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A Survey of the Statistical Theory of Shape
Open accessAbstract
This is a review of the current state of the "theory of shape" introduced by the author in 1977. It starts with a definition of "shape" for a set of $k$ points in $m$ dimensions. The first task is to identify the shape spaces in which such objects naturally live, and then to examine the probability structures induced on such a shape space by corresponding structures in $\mathbf{R}^m$. Against this theoretical background one formulates and solves statistical problems concerned with shape characteristics of empirical sets of points. Some applications (briefly sketched here) are to archeology, astronomy, geography and physical chemistry. We also outline more recent work on "size-and-shape," on shapes of sets of points in riemannian spaces, and on shape-theoretic aspects of random Delaunay tessellations.
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Cited by
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Bookstein, F. L. (1989) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.24792 · Cited by 4,913
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Schlager, S. (2017) · Statistical Shape and Deformation Analysis · doi:10.1016/b978-0-12-810493-4.00011-0 · Cited by 894
Thermal Fluctuations of Singular Bar-Joint Mechanisms
Mannattil, M., Schwarz, J. M., & Santangelo, C. D. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.208005 · Cited by 7
Metadata
- Authors
- Kendall, D. G.
- Venue
- Statistical Science
- Publisher
- Institute of Mathematical Statistics
- Published
- 1989-05-01
- Volume
- 4
- Issue
- 2
- ISSN
- 0883-4237 (ISSN-L)
- OpenAlex
- W1986442311
- Cited by
- 568
- References
- 0
- FWCI
- 15.28
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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