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A geometric approach to projective shape and the cross ratio

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  • John T. Kent
  • Kanti V. Mardia

Abstract

Projective shape consists of the information about a configuration of points that is invariant under projective transformations. It is an important tool in machine vision to pick out features that are invariant to the choice of camera view. The simplest example is the cross ratio for a set of four collinear points. Recent work involving ideas from multivariate robustness enables us to introduce here a natural preshape on projective shape space. This makes it possible to adapt the Procrustes analysis that forms the basis of much methodology in the simpler setting of similarity shape space. Copyright 2012, Oxford University Press.

Suggested Citation

  • John T. Kent & Kanti V. Mardia, 2012. "A geometric approach to projective shape and the cross ratio," Biometrika, Biometrika Trust, vol. 99(4), pages 833-849.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:4:p:833-849
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    File URL: http://hdl.handle.net/10.1093/biomet/ass055
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