Shape Statistics: Procrustes Superimpositions and Tangent Spaces

F. James Rohlf

Journal of Classification, 1999, vol. 16, issue 2, 197-223

Abstract: The shape of a set of labeled points corresponds to those attributes of the configuration that are invariant to the effects of translation, rotation, and scale. Procrustes distance may be used to compare different shapes and also serve as a metric that may be used to define multidimensional shape spaces. This paper demonstrates that the preshape space of planar triangles Procrustes aligned to a reference triangle corresponds to a unit hemisphere. An overview of methods used as linear approximations of D. G. Kendall's non-Euclidean shape space is given, and the equivalence of several methods based on orthogonal projections is shown. Some problems with approximations based on stereo graphic projections are also discussed. A simple example using artificial data is included. Copyright Springer-Verlag New York Inc. 1999

Keywords: Key words: Kendall shape space; Preshape space; Tangent space; Partial warps; Multivariate analysis., (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://hdl.handle.net/10.1007/s003579900054 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jclass:v:16:y:1999:i:2:p:197-223

Ordering information: This journal article can be ordered from
http://www.springer. ... hods/journal/357/PS2

DOI: 10.1007/s003579900054

Access Statistics for this article

Journal of Classification is currently edited by Douglas Steinley

More articles in Journal of Classification from Springer, The Classification Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().