IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i9p1867-1882.html
   My bibliography  Save this article

Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging

Author

Listed:
  • Bandulasiri, Ananda
  • Bhattacharya, Rabi N.
  • Patrangenaru, Vic

Abstract

For all p>2,k>p, a size-and-reflection-shape space of k-ads in general position in , invariant under translation, rotation and reflection, is shown to be a smooth manifold and is equivariantly embedded in a space of symmetric matrices, allowing a nonparametric statistical analysis based on extrinsic means. Equivariant embeddings are also given for the reflection-shape-manifold , a space of orbits of scaled k-ads in general position under the group of isometries of , providing a methodology for statistical analysis of three-dimensional images and a resolution of the mathematical problems inherent in the use of the Kendall shape spaces in p-dimensions, p>2. The Veronese embedding of the planar Kendall shape manifold is extended to an equivariant embedding of the size-and-shape manifold , which is useful in the analysis of size-and-shape. Four medical imaging applications are provided to illustrate the theory.

Suggested Citation

  • Bandulasiri, Ananda & Bhattacharya, Rabi N. & Patrangenaru, Vic, 2009. "Nonparametric inference for extrinsic means on size-and-(reflection)-shape manifolds with applications in medical imaging," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1867-1882, October.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:1867-1882
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00065-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. Gordana Derado & Kanti Mardia & Vic Patrangenaru & Hilary Thompson, 2004. "A Shape-based Glaucoma Index for Tomographic Images," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(10), pages 1241-1248.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Kovacev-Nikolic Violeta & Bubenik Peter & Nikolić Dragan & Heo Giseon, 2016. "Using persistent homology and dynamical distances to analyze protein binding," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(1), pages 19-38, March.
    2. Crane, M. & Patrangenaru, V., 2011. "Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 225-237, February.
    3. Osborne, Daniel & Patrangenaru, Vic & Ellingson, Leif & Groisser, David & Schwartzman, Armin, 2013. "Nonparametric two-sample tests on homogeneous Riemannian manifolds, Cholesky decompositions and Diffusion Tensor Image analysis," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 163-175.
    4. Ellingson, Leif & Patrangenaru, Vic & Ruymgaart, Frits, 2013. "Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 317-333.
    5. Ruite Guo & Hwiyoung Lee & Vic Patrangenaru, 2023. "Test for Homogeneity of Random Objects on Manifolds with Applications to Biological Shape Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1178-1204, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Crane, M. & Patrangenaru, V., 2011. "Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 225-237, February.

    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:eee:jmvana:v:100:y:2009:i:9:p:1867-1882. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.