Two Sample Tests for Mean 3D Projective Shapes from Digital Camera Images

  • Vic Patrangenaru
  • Mingfei Qiu
  • Marius Buibas


In this article, we extend mean 3D projective shape change in matched pairs to independent samples. We provide a brief introduction of projective shapes of spatial configurations obtained from their digital camera images, building on previous results of Crane and Patrangenaru (J Multivar Anal 102:225–237, 2011). The manifold of projective shapes of k-ads in 3D containing a projective frame at five given landmark indices has a natural Lie group structure, which is inherited from the quaternion multiplication. Here, given the small sample size, one estimates the mean 3D projective shape change in two populations, based on independent random samples of possibly different sizes using Efron’s nonparametric bootstrap. This methodology is applied in three relevant applications of analysis of 3D scenes from digital images: visual quality control, face recognition, and scene recognition.


3D scene reconstruction from a pair of uncalibrated camera views 3D projective shape Quaternions Fréchet means Extrinsic mean change on a Lie group Asymptotic statistics on manifolds Nonparametric bootstrap on manifolds Computational statistics Visual quality control Face recognition 

AMS 2000 Subject Classifications

Primary 62H11; Secondary 62H10 62H35 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of StatisticsFlorida State UniversityTallahasseeUSA
  2. 2.Brain CorporationSan DiegoUSA

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