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Structurally Complex Data

Statistical Analysis of Locally Parameterized Shapes

ORCID Icon & ORCID Icon
Pages 658-670 | Received 16 Aug 2021, Accepted 29 Jul 2022, Published online: 14 Oct 2022

References

  • Amaral, G. A., Dryden, I., and Wood, A. T. A. (2007), “Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis,” Journal of the American Statistical Association, 102, 695–707. DOI: 10.1198/016214506000001400.
  • Apostolova, L., Alves, G., Hwang, K. S., Babakchanian, S., Bronnick, K. S., Larsen, J. P., Thompson, P. M., Chou, Y. Y., Tysnes, O. B., and Vefring, H. K. (2012), “Hippocampal and Ventricular Changes in Parkinson’s Disease Mild Cognitive Impairment,” Neurobiology of Aging, 33, 2113–2124. DOI: 10.1016/j.neurobiolaging.2011.06.014.
  • Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x.
  • Berger, J. (1985), Statistical Decision Theory and Bayesian Analysis. Springer Series in Statistics, Berlin: Springer. https://books.google.no/books?id=oY/_x7dE15/_AC.
  • Blum, H. (1967), “A Transformation for Extracting New Descriptors of Shape,” Symp. on Models for the Perception of Speech and Visual Form. Cambridge, MA: MIT Press.
  • Bonferroni, C. (1936), “Teoria Statistica delle Classi e Calcolo delle Probabilita,” Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commericiali di Firenze, 8, 3–62.
  • Cartan, E. (1937), La théorie des groupes finis et continus et la géométrie différentielle: traitées par la méthode du repère mobile/leçons professées la Sorbonne par Elie Cartan,…; rédigées par Jean Leray,…Cahiers scientifiques, Paris: Gauthier-Villars.
  • Damon, J. (2008), “Swept Regions and Surfaces: Modeling and Volumetric Properties,” Theoretical Computer Science, 392, 66–91. DOI: 10.1016/j.tcs.2007.10.004.
  • Damon, J., and Marron, J. (2014), “Backwards Principal Component Analysis and Principal Nested Relations,” Journal of Mathematical Imaging and Vision, 50, 107–114. DOI: 10.1007/s10851-013-0463-2.
  • Dhillon, I. S., and Sra, S. (2003), “Modeling Data Using Directional Distributions,” Technical Report, Citeseer.
  • Dryden, I., and Mardia, K. (2016), Statistical Shape Analysis: With Applications in R. (Vol. 995). Chichester: John Wiley & Sons.
  • Fletcher, P. T., Lu, C., and Joshi, S. (2003), “Statistics of Shape via Principal Geodesic Analysis on Lie Groups,” In Proceedings, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. IEEE, vol 1, pp. I–I.
  • Fletcher, P. T., Lu, C., Pizer, S. M., and Joshi, S. (2004), “Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape,” IEEE Transactions on Medical Imaging, 23, 995–1005. DOI: 10.1109/TMI.2004.831793.
  • Gamble, J., and Heo, G. (2010), “Exploring Uses of Persistent Homology for Statistical Analysis of Landmark-Based Shape Data,” Journal of Multivariate Analysis, 101, 2184–2199. DOI: 10.1016/j.jmva.2010.04.016.
  • Huynh, D. Q. (2009), “Metrics for 3D Rotations: Comparison and Analysis,” Journal of Mathematical Imaging and Vision, 35, 155–164. DOI: 10.1007/s10851-009-0161-2.
  • Jermyn, I. H., Kurtek, S., Laga, H., Srivastava, A. (2017), “Elastic Shape Analysis of Three-Dimensional Objects,” Synthesis Lectures on Computer Vision, 12, 1–185.
  • Jung, S., Dryden, I. L., and Marron, J. (2012), “Analysis of Principal Nested Spheres,” Biometrika, 99, 551–568. DOI: 10.1093/biomet/ass022.
  • Kendall, D. G. (1977), “The Diffusion of Shape,” Advances in Applied Probability, 9, 428–430. DOI: 10.2307/1426091.
  • Kim, B., Huckemann, S., Schulz, J., and Jung, S. (2019), “Small-Sphere Distributions for Directional Data with Application to Medical Imaging,” Scandinavian Journal of Statistics, 46, 1047–1071. DOI: 10.1111/sjos.12381.
