Converting Truss Interlandmark Distances to Cartesian Coordinates
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.
KeywordsRedundant Measurement Landmark Data Caudal Skeleton Temporary Flattener Iterative Relaxation
Unable to display preview. Download preview PDF.
- 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
- Bookstein, F. L. 1991. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.Google Scholar
- 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
- Davison, M.L. 1983. Multidimensional Scaling. John Wiley and Sons: New York.Google Scholar
- Goodall, C. 1991. Procrustes methods in the statistical analysis of shape. Journal of the Royal Statistical Society, B 53: 285–339.Google Scholar
- Kruskal, J. B. 1964b. Nonmetric multidimensional scaling: a numerical method. Psychometrika. 29: 28–42.Google Scholar
- Rohlf, F. J. 1993. NTSYS-pc, Version 1. 8. Exeter Publishing: Setauket, New York.Google Scholar
- 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
- SAS for Personal Computers, Release 6.03. 1988. SAS Institute: Cary, North Carolina.Google Scholar