Converting Truss Interlandmark Distances to Cartesian Coordinates

  • Kent E. Carpenter
  • H. Joseph SommerIII
  • Leslie F. Marcus
Chapter
Part of the NATO ASI Series book series (NSSA, volume 284)

Abstract

Coordinate-based landmark data are required to use many of the recent advances in morphometrics, although interlandmark distance measurements were used extensively in the past. In many cases the latter are still being used in morphometric research. The conversion of distance data to coordinate data is not straightforward because insufficient measurement redundancy among landmarks and measurement error obscures the possibility of direct geometric reconstruction. Iterative multivariate methods and redundant measurements, such as the truss protocol, allow for a reasonably accurate conversion of interlandmark distance data into coordinate landmark data. We examine two multidimensional scaling methods for making this conversion. One is based on the nonmetric method found in the statistical package, NTSYS-pc, and the other is a simplified weighted least squares method tailored for this type of conversion. The latter method is amenable to heuristic modification and found to be more accurate than the former, although the NTSYS-pc based method may be more convenient for some users.

Keywords

Redundant Measurement Landmark Data Caudal Skeleton Temporary Flattener Iterative Relaxation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Becerra, J. M., E. Bello, and A. García-Valdecasas. 1993. Building your own machine image system for morphometric analysis: a user point of view. In: L. F. Marcus, E. Bello, and A. García-Valdecasas (eds.), Contributions to morphometrics. Monografias del Museo Nacional de Ciencias Naturales 8, Madrid. Pages 65–94.Google Scholar
  2. 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.CrossRefGoogle Scholar
  3. Bookstein, F. L. 1991. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.Google Scholar
  4. Bookstein, F. L., B. Grayson, C. B. Cutting, H. C. Kim, and J. G. Mc Carthy. 1991. Landmarks in three dimensions: reconstruction from cephalograms versus direct observation. American Journal of Orthod. Dentofacial Orthop. 100 (2): 133–140.CrossRefGoogle Scholar
  5. Bookstein, F. L., B. Chemoff, R. L. Elder, J. M. Humphries, Jr., G. R. Smith, and R. E. Strauss, (eds.), 1985. Morphometrics in evolutionary biology: The geometry of size and shape change, with examples from fishes. Academy of Natural Sciences of Philadelphia Special Publication 15.Google Scholar
  6. Davison, M.L. 1983. Multidimensional Scaling. John Wiley and Sons: New York.Google Scholar
  7. Goodall, C. 1991. Procrustes methods in the statistical analysis of shape. Journal of the Royal Statistical Society, B 53: 285–339.Google Scholar
  8. Kruskal, J. B. 1964a. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika. 29: 1–27.CrossRefGoogle Scholar
  9. Kruskal, J. B. 1964b. Nonmetric multidimensional scaling: a numerical method. Psychometrika. 29: 28–42.Google Scholar
  10. Lele, S. and J. T. Richtsmeier 1992. On comparing biological shapes: detection of influential landmarks. American Journal of Physical Anthropology 87: 49–65.PubMedCrossRefGoogle Scholar
  11. Rohlf, F. J. 1993. NTSYS-pc, Version 1. 8. Exeter Publishing: Setauket, New York.Google Scholar
  12. Rohlf, F. J. and J. W. Archie. 1978. Least-squares mapping using interpoint distances. Ecology. 59: 26–132.CrossRefGoogle Scholar
  13. Roth, V. L. 1993. On three-dimensional morphometrics, and on the identification of landmark points. In: L. F. Marcus, E. Bello, and A. García-Valdecasas, (eds.), Contributions to morphometrics. Monografias del Museo Nacional de Ciencias Naturales 8, Madrid. Pages 41–66.Google Scholar
  14. SAS for Personal Computers, Release 6.03. 1988. SAS Institute: Cary, North Carolina.Google Scholar
  15. Strauss, R. E., and F. L. Bookstein 1982. The truss: body form reconstruction in morphometrics. Systematic Zoology 31 (2): 113–135.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Kent E. Carpenter
    • 1
  • H. Joseph SommerIII
    • 2
  • Leslie F. Marcus
    • 3
  1. 1.Department of Biological SciencesOld Dominion UniversityNorfolkUSA
  2. 2.Department of Mechanical EngineeringThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of BiologyQueens College of the City University of New YorkFlushingUSA

Personalised recommendations