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Point Processes of Cylinders, Particles and Flats

In: Stochastic and Integral Geometry

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  • Wolfgang Weil

    (Universität Karlsruhe, Mathematisches Institut II)

Abstract

Point processes X of cylinders, compact sets (particles), or flats in ℝ d are mathematical models for fields of sets as they occur, e.g., in practical problems of image analysis and stereology. For the estimation of geometric quantities of such fields, mean value formulas for X are important. By a systematic approach, integral geometric formulas for curvature measures are transformed into density formulas for geometric point processes. In particular, a number of results which are known for stationary and isotropic Poisson processes of convex sets are generalized to nonisotropic processes, to non-Poissonian processes, and to processes of nonconvex sets. The integral geometric background (including recent results from translative integral geometry), the fundamentals of geometric point processes, and the resulting density formulas are presented in detail. Generalizations of the theory and applications in image analysis and stereology are mentioned shortly.

Suggested Citation

  • Wolfgang Weil, 1987. "Point Processes of Cylinders, Particles and Flats," Springer Books, in: R. V. Ambartzumian (ed.), Stochastic and Integral Geometry, pages 103-136, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3921-9_8
    DOI: 10.1007/978-94-009-3921-9_8
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