A nonparametric approach to 3D shape analysis from digital camera images – II

References

• R. Bhattacharya and V. Patrangenaru, Large sample theory of intrinsic and extrinsic sample means on manifolds. I, Ann. Statist. 31 (2003), pp. 1–29. doi: 10.1214/aos/1046294456
   Web of Science ®Google Scholar
• R. Bhattacharya and V. Patrangenaru, Large sample theory of intrinsic and extrinsic sample means on manifolds. II, Ann. Statist. 33 (2005), pp. 1225–1259. doi: 10.1214/009053605000000093
   Web of Science ®Google Scholar
• M. Crane and V. Patrangenaru, Random change on a Lie group and mean glaucomatous projective shape change detection from stereo pair images, J. Multivariate Anal. 102 (2011), pp. 225–237. doi: 10.1016/j.jmva.2010.08.012
   Web of Science ®Google Scholar
• B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Statist. 7 (1979), pp. 1–26. doi: 10.1214/aos/1176344552
   Web of Science ®Google Scholar
• L. Ellingson, V. Patrangenaru, and F Ruymgaart, Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours, J. Multivar. Anal. 122 (2013), pp. 317–333. doi: 10.1016/j.jmva.2013.08.010
   Web of Science ®Google Scholar
• O. Faugeras, What can be seen in three dimensions with an uncalibrated stereo rig?, in Proc. European Conference on Computer Vision, Santa Margherita Ligure, LNCS, Vol. 588, 1992, pp. 563–578.
   Google Scholar
• R.I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed., Cambridge University Press, New York, NY, 2004.
   Google Scholar
• R.I. Hartley, R. Gupta, and T. Chang, Stereo from uncalibrated cameras, in Proceedings IEEE Conference on Computer Vision and Pattern Recognition, Champaign, IL, 1992, pp. 761–764.
   Google Scholar
• S.F. Huckemann, Intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth, Ann. Statist. 39 (2011), pp. 1098–1124. doi: 10.1214/10-AOS862
   Web of Science ®Google Scholar
• D.G. Kendall, Shape manifolds, Procrustean metrics, and complex projective spaces, Bull. London Math. Soc. 16 (1984), pp. 81–121. doi: 10.1112/blms/16.2.81
   Web of Science ®Google Scholar
• A. Kriegl and P. Michor, The Convenient Setting of Global Analysis, Mathematical Surveys and Monographs, vol. 52, American Mathematical Society, Providence, Rhode Island, 1997.
   Google Scholar
• E. Kreyszig, Introductory Functional Analysis with Applications, Wiley, New York, 1989.
   Google Scholar
• Y. Ma, S. Soatto, J. Kosecka, and S.S. Sastry, An Invitation to 3-D Vision, Springer, New York, 2006.
   Google Scholar
• K.V. Mardia and V. Patrangenaru, Directions and projective shapes, Ann. Statist. 33 (2005), pp. 1666–1699. doi: 10.1214/009053605000000273
   Web of Science ®Google Scholar
• A. Munk, R. Paige, J. Pang, V. Patrangenaru, and F.H. Ruymgaart, The one- and multi-sample problem for functional data with application to projective shape analysis, J. Multivariate Anal. 99 (2008), pp. 815–833. doi: 10.1016/j.jmva.2007.04.007
   Web of Science ®Google Scholar
• V. Patrangenaru, New large sample and bootstrap methods on shape spaces in high level analysis of natural images, Comm. Statist. Theory Methods 30 (2001), pp. 1675–1693. doi: 10.1081/STA-100105692
   Web of Science ®Google Scholar
• V. Patrangenaru and L.E. Ellingson, Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis, CRC Texts in Statistical Science, CRC Press, Boca Raton, FL, 2015.
   Google Scholar
• V. Patrangenaru, X. Liu, and S. Sugathadasa, Nonparametric 3D projective shape estimation from pairs of 2D images - I, In memory of W.P. Dayawansa, J. Multivariate Anal. 101 (2010), pp. 11–31. doi: 10.1016/j.jmva.2009.02.010
   Google Scholar
• V. Patrangenaru, M. Qiu, and M Buibas, Two sample tests for mean 3D projective shapes from digital camera images, Methodol. Comput. Appl. Probab. 16 (2014), pp. 485–506. doi: 10.1007/s11009-013-9363-6
   Web of Science ®Google Scholar
• M. Qiu, V. Patrangenaru, and L. Ellingson, How far is the Corpus Callosum of an Average Individual from Albert Einstein's? in Proceedings of COMPSTAT-2014, The 21st International Conference on Computational Statistics, Geneva, August 19–22, G. Manfred, G.-R. Gil and N.-R. Alicia, eds., 2014, pp. 403–410.
   Google Scholar
• O. Rodrigues, Des lois géométriques qui régissent les déplacements d'un système solide dans l'éspace, et la variation des coordonnées provenant de ses déplacements considérés indépendamment des causes qui peuvent les produire, J. Math. Pures Appl. 5 (1840), pp. 380–440.
   Google Scholar