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A nonparametric approach to 3D shape analysis from digital camera images -- I

Author

Listed:
  • Patrangenaru, V.
  • Liu, X.
  • Sugathadasa, S.

Abstract

This article for the first time develops a nonparametric methodology for the analysis of projective shapes of configurations of landmarks on real 3D objects from their regular camera pictures. A fundamental result in computer vision, emulating the principle of human vision in space, claims that, generically, a finite 3D configuration of points can be retrieved from corresponding configurations in a pair of camera images, up to a projective transformation. Consequently, the projective shape of a 3D configuration can be retrieved from two of its planar views, and a projective shape analysis can be pursued from a sample of images. Projective shapes are here regarded as points on projective shape manifolds. Using large sample and nonparametric bootstrap methodology for extrinsic means on manifolds, one gives confidence regions and tests for the mean projective shape of a 3D configuration from its 2D camera images. Two examples are given: an example of testing for accuracy of a simple manufactured object using mean projective shape analysis, and a face identification example. Both examples are data driven based on landmark registration in digital images.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:11-31
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Rabi Bhattacharya & Rachel Oliver, 2019. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-36, February.

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