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Procrustes Shape Distance

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Encyclopedia of Biometrics
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Statistical shape analysis


Procrustes was a villainous son of Poseidon in Greek mythology who robbed travelers on the road from Eleusis to Athens. He offered travelers a room for the night and fit them into his bed by stretching them if they were too short or cutting off their legs if they were too tall (Webster’s dictionary). In statistics, Procrustes analysis is used to describe the distribution of a set of shapes. It compares the differences in shape between two point sets by transforming one point set in order to match the other [1,2,5]. The transformations allowed in a standard analysis are the similarity (shape-preserving) ones: scale changes, rotations, and translations. One can regard by analogy, one point set as the bed and the other as the person being “translated,” “rotated,” and “rescaled” so as to fit as close as possible to the bed. After one of the point sets has been transformed to match the other, the sum of squared differences of the coordinates...

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  1. F.L. Bookstein, Morphometric Tools for Landmark Data (Cambridge University Press, Cambridge, 1991)

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  2. I.L. Dryden, K.V. Mardia, Statistical Shape Analysis (Wiley, Chichester, 1998)

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  3. N. Duta, M. Sonka, Segmentation and interpretation of MR brain images: an improved active shape model. IEEE Trans. Med. Imaging 17(6), 1049–1062 (1998)

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  5. C.G. Small, The Statistical Theory of Shape (Springer, Berlin, 1996)

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Correspondence to Nicolae Duta .

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Duta, N. (2014). Procrustes Shape Distance. In: Li, S., Jain, A. (eds) Encyclopedia of Biometrics. Springer, Boston, MA.

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