The Morphometric Synthesis: A Brief Intellectual History

  • Fred L. Bookstein
Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 100)

Abstract

For most of the twentieth century, techniques for the biometric analysis of organic form fell into one of two incompatible styles. In the first, more indigenous style, a direct extension of techniques introduced into statistics by Galton, Pearson, and their heirs, conventional multivariate techniques were applied to a diverse roster of measures of single forms. The only algebraic structures involved were those of multivariate statistics, limited mainly to covariance matrices; no aspect of the geometric organization of the measures, or their biological rationale, was reflected in the method. Analyses of this mode led at best to path diagrams, not to sketches of typical organisms expressing the developmental or functional import of the coefficients computed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blackith, R. Morphometrics. Pp. 225–249 in T. H. Waterman and H. J. Morowitz, eds., Theoretical and Mathematical Biology. New York: Blaisdell, 1965.Google Scholar
  2. Blackith, R., and R. Reyment. Multivariate Morphometries. New York: Academic Press, 1971.Google Scholar
  3. Bookstein, F. L. The Measurement of Biological Shape and Shape Change. Lecture Notes in Biomathematics, v. 24. New York: Springer-Verlag, 1978.MATHCrossRefGoogle Scholar
  4. Bookstein, F. L. On the cephalometrics of skeletal change. American Journal of Orthodontics 82:177–198, 1982a.CrossRefGoogle Scholar
  5. Bookstein, F. L. Foundations of morphometries. Annual Reviews of Ecology and Systematics 13:451–470, 19826.Google Scholar
  6. Bookstein, F. L. A statistical method for biological shape comparisons. Journal of Theoretical Biology 107:475–520, 1984a.CrossRefGoogle Scholar
  7. Bookstein, F. L. Tensor biometrics for changes in cranial shape. Annals of Human Biology 11:413–437, 19846.Google Scholar
  8. Bookstein, F. L. Size and shape spaces for landmark data in two dimensions. Statistical Science 1:181–242, 1986.MATHCrossRefGoogle Scholar
  9. Bookstein, F. L. Principal warps: thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:567–585, 1989a.MATHCrossRefGoogle Scholar
  10. Bookstein, F. L. “Size and shape”: a comment on semantics. Systematic Zoology 38:173–180, 1989b.CrossRefGoogle Scholar
  11. Bookstein, F. L. Morphometric Tools for Landmark Data. New York: Cambridge University Press, 1991.MATHGoogle Scholar
  12. Bookstein, F. L., B. Chernoff, R. Elder, J. Humphries, G. Smith, and R. Strauss. Morphometries in Evolutionary Biology. Philadelphia: Academy of Natural Sciences of Philadelphia, 1985.Google Scholar
  13. Bookstein, F. L., and W. D. K. Green. A feature space for edgels in images with landmarks. Journal of Mathematical Imaging and Vision 3: 231–261, 1993.MATHCrossRefGoogle Scholar
  14. Boyd, E. Origins of the Study of Human Growth. University of Oregon Health Sciences Center, 1980.Google Scholar
  15. Burnaby, T. P. Growth-invariant discriminant functions and generalized distances. Biometrics 22:96–110, 1966.MathSciNetMATHCrossRefGoogle Scholar
  16. Corruccini, R. S. Analytical techniques for Cartesian coordinate data with reference to the relationships between Hylobates and Symphalangus. Systematic Zoology 30:32–40, 1981.CrossRefGoogle Scholar
  17. Duncan, O. D. Notes on Social Measurement: Historical and Critical. New York: Russell Sage Foundation, 1984.Google Scholar
  18. Dürer, A. Vier Bücher von Menschlicher Proportion. Somewhere in Northern Europe, 1528.Google Scholar
  19. Goodall, C. R. The statistical analysis of growth in two dimensions. Doctoral dissertation, Department of Statistics, Harvard University, 1983.Google Scholar
  20. Goodall, C. R. Procrustes methods in the statistical analysis of shape. Journal of the Royal Statistical Society B53:285–339, 1991.MathSciNetGoogle Scholar
  21. Goodall, C. R., and K. Mardia. A geometric derivation of the shape density. Advances in Applied Probability 23:496–514, 1991.MathSciNetMATHCrossRefGoogle Scholar
