Journal of Classification

, Volume 16, Issue 2, pp 197–223 | Cite as

Shape Statistics: Procrustes Superimpositions and Tangent Spaces

  • F. James Rohlf


The shape of a set of labeled points corresponds to those attributes of the configuration that are invariant to the effects of translation, rotation, and scale. Procrustes distance may be used to compare different shapes and also serve as a metric that may be used to define multidimensional shape spaces. This paper demonstrates that the preshape space of planar triangles Procrustes aligned to a reference triangle corresponds to a unit hemisphere. An overview of methods used as linear approximations of D. G. Kendall's non-Euclidean shape space is given, and the equivalence of several methods based on orthogonal projections is shown. Some problems with approximations based on stereo graphic projections are also discussed. A simple example using artificial data is included.

Key words: Kendall shape space; Preshape space; Tangent space; Partial warps; Multivariate analysis. 


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Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • F. James Rohlf
    • 1
  1. 1.Department of Ecology and EvolutionState University of New YorkUSA

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