  • Kim, B., Schulz, J., and Jung, S. (2020), “Kurtosis Test of Modality for Rotationally Symmetric Distributions on Hyperspheres,” Journal of Multivariate Analysis, 178, 104603. DOI: 10.1016/j.jmva.2020.104603.
  • Laga, H., Guo, Y., Tabia, H., Fisher, R., and Bennamoun, M. (2018), 3D Shape Analysis: Fundamentals, Theory, and Applications. Hoboken, NJ: Wiley. https://books.google.no/books?id=ds16DwAAQBAJ.
  • Lele, S. R., 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, 415–427. DOI: 10.1002/ajpa.1330860307.
  • Lele, S. R., and Richtsmeier, J. T. (2001), An Invariant Approach to Statistical Analysis of Shapes. Boca Raton, FL: Chapman and Hall/CRC.
  • Liu, Z., Hong, J., Vicory, J., Damon, J. N., and Pizer, S. M. (2021), “Fitting Unbranching Skeletal Structures to Objects,” Medical Image Analysis, 70, 102020. DOI: 10.1016/j.media.2021.102020.
  • Martin, N., and H. Maes. (1979). Multivariate analysis. London, UK: Academic Press.
  • Moakher, M. (2002), “Means and Averaging in the Group of Rotations,” SIAM Journal on Matrix Analysis and Applications, 24, 1–16 DOI: 10.1137/S0895479801383877.
  • Pizer, S. M., Fritsch, D. S., Yushkevich, P. A., Johnson, V. E., and Chaney, E. L. (1999), “Segmentation, Registration, and Measurement of Shape Variation via Image Object Shape,” IEEE Transactions on Medical Imaging, 18, 851–865. DOI: 10.1109/42.811263.
  • Pizer, S. M., Fletcher, P. T., Thall, A., Styner, M., Gerig, G., and Joshi, S. (2003), “Object Models in Multiscale Intrinsic Coordinates via m-Reps,” Image and Vision Computing, 21, 5–15. DOI: 10.1016/S0262-8856(02)00130-0.
  • Pizer, S. M., Jung, S., Goswami, D., Vicory, J., Zhao, X., Chaudhuri, R., Damon, J. N., Huckemann, S., and Marron, J. (2013), “Nested Sphere Statistics of Skeletal Models,” in Innovations for Shape Analysis, Berlin, Heidelberg: Springer, pp. 93–115.
  • Rustamov, R. M., Lipman, Y., and Funkhouser, T. (2009), “Interior Distance Using Barycentric Coordinates,” in Computer Graphics Forum, Oxford, UK: Blackwell Publishing Ltd, Vol. 28, pp. 1279–1288. DOI: 10.1111/j.1467-8659.2009.01505.x.
  • Schulz, J. (2013), “Statistical Analysis of Medical Shapes and Directional Data,” PhD thesis, UiT Norges arktiske universitet.
  • Siddiqi, K., and Pizer, S. (2008), Medial Representations: Mathematics, Algorithms and Applications. Computational Imaging and Vision, Dordrecht, Netherlands: Springer Netherlands
  • Sorkine, O. (2006), “Differential Representations for Mesh Processing,” in Computer Graphics Forum, Oxford, UK: Blackwell Publishing Ltd, vol. 25, pp. 789–807. DOI: 10.1111/j.1467-8659.2006.00999.x.
  • Srivastava, A. and Klassen, E. (2016), Functional and Shape Data Analysis. Springer. Series in Statistics, New York: Springer, https://books.google.no/books?id=0cMwDQAAQBAJ.
  • Styner, M., Oguz, I., Xu, S., Brechbühler, C., Pantazis, D., Levitt, J. J., Shenton, M. E., and Gerig, G. (2006), “Framework for the Statistical Shape Analysis of Brain Structures Using spharm-pdm.” The Insight Journal, 242–250. DOI: 10.54294/owxzil.
  • Tabia, H., and Laga, H. (2015), “Covariance-Based Descriptors for Efficient 3D Shape Matching, Retrieval, and Classification,” IEEE Transactions on Multimedia, 17, 1591–1603. DOI: 10.1109/TMM.2015.2457676.
  • Turner, K., Mukherjee, S., and Boyer, D. M. (2014), “Persistent Homology Transform for Modeling Shapes and Surfaces,” Information and Inference: A Journal of the IMA, 3, 310–344. DOI: 10.1093/imaiai/iau011.
  • Van Kaick, O., Zhang, H., Hamarneh, G., and Cohen-Or, D. (2011), “A Survey on Shape Correspondence,” in Computer Graphics Forum, Oxford, UK: Blackwell Publishing Ltd, vol. 30, pp. 1681–1707. DOI: 10.1111/j.1467-8659.2011.01884.x.