Abstract
The resistant-fit methods of superimposing configurations of landmarks are extended to three-dimensional data. Algorithms are described for fitting one configuration to another and for the fitting of a sample of configurations to a iteratively estimated consensus configuration. In addition, several topics relating to the practical use of the superimposition methods are discussed. These topics include missing data, visualization of results and the display and interpretation of affine components. Finally, an example is presented of how to use different graphical comparisons of resistant-fit and least-squares (Procrustes) residuals to identify subsets of landmarks contributing to localized shape differences. These procedures are shown to suggest considerable local variation in the posterior region of the carapace of certain individual yellow-bellied slider turtles, Trachemys scripta scripta.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anton, H. 1984. Calculus, with analytic geometry. John Wiley & Sons: New York.
Bookstein, F. L. 1984. Tensor biometrics for changes in cranial shape. Annals of Human Biology 11: 413–437
Bookstein, F. L. 1989. Principal warps: Thin-plate splines and the decomposition of deformations. I. E. E. E. Transactions on Pattern Analysis and Machine Intelligence 11: 567–585.
Bookstein, F. L. 1991. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.
Bookstein, F. L. and P. Sampson. 1987. Statistical models for geometric components of shape change. Pages 18–27 in Proceedings of the Section on Statistical Graphics, 1987 Annual Meeting of the American Statistical Association. American Statistical Association: Alexandria, Virginia.
Cagle, F. R. 1950. The life history of the slider turtle, Pseudemys scripta troostii (Holbrook). Ecological Monographs 20 (1): 32–54.
Dryden, I. L., and K. V. Mardia. 1991. General shape distributions in a plane. Advances in Applied Probability 23: 259–276.
Eves, H. 1966. Elementary matrix theory. Allyn and Bacon, Inc.: Boston.
Goodall, C. R. 1991. Procrustes methods in the statistical analysis of shape (with discussion and rejoinder). Journal of the Royal Statistical Society, Series B, 53 (2): 285–339.
Goodall, C. R. 1992. Dynamic graphics in non-Euclidean spaces: the visualization and statistical analysis of shape. 1992 Proceedings of the Statistical Graphics Section. American Statistical Association: Alexandria, Virginia.
Goodall, C. R., and P. B. Green. 1986. Quantitative analysis of surface growth. Botanical Gazette 147: 1–15.
Goodall, C. R., and K. V. Mardia. 1991. A geometrical derivation of the shape density. Advances in Applied Probability 23: 496–514.
Gower, J. C. 1970. Statistical methods of comparing different multivariate analyses of the same data. Pages 138–149 in F. R. Hodson, D. G. Kendall, and P. Tautu (eds.), Mathematics in the archaeological and historical sciences. Edinburgh University Press: Edinburgh.
Gower, J. C. 1975. Generalized Procrustes analysis. Psychometrika 40: 33–51.
Hartman, S. E. 1989. Stereophotographic analysis of occlusal morphology of extant hominoid molars: phenetics and function. American Journal of Physical Anthropology 80 (2): 145–166.
Jolicoeur, P., and J. E. Mosimann. 1960. Size and shape variation in the painted turtle, a principal component analysis. Growth 24: 339–354.
Mardia, K. V. and I. L. Dryden. 1989. Shape distributions for landmark data. Advances in Applied Probability 21: 742–755.
Mosier, C. I. 1939. Determining a simple structure when loadings for certain tests are known. Psychometrika 4: 149–162.
Rohlf, F. J. and L. F. Marcus. 1993. A revolution in morphometrics. Trends in Ecology and Evolution 8 (4): 129–132.
Rohlf, F. J., and D. E. Slice. 1990. Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Zoology. 39: 40–59.
Siegel, A. F., and R. H. Benson. 1982. A robust comparison of biological shapes. Biometrics 38: 341–350.
Siegel, A. F., and J. R. Pinkerton. 1982. Robust comparison of three-dimensional shapes with an application to protein molecule configurations. Technical Report 217, Series 2, Department of Statistics, Princeton University.
Slice, D. E. 1991. DS-DIGIT: Basic digitizing software. Department of Ecology and Evolution, State University of New York at Stony Brook, Stony Brook, New York 117–94.
Slice, D. E. 1993. Extensions, comparisons, and applications of superimposition methods for morphometric analysis. Ph. D. dissertation. State University of New York at Stony Brook.
Slice, D. E. 1994. GRF-ND: Generalized rotational fitting of N-dimensional data. Department of Ecology and Evolution. State University of New York at Stony Brook, Stony Brook, New York 11794.
Sneath, P. H. A. 1967. Trend-surface analysis of transformation grids. Journal of Zoology 151: 65–122.
Walker, J. A. 1994. Morphometrika. Geometric morphometrics for the Macintosh. Department of Anatomical Sciences. State University of New York at Stony Brook, Stony Brook, New York, 11794.
Zangerl, R. 1969. The turtle shell. Pages 311–339 in C. A. Gans, A. d’A. Bellairs, and T. S. Parsons (eds.), Biology of the Reptilia. Volume 1. Academic Press: New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Slice, D.E. (1996). Three-Dimensional Generalized Resistant Fitting and the Comparison of Least-Squares and Resistant-Fit Residuals. In: Marcus, L.F., Corti, M., Loy, A., Naylor, G.J.P., Slice, D.E. (eds) Advances in Morphometrics. NATO ASI Series, vol 284. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9083-2_15
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9083-2_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9085-6
Online ISBN: 978-1-4757-9083-2
eBook Packages: Springer Book Archive