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Theoretical and Distributional Aspects of Shape Analysis

In: Probability Measures on Groups X

Author

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  • I. L. Dryden

    (University of Leeds, Department of Statistics)

  • K. V. Mardia

    (University of Leeds, Department of Statistics)

Abstract

Summary The concept of general shape is introduced and particular cases for point sets in ℝk are considered. General shape spaces are orbit spaces and the principal groups of interest are the Euclidean similarity group and the isometry group. Distributional results for Gaussian configurations provide the main focus of the paper. Recent developments are reviewed, including using the QR decomposition, Bartlett’s decomposition and integration of the orthogonal group 0(K). Connections are made with existing work, especially with distributional results for the important K=2 dimensional case. Finally, possible extensions of all the work are considered in a discussion.

Suggested Citation

  • I. L. Dryden & K. V. Mardia, 1991. "Theoretical and Distributional Aspects of Shape Analysis," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 95-116, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_7
    DOI: 10.1007/978-1-4899-2364-6_7
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