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  • On mean densities of inhomogenous geomtreic processes arising in material science and medicine
    Capasso, Vincenzo, 1945- ; Villa, Elena
    The scope of this paper is to offer an overview of the main results obtained by the authors in recent literature in connection with the introduction of a Delta formalism, a la Dirac-Schwartz, for ... random generalized functions (distributions) associated with random closed sets, having an integer Hausdorff dimension n lower than the full dimension d of the environment spaceRd. A concept of absolute continuity of random closed sets arises in a natural way in terms of the absolute continuity of suitable mean content measures, with respect to the usual Lebesgue measure on Rd. Correspondingly mean geometric densities are introduced with respect to the usual Lebesgue measure; approximating sequences are provided, that are of interest for the estimation of mean geometric densities of lower dimensional random sets such as fibre processes, surface processes, etc. Many models in material science and in biomedicine include time evolution of random closed sets, describing birthand- growth processes; the Delta formalism provides a natural framework for deriving evolution equations for mean densities at all (integer) Hausdorffdimensions, in terms of the relevant kinetic parameters.
    Source: Image analysis & stereology : official journal of the International Society for Stereology. - ISSN 1580-3139 (Vol. 26, no. 1, mar. 2007, str. 23-36)
    Type of material - article, component part
    Publish date - 2007
    Language - english
    COBISS.SI-ID - 23922137

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