Introduction to Outlines

  • F. James Rohlf
Part of the NATO ASI Series book series (NSSA, volume 284)


The articles in this section demonstrate that despite the emphasis in recent years on landmark-based morphometric methods (e.g., Bookstein, 1991; Rohlf and Marcus, 1993) there have also been important advances in methods for the analysis of outline data. This is important because in many cases there are not enough landmarks, or not enough in the right places to capture the variation in shape of the biological structure of interest adequately. The methods Rohlf and Bookstein ( 1990) discussed consisted simply of fitting various functions (usually weighted sums of sine and cosine terms) to an outline curve-or else deriving an “empirical function” (actually, just weighted linear combinations of tangent angles) to describe an outline as in eigenshape analysis. The four papers in this section represent distinct new approaches or important extensions to existing approaches.


Empirical Function Weighted Linear Combination Important Extension Bezier Curve Space Curf 
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  1. Bookstein, F. L., and W. D. K. Green. 1993a. A thin-plate spline for deformations with specified derivatives. Pages 14–28 in Mathematical methods in medical Imaging II. S.P.I.E. Proceedings vol. 2035.CrossRefGoogle Scholar
  2. Bookstein, F. L., and W. D. K. Green 1993b. A feature space for edgels in images with landmarks. Journal of Mathematical Imaging and Vision 3: 231–261.CrossRefGoogle Scholar
  3. Bookstein, F. L. 1991. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.Google Scholar
  4. Roth, L. 1993. On three-dimensional morphometries, and on the identification oflandmark points. Pages 41–61 in L. F. Marcus, E. Bello, and A. Garcia-Valdecasas, (eds.), Contributions to morphometries. Monografias del Museo Nacional de Ciencias 8, Madrid.Google Scholar
  5. Rohlf, F. J., and F. L. Bookstein (eds.) 1990. Proceedings of the Michigan morphometrics workshop. University of Michigan Museum of Zoology Special Publication 2.Google Scholar
  6. Rohlf, F. J., and L. F. Marcus. 1993. A revolution in morphometrics. Trends in Ecology and Evolution 8: 129–132.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 1996

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  • F. James Rohlf

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