Theoretical and Distributional Aspects of Shape Analysis

I. L. Dryden and K. V. Mardia
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I. L. Dryden: University of Leeds, Department of Statistics
K. V. Mardia: University of Leeds, Department of Statistics

A chapter in Probability Measures on Groups X, 1991, pp 95-116 from Springer

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.

Keywords: Gaussian distribution; Orthogonal group; Reflection; Shape; Shape space; Size; Special orthogonal group (search for similar items in EconPapers)
Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2364-6_7

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DOI: 10.1007/978-1-4899-2364-6_7

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