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CHARACTERIZATION OF MAMMARY GLAND TISSUE USING
JOINT ESTIMATORS OF MINKOWSKI FUNCTIONALS
June 2005
TORSTEN MATTFELDT, DANIEL MESCHENMOSER, URSA PANTLE AND VOLKER
SCHMIDT
A theoretical approach to estimate the Minkowski functionals, i.e., area fraction, specific boundary length and
specific Euler number in 2D, and their asymptotic covariance matrix proposed by Spodarev and Schmidt (2005)
and Pantle et al. (2006a;b) is applied to real image data. These two-dimensional images show mammary gland
tissue and should be classified automatically as tumor-free or mammary cancer, respectively. The estimation
procedure is illustrated step-by-step and the calculations are described in detail. To reduce dependencies from
chosen parameters, a least-squares approach is considered as recommended by Klenk et al. (2006). Emphasis
is placed on the detailed description of the estimation procedure and the application of the theory to real image
data.
Asymptotic Covariance Matrix, Breast Cancer, Mammary Carcinoma, Mammary Gland Tissue,
Minkowski Functionals, Random Closed Set, Specific Intrinsic Volumes.
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