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On the Relation between Edge and Vertex Modelling in Shape Analysis

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  • ASGER HOBOLTH
  • JOHN T. KENT
  • IAN L. DRYDEN

Abstract

Objects in the plane with no obvious landmarks can be described by either vertex transformation vectors or edge transformation vectors. In this paper we provide the relation between the two transformation vectors. Grenander & Miller (1994) use a multivariate normal distribution with a block circulant covariance matrix to model the edge transformation vector. This type of model is also feasible for the vertex transformation vector and in certain cases the free parameters of the two models match up in a simple way. A vertex model and an edge model are applied to a data set of sand particles to explore shape variability.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:3:p:355-374
    DOI: 10.1111/1467-9469.00295
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    Cited by:

    1. Asger Hobolth & Jan Pedersen & Eva Jensen, 2003. "A continuous parametric shape model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 227-242, June.
    2. 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.

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