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

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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.

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Acknowledgments

The authors would like to thank Vlad P. Patrangenaru for introducing us to the software in Sect. 5. We are also grateful to two referees for their reports that helped us improve the quality of the paper. Victor Patrangenaru was Research supported by NSA-MSP- H98230-14-1-0135 and NSF-DMS-1106935, K. David Yao was Research supported by NSA-MSP- H98230-14-1-0135 and NSF-DMS-1106935, Mingfei Qiu was Research supported by NSF-DMS-1106935, David Lester was Research supported by NSA-MSP- H98230-14-1-0135

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Authors and Affiliations

  1. Department of Statistics, Florida State University, Tallahassee, USA

    Victor Patrangenaru, K. David Yao, Mingfei Qiu & David Lester

  2. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, USA

    Robert Paige

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  1. Victor Patrangenaru
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  2. Robert Paige
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  3. K. David Yao
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  4. Mingfei Qiu
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  5. David Lester
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Correspondence to Victor Patrangenaru.

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Patrangenaru, V., Paige, R., Yao, K.D. et al. Projective shape analysis of contours and finite 3D configurations from digital camera images. Stat Papers 57, 1017–1040 (2016). https://doi.org/10.1007/s00362-016-0824-1

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  • DOI: https://doi.org/10.1007/s00362-016-0824-1

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