The Offset Normal Shape Distribution for Dynamic Shape Analysis

References

• Al-Jewair, T., Stellrecht, E., Lewandowski, L., and Chakakic, R. (2018), “American Association of Orthodontists Foundation Craniofacial Growth Legacy Collection in the Orthodontic Literature Use and Trends: A Systematic Review,” American Journal of Orthodontics and Dentofacial Orthopedics, 153, 15–25. DOI: 10.1016/j.ajodo.2017.07.015.
   PubMed Web of Science ®Google Scholar
• Boda, R., and Priyadarsini, M. J. P. (2016), “Face Detection and Tracking Using KLT and Viola Jones,” ARPN Journal of Engineering and Applied Sciences, 11, 13472–13476.
   Google Scholar
• Bookstein, F. L. (1986), “Size and Shape Spaces for Landmark Data in Two Dimensions,” Statistical Science, 1, 181–242. DOI: 10.1214/ss/1177013696.
   Google Scholar
• Bookstein, F. L. (2014), Measuring and Reasoning: Numerical Inference in the Sciences, Cambridge: Cambridge University Press.
   Google Scholar
• Brombin, C., Salmaso, L., Fontanella, L., and Ippoliti, L. (2015), “Nonparametric Combination-Based Tests in Dynamic Shape Analysis,” Journal of Nonparametric Statistics, 27, 460–484. DOI: 10.1080/10485252.2015.1071811.
   Web of Science ®Google Scholar
• Brombin, C., Salmaso, L., Fontanella, L., Ippoliti, L., and Fusilli, C. (2016), Parametric and Nonparametric Inference for Statistical Dynamic Shape Analysis with Applications (SpringerBriefs in Statistics), Berlin: Springer.
   Google Scholar
• Dempster, A. P. Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 34, 1–38. DOI: 10.1111/j.2517-6161.1977.tb01600.x.
   Google Scholar
• Dryden, I. L., and Mardia, K. V. (1991), “General Shape Distributions in the Plane,” Advances in Applied Probability, 23, 259–276. DOI: 10.2307/1427747.
   Web of Science ®Google Scholar
• Dryden, I. L., and Mardia, K. V. (2016), Statistical Shape Analysis with Applications in R (Wiley Series in Probability and Statistics), Chichester: Wiley.
   Google Scholar
• Ekman, P., Friesen, W. V., and Hager, J. C. (2002), Facial Action Coding System Investigator’s Guide, Salt Lake City, UT: Consultant Pschologists Press.
   Google Scholar
• Franchi, L., Baccetti, T., and McNamara, J. A. (2001), “Thin-Plate Spline Analysis of Mandibular Growth,” Angle Orthodontist, 71, 83–89. DOI: 10.1043/0003-3219(2001)071<0083:TPSAOM>2.0.CO;2.
   PubMed Web of Science ®Google Scholar
• Genton, M. G. (2007), “Separable Approximations of Space-Time Covariance Matrices,” Environmetrics, 18, 681–695. DOI: 10.1002/env.854.
   Web of Science ®Google Scholar
• He, Q., Duan, Y., Karsch, K., and Miles, J. (2010), “Detecting Corpus Callosum Abnormalities in Autism Based on Anatomical Landmarks,” Psychiatry Research: Neuroimaging, 183, 126–132. DOI: 10.1016/j.pscychresns.2010.05.006.
   Web of Science ®Google Scholar
• Huang, C., Styner, M., and Zhu, H. (2015), “Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data,” Journal of the American Statistical Association, 110, 946–961. DOI: 10.1080/01621459.2015.1034802.
   PubMed Web of Science ®Google Scholar
• Kan, R. (2008), “From Moments of Sum to Moments of Product,” Journal of Multivariate Analysis, 99, 542–554. DOI: 10.1016/j.jmva.2007.01.013.
   Web of Science ®Google Scholar
• Kendall, D. G. (1991), “The Mardia-Dryden Distribution for Triangles: A Stochastic Calculus Approach,” Journal of Applied Probability, 28, 239–247.
   Web of Science ®Google Scholar
• Kenobi, K., Dryden, I. L., and Le, H. (2010), “Shape Curves and Geodesic Modeling,” Biometrika, 97, 567–584. DOI: 10.1093/biomet/asq027.
   Web of Science ®Google Scholar
• Kent, J. T., and Mardia, K. V. (1997), “Consistency of Procrustes Estimators,” Journal of the Royal Statistical Society, Series B, 59, 281–290. DOI: 10.1111/1467-9868.00069.
   Google Scholar
• Kent, J. T., Mardia, K. V., Morris, R. J., and Aykroyd, R. G. (2001), “Functional Models of Growth for Landmark Data,” in Proceedings in Functional and Spatial Data Analysis, eds. K. V. Mardia, J. T. Kent, and R. G. Aykroyd, Berlin: Springer, pp. 109–115.
