IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v57y2016i4d10.1007_s00362-016-0824-1.html
   My bibliography  Save this article

Projective shape analysis of contours and finite 3D configurations from digital camera images

Author

Listed:
  • Victor Patrangenaru

    (Florida State University)

  • Robert Paige

    (Missouri University of Science and Technology)

  • K. David Yao

    (Florida State University)

  • Mingfei Qiu

    (Florida State University)

  • David Lester

    (Florida State University)

Abstract

We analyze infinite dimensional projective shape data collected from digital camera images, focusing on two-sample hypothesis testing for both finite and infinite extrinsic mean configurations. The two sample test methodology is based on a Lie group technique that was derived by Crane and Patrangenaru (J Multivar Anal 102:225–237, 2011) and Qiu et al. (Neighborhood hypothesis testing for mean change on infinite dimensional Lie groups and 3D projective shape analysis of matched contours, 2015). In infinite dimensions, the equality of two extrinsic means is likely to be rejected, thus a neighborhood hypothesis is suitably tested, combining the ideas in these two papers with data analysis methods on Hilbert manifolds in Ellingson et al. (J Multivar Anal 122:317–333, 2013). In this manuscript, we apply these general results to the two sample problem for independent projective shapes of 3D facial configurations and for matched projective shapes of 2D and 3D contours. Digital images of 3D scenes are today at the fingertips of any statistician. Here and in the literature referenced in the in this paper, we provide a methodology for properly analyzing such data, when more pictures of a given scene are available.

Suggested Citation

  • Victor Patrangenaru & Robert Paige & K. David Yao & Mingfei Qiu & David Lester, 2016. "Projective shape analysis of contours and finite 3D configurations from digital camera images," Statistical Papers, Springer, vol. 57(4), pages 1017-1040, December.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0824-1
    DOI: 10.1007/s00362-016-0824-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0824-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0824-1?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.

    References listed on IDEAS

    as
    1. Munk, A. & Paige, R. & Pang, J. & Patrangenaru, V. & Ruymgaart, F., 2008. "The one- and multi-sample problem for functional data with application to projective shape analysis," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 815-833, May.
    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. 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.
    4. Vic Patrangenaru & Mingfei Qiu & Marius Buibas, 2014. "Two Sample Tests for Mean 3D Projective Shapes from Digital Camera Images," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 485-506, June.
    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. Vic Patrangenaru & Peter Bubenik & Robert L. Paige & Daniel Osborne, 2019. "Challenges in Topological Object Data Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 244-271, February.
    2. Luca Frigau & Claudio Conversano & Francesco Mola, 2021. "Consistent validation of gray-level thresholding image segmentation algorithms based on machine learning classifiers," Statistical Papers, Springer, vol. 62(3), pages 1363-1386, June.
    3. 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.
    4. Bhattacharya, Rabi & Oliver, Rachel, 2020. "Superiority of Bayes estimators over the MLE in high dimensional multinomial models and its implication for nonparametric Bayes theory," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

    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. Fabian J.E. Telschow & Michael R. Pierrynowski & Stephan F. Huckemann, 2021. "Functional inference on rotational curves under sample‐specific group actions and identification of human gait," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1256-1276, December.
    2. Vic Patrangenaru & Peter Bubenik & Robert L. Paige & Daniel Osborne, 2019. "Challenges in Topological Object Data Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 244-271, February.
    3. Vic Patrangenaru & Mingfei Qiu & Marius Buibas, 2014. "Two Sample Tests for Mean 3D Projective Shapes from Digital Camera Images," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 485-506, June.
    4. Vic Patrangenaru & Yifang Deng, 2021. "Extrinsic Regression and Anti-Regression on Projective Shape Manifolds," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 629-646, June.
    5. 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.
    6. Patrangenaru, V. & Liu, X. & Sugathadasa, S., 2010. "A nonparametric approach to 3D shape analysis from digital camera images -- I," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 11-31, January.
    7. Amanda Plunkett & Junyong Park, 2019. "Two-sample test for sparse high-dimensional multinomial distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 804-826, September.
    8. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    9. 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.
    10. 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.
    11. Luis Gutiérrez & Ramsés H. Mena & Carlos Díaz-Avalos, 2020. "Linear models for statistical shape analysis based on parametrized closed curves," Statistical Papers, Springer, vol. 61(3), pages 1213-1229, June.
    12. 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.

    More about this item

    Statistics

    Access and download statistics

    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:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0824-1. 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: 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.