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  • Limit distributions of some stereological estimators in Wicksell's corpuscle problem
    Heinrich, Lothar
    Suppose that a homogeneous system of spherical particles (d-spheres) with independent identically distributed radii is contained in some opaque d-dimensional body, and one is interested to estimate ... the common radius distribution. The only information one can get is by making a cross-section ofthat body with an s-flat (1 <= s <= d - 1) and measuring the radii of the s-spheres and their midpoints. The analytical solution of (the hyper-stereological version of) Wicksell's corpuscle problem is used to construct an empirical radius distribution of the d-spheres. In this paper we study the asymptotic behaviour of this empirical radius distribution for s = d- 1 and s = d - 2 under the assumption that the s-dimensional intersection volume becomes unboundedly large and the point process of the midpoints of thed-spheres is Brillinger-mixing. Of course, in stereological practice the only relevant cases are d = 3, s = 2 or s = 1 and d = 2, s = 1. Among others we generalize and extend some results obtained in Franklin (1981) and Groeneboom and Jongbloed (1995) under the Poisson assumption for the special case d = 3, s = 2.
    Vir: Image analysis & stereology : official journal of the International Society for Stereology. - ISSN 1580-3139 (Vol. 26, no. 2, jun. 2007, str. 63-71)
    Vrsta gradiva - članek, sestavni del
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 23777753

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    Digitalna knjižnica Slovenije - dLib.si

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