   Google Scholar
• Kent, J. T., Mardia, K. V., and McDonnell, P. (2006), “The Complex Bingham Quartic Distribution and Shape Analysis,” Journal of the Royal Statistical Society, Series B, 68, 747–765. DOI: 10.1111/j.1467-9868.2006.00565.x.
   Google Scholar
• Kume, A., and Welling, M. (2010), “Maximum Likelihood Estimation for the Offset-Normal Shape Distributions Using EM,” Journal of Computational and Graphical Statistics, 19, 702–723. DOI: 10.1198/jcgs.2010.09190.
   Web of Science ®Google Scholar
• Kume, A., Dryden, I. L., and Le, H. (2007), “Shape Space Smoothing Splines for Planar Landmark Data,” Biometrika, 94, 513–528. DOI: 10.1093/biomet/asm047.
   Web of Science ®Google Scholar
• Kume, A., Dryden, I. L., and Wood, A. T. A. (2017), “Shape Inference Based on Multivariate Normal Matrix Distributions,” Technical Report, University of Kent.
   Google Scholar
• Le, H. (1998), “On the Consistency of Procrustean Mean Shapes,” Advances in Applied Probability, 30, 53–63. DOI: 10.1239/aap/1035227991.
   Web of Science ®Google Scholar
• Le, H., and Kume, A. (2000), “Detection of Shape Changes in Biological Features,” Journal of Microscopy, 2, 140–147.
   Google Scholar
• Le, H., and Small, C. G. (1999), “Multidimensional Scaling of Simplex Shapes,” Pattern recognition, 32, 1601–1613. DOI: 10.1016/S0031-3203(99)00023-0.
   Web of Science ®Google Scholar
• Lele, S., and Richtsmeier, J. T. (1991), “Euclidean Distance Matrix Analysis: A Coordinate-Free Approach for Comparing Biological Shapes Using Landmark Data,” American Journal of Physical Anthropology, 86, 239–359.
   Web of Science ®Google Scholar
• Magnus, J. (1986), “The Exact Moments of a Ratio of Quadratic Forms in Normal Variables,” Annales d’Economie et de Statistique, 4, 95–109.
   Google Scholar
• Mardia, K. V., and Dryden, I. L. (1989), “The Statistical Analysis of Shape Data,” Biometrika, 76, 271–281. DOI: 10.1093/biomet/76.2.271.
   Web of Science ®Google Scholar
• Mardia, K. V., and Walder, A. N. (1994), “Shape Analysis of Paired Landmark Data,” Biometrika, 81, 185–196. DOI: 10.1093/biomet/81.1.185.
   Web of Science ®Google Scholar
• Mathai, A. M., and Provost, S. B. (1992), Quadratic Forms in Random Variables: Theory and Applications. New York: Marcel Dekker.
   Google Scholar
• Moyers, R. E., and Bookstein, F. L. (1979), “The Inappropriateness of Conventional Cephalometrics,” American Journal of Orthodontics, 75, 599–617. DOI: 10.1016/0002-9416(79)90093-9.
   PubMedGoogle Scholar
• Neeser, F. D., and Massey, J. L. (1993), “Proper Complex Random Processes With Applications to Information Theory,” IEEE Transaction on Information Theory, 39, 1293–1302. DOI: 10.1109/18.243446.
   Web of Science ®Google Scholar
• Oyonarte, R., Hurtado, M., and Castro, M. V. (2016), “Evolution of ANB and SN-GoGn Angles During Craniofacial Growth: A Retrospective Longitudinal Study,” APOS Trends in Orthodontics, 6, 295–301. DOI: 10.4103/2321-1407.194796.
   Google Scholar
• Pantic, M., Cowie, R., Drrico, F., Heylen, D., Mehu, M., and Pelachaud, P. (2011), “Social Signal Processing: The Research Agenda,” in Visual Analysis of Humans, London: Springer, pp. 511–538.
   Google Scholar
• Sridhar, P. K. (2011), Textbook of Craniofacial Growth, New Delhi: Jaypee Brothers Medical Publishers.
   Google Scholar
• Stuart, A., and Ord, K. (1994), “Kendall’s Advanced Theory of Statistics,” in Distribution Theory, London: Arnold.
   Google Scholar
• Wallhoff, F. (2006), “Facial Expressions and Emotion Database,” available at http://www.mmk.ei.tum.de/∼waf/fgnet/feedtum.html.
   Google Scholar
• Wang, N., Xinbo, G., Dacheng, T., Heng, Y., and Xuelong, L. (2018), “Facial Feature Point Detection: A Comprehensive Survey,” Neurocomputing, 275, 50–65. DOI: 10.1016/j.neucom.2017.05.013.
   Web of Science ®Google Scholar