IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v16y1999i2p197-223.html
   My bibliography  Save this article

Shape Statistics: Procrustes Superimpositions and Tangent Spaces

Author

Listed:
  • F. James Rohlf

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

Suggested Citation

  • F. James Rohlf, 1999. "Shape Statistics: Procrustes Superimpositions and Tangent Spaces," Journal of Classification, Springer;The Classification Society, vol. 16(2), pages 197-223, July.
    • Handle: RePEc:spr:jclass:v:16:y:1999:i:2:p:197-223
    DOI: 10.1007/s003579900054
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s003579900054
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s003579900054?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Robert G Wallace, 2002. "The Shape of Space: Applying Geometric Morphometrics to Geographic Data," Environment and Planning A, , vol. 34(1), pages 119-144, January.
    2. Sean T. Osis & Blayne A. Hettinga & Shari L. Macdonald & Reed Ferber, 2015. "A novel method to evaluate error in anatomical marker placement using a modified generalized Procrustes analysis," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(10), pages 1108-1116, July.
    3. Yousuke Kaifu & Iwan Kurniawan & Soichiro Mizushima & Junmei Sawada & Michael Lague & Ruly Setiawan & Indra Sutisna & Unggul P. Wibowo & Gen Suwa & Reiko T. Kono & Tomohiko Sasaki & Adam Brumm & Gerri, 2024. "Early evolution of small body size in Homo floresiensis," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    4. Irene Epifanio & María Victoria Ibáñez & Amelia Simó, 2018. "Archetypal shapes based on landmarks and extension to handle missing data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 705-735, September.
    5. Manuel Dehon & Denis Michez & André Nel & Michael S Engel & Thibaut De Meulemeester, 2014. "Wing Shape of Four New Bee Fossils (Hymenoptera: Anthophila) Provides Insights to Bee Evolution," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-16, October.
    6. Maria Carla de Francesco & Anna Loy, 2016. "Intra- and Interspecific Interactions as Proximate Determinants of Sexual Dimorphism and Allometric Trajectories in the Bottlenose Dolphin Tursiops truncatus (Cetacea, Odontoceti, Delphinidae)," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-19, October.
    7. Brandon P Hedrick & Peter Dodson, 2013. "Lujiatun Psittacosaurids: Understanding Individual and Taphonomic Variation Using 3D Geometric Morphometrics," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-13, August.
    8. Katherine L Bell & Christopher A Hamm & Arthur M Shapiro & Chris C Nice, 2017. "Sympatric, temporally isolated populations of the pine white butterfly Neophasia menapia, are morphologically and genetically differentiated," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-17, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jclass:v:16:y:1999:i:2:p:197-223. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.