  22. Hopkins, J. W. Some considerations in multivariate allometry. Biometrics 22:747–760, 1966.CrossRefGoogle Scholar
  23. Hotelling, H. Relations between two sets of variables. Biometrika 28:321–377, 1936.MATHGoogle Scholar
  24. Humphries, J. M., F. Bookstein, B. Chernoff, G. Smith, R. Elder, and S. Poss. Multivariate discrimination by shape in relation to size. Systematic Zoology 30:291–308, 1981.CrossRefGoogle Scholar
  25. Huxley, J. Principles of Relative Growth. London: Methuen, 1932.Google Scholar
  26. Jolicoeur, P. The multivariate generalization of the allometry equation. Biometrics 19:497–499, 1963.CrossRefGoogle Scholar
  27. Kendall, D. G. Shape-manifolds, procrustean metrics, and complex projective spaces. Bulletin of the London Mathematical Society 16:81–121, 1984.MathSciNetMATHCrossRefGoogle Scholar
  28. Kuhn, T. S. The function of measurement in modern physical science. Pp. 31–63 in H. Woolf, ed., Quantification. Indianapolis: Bobbs-Merrill, 1959.Google Scholar
  29. Latour, B. Science in Action. Cambridge: Harvard University Press, 1987.Google Scholar
  30. Lewis, J. L., W. Lew, and J. Zimmerman. A nonhomogeneous anthropometric scaling method based on finite element principles. Journal of Biomechanics 13:815–824, 1980.CrossRefGoogle Scholar
  31. Lohmann, G. P. Eigenshape analysis of microfossils: a general morphometric procedure for describing changes in shape. Mathematical Geology 15:659–672, 1983.CrossRefGoogle Scholar
  32. Mackenzie, D. A. Statistics in Britain, 1865–1930: The Social Construction of Scientific Knowledge. Edinburgh: Edinburgh University Press, 1981.Google Scholar
  33. Mardia, K. V., and I. Dryden. The statistical analysis of shape data. Biometrika 76:271–282, 1989.MathSciNetMATHCrossRefGoogle Scholar
  34. Mosimann, J. E. Size allometry: size and shape variables with characterizations of the log-normal and generalized gamma distributions. Journal of the American Statistical Association 65:930–945, 1970.MATHGoogle Scholar
  35. Oxnard, C. E. Form and Pattern in Human Evolution. Chicago: University of Chicago Press, 1973.Google Scholar
  36. Oxnard, C. E. One biologist’s view of morphometrics. Annual Reviews of Ecology and Systematics 9:219–241, 1978.CrossRefGoogle Scholar
  37. Reyment, R. A. Multivariate Paleobiology. Oxford: Pergamon, 1991.Google Scholar
  38. Richards, O. W., and A. C. Kavanagh. The analysis of relative growth-gradients and changing form of growing organisms: illustrated by the tobacco leaf. American Naturalist 77:385–399, 1943.CrossRefGoogle Scholar
  39. Rohlf, F. J. The relationships among eigenshape analysis, Fourier analysis, and the analysis of coordinates. Mathematical Geology 18:845–854, 1986.CrossRefGoogle Scholar
  40. Rohlf, F. J. Relative warp analysis and an example of its application to mosquito wings. Pp. 131–159 in L. F. Marcus, E. Bello, and A. G. Valdecasas, eds., Contributions to Morphometrics., Madrid: Museo Nacional de Ciencias Naturales, 1993.Google Scholar
  41. Rohlf, F. J., and F. Bookstein, eds. Proceedings of the Michigan Morphometries Workshop. Ann Arbor: University of Michigan Museums, 1990.Google Scholar
  42. Sampson, P. D., F. Bookstein, S. Lewis, C. Hurley, and P. Guttorp. Computation and application of deformations for landmark data in morphometries and environmetrics. Pp. 534–541 in E. Keramidas, ed., Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface. Fairfax Station, VA: Interface Foundation of North America, Inc., 1991.Google Scholar
  43. Sneath, P. H. A., and R. R. Sokal. Principles of Numerical Taxonomy. San Francisco: W. H. Freeman, 1963.Google Scholar
  44. Sneath, P. H. A. Trend-surface analysis of transformation grids. Journal of Zoology 151:65–122, 1967.CrossRefGoogle Scholar
  45. Thompson, D. A. W. On Growth and Form. London: Macmillan, 1917.Google Scholar
  46. Wright, S. Evolution and the Genetics of Populations. Vol. 1: Genetic and Biometrie Foundations. Chicago: University of Chicago Press, 1968.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Fred L. Bookstein
    • 1
  1. 1.Center for Human Growth & DevelopmentUniversity of MichiganAnn ArborUSA

Personalised recommendations