Converting Truss Interlandmark Distances to Cartesian Coordinates

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.