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1 results

  • Stereological versions of integral geometric formulae for n-dimensional ellipsoids

  • E. B. Jensen, J. Møller
  • Journal:
    Journal of Applied Probability / Volume 23 / Issue 4 / December 1986
    Published online by Cambridge University Press:
    24 August 2016, pp. 1031-1037
    Print publication:
    December 1986

  • Recently, unbiased stereological estimators of moments of particle volume, based on measurements on lower-dimensional sections through the particles, have been developed by Jensen and Gundersen (1985). In this note, we derive an explicit form of these unbiased estimators valid for particles in Rn of ellipsoidal shape, and we establish a close relationship between the estimators and a known integral geometric formula for ellipsoids, due to Furstenberg and Tzkoni (1971). Furthermore, a stereological version of another integral geometric formula for n-dimensional ellipsoids, due to Guggenheimer (1973), is derived.