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Shape spaces for prealigned star‐shaped objects—studying the growth of plants by principal components analysis

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  • T. Hotz
  • S. Huckemann
  • A. Munk
  • D. Gaffrey
  • B. Sloboda

Abstract

Summary. We analyse the shapes of star‐shaped objects which are prealigned. This is motivated from two examples studying the growth of leaves, and the temporal evolution of tree rings. In the latter case measurements were taken at fixed angles whereas in the former case the angles were free. Subsequently, this leads to different shape spaces, related to different concepts of size, for the analysis. Whereas several shape spaces already existed in the literature when the angles are fixed, a new shape space for free angles, called spherical shape space, needed to be introduced. We compare these different shape spaces both regarding their mathematical properties and in their adequacy to the data at hand; we then apply suitably defined principal component analysis on these. In both examples we find that the shapes evolve mainly along the first principal component during growth; this is the ‘geodesic hypothesis’ that was formulated by Le and Kume. Moreover, we could link change‐points of this evolution to significant changes in environmental conditions.

Suggested Citation

  • T. Hotz & S. Huckemann & A. Munk & D. Gaffrey & B. Sloboda, 2010. "Shape spaces for prealigned star‐shaped objects—studying the growth of plants by principal components analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(1), pages 127-143, January.
    • Handle: RePEc:bla:jorssc:v:59:y:2010:i:1:p:127-143
    DOI: 10.1111/j.1467-9876.2009.00683.x
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    References listed on IDEAS

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    1. Asger Hobolth & John T. Kent & Ian L. Dryden, 2002. "On the Relation between Edge and Vertex Modelling in Shape Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 355-374, September.
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    Cited by:

    1. Ian L. Dryden & Kwang-Rae Kim & Huiling Le, 2019. "Bayesian Linear Size-and-Shape Regression with Applications to Face Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 83-103, February.

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