Initial Results of Multilevel Principal Components Analysis of Facial Shape

  • D. J. J. Farnell
  • J. Galloway
  • A. Zhurov
  • S. Richmond
  • P. Perttiniemi
  • V. Katic
Conference paper
First Online:
Part of the Communications in Computer and Information Science book series (CCIS, volume 723)

Abstract

Traditionally, active shape models (ASMs) do not make a distinction between groups in the subject population and they rely on methods such as (single-level) principal components analysis (PCA). Multilevel principal components analysis (mPCA) allows one to model between-group effects and within-group effects explicitly. Three dimensional (3D) laser scans were taken from 250 subjects (38 Croatian female, 35 Croatian male, 40 English female, 40 English male, 23 Welsh female, 27 Welsh male, 23 Finnish female, and 24 Finnish male) and 21 landmark points were created subsequently for each scan. After Procrustes transformation, eigenvalues from mPCA and from single-level PCA based on these points were examined. mPCA indicated that the first two eigenvalues of largest magnitude related to within-groups components, but that the next eigenvalue of largest magnitude related to between-groups components. Eigenvalues from single-level PCA always had a larger magnitude than either within-group or between-group eigenvectors at equivalent eigenvalue number. An examination of the first mode of variation indicated possible mixing of between-group and within-group effects in single-level PCA. Component scores for mPCA indicated clustering with country and gender for the between-groups components (as expected), but not for the within-group terms (also as expected). Clustering of component scores for single-level PCA was harder to resolve. In conclusion, mPCA is viable method of forming shape models that offers distinct advantages over single-level PCA when groups occur naturally in the subject population.

Keywords

Multilevel principal components analysis Active shape models Facial shape 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Cootes, T.F., Hill, A., Taylor, C.J., Haslam, J.: Use of active shape models for locating structure in medical images. Image Vis. Comput. 12, 355–365 (1994)CrossRefGoogle Scholar
  2. 2.
    Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models - their training and application. Comput. Vis. Image Underst. 61, 38–59 (1995)CrossRefGoogle Scholar
  3. 3.
    Hill, A., Cootes, T.F., Taylor, C.J.: Active shape models and the shape approximation problem. Image Vis. Comput. 14, 601–607 (1996)CrossRefGoogle Scholar
  4. 4.
    Taylor, C.J., Cootes, T.F., Lanitis, A., Edwards, G., Smyth, P., Kotcheff, A.C.W.: Model-based interpretation of complex and variable images. Philos. Trans. R. Soc. Lond. Ser. B-Biol. Sci. 352, 1267–1274 (1997)CrossRefGoogle Scholar
  5. 5.
    Cootes, T.F., Taylor, C.J.: A mixture model for representing shape variation. Image Vis. Comput. 17, 567–573 (1999)CrossRefGoogle Scholar
  6. 6.
    Cootes, T.F., Edwards, G.J., Taylor, C.J.: Active appearance models. IEEE Trans. Pattern Anal. Mach. Intell. 23, 681–685 (2001)CrossRefGoogle Scholar
  7. 7.
    Cootes, T.F., Taylor, C.J.: Anatomical statistical models and their role in feature extraction. Br. J. Radiol. 77, S133–S139 (2004)CrossRefGoogle Scholar
  8. 8.
    Allen, P.D., Graham, J., Farnell, D.J.J., Harrison, E.J., Jacobs, R., Nicopolou-Karayianni, K., Lindh, C., van der Stelt, P.F., Horner, K., Devlin, H.: Detecting reduced bone mineral density from dental radiographs using statistical shape models. IEEE Trans. Inf Technol. Biomed. 11, 601–610 (2007)CrossRefGoogle Scholar
  9. 9.
    Lecron, F., Boisvert, J., Benjelloun, M., Labelle, H., Mahmoudi, S.: Multilevel statistical shape models: a new framework for modeling hierarchical structures. In: 9th IEEE International Symposium on Biomedical Imaging (ISBI), pp. 1284–1287 (2012)Google Scholar
  10. 10.
    Farnell, D.J.J., Popat, H., Richmond, S.: Multilevel principal component analysis (mPCA) in shape analysis: a feasibility study in medical and dental imaging. Comput. Methods Programs Biomed. 129, 149–159 (2016)CrossRefGoogle Scholar
  11. 11.
    Kau, C.H., Cronin, A., Durning, P., Zhurov, A.I., Sandham, A., Richmond, S.: A new method for the 3D measurement of postoperative swelling following orthognathic surgery. Orthod. Craniofac. Res. 9, 31–37 (2006)CrossRefGoogle Scholar
  12. 12.
    Kau, C.H., Hartles, F.R., Knox, J., Zhurov, A.I., Richmond, S.: Natural head posture for measuring three-dimensional soft tissue morphology. In: Middleton, J., Shrive, M.G., Jones, M.L. (eds.) Computer Methods in Biomechanics and Biomedical Engineering – 5 First Numerics Ltd., Cardiff University (2005)Google Scholar
  13. 13.
    Kau, C.H., Richmond, S.: Three-dimensional analysis of facial morphology surface changes in untreated children from 12 to 14 years of age. Am. J. Orthod. Dentofac. Orthop. 134, 751–760 (2008)CrossRefGoogle Scholar
  14. 14.
    Farkas, L.G.: Anthropometry of the Head and Face. Raven Press, New York (1994). pp 21–25Google Scholar
  15. 15.
    Hopman, S.M., Merks, J.H., Suttie, M., Hennekam, R.C., Hammond, P.: Face shape differs in phylogenetically related populations. Eur. J. Hum. Genet. 22, 1268–1271 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of DentistryCardiff UniversityCardiffUK
  2. 2.Faculty of MedicineUniversity of OuluOuluFinland
  3. 3.Department of Orthodontics, School of MedicineUniversity of RijekaRijekaCroatia

Personalised recommendations