similarity transformations. In this chapter we shall discuss these methods by introducing basic concepts and definitions that will be used throughout the book.
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Brombin, C., Salmaso, L., Fontanella, L., Ippoliti, L., Fusilli, C. (2016). Basic Concepts and Definitions. In: Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-26311-3_1
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DOI: https://doi.org/10.1007/978-3-319-26311-3_1
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