CHARACTERIZATION OF MAMMARY GLAND TISSUE USING JOINT ESTIMATORS OF MINKOWSKI FUNCTIONALS

Torsten Mattfeldt, Daniel Meschenmoser, Ursa Pantle, Volker Schmidt

Abstract

A theoretical approach to estimate the Minkowski functionals, i.e., area fraction, specifc boundary length and specifc 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 classifed 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.

Keywords
asymptotic covariance matrix; breast cancer; mammary carcinoma; mammary gland tissue; Minkowski functionals; random closed set; specifc intrinsic volumes

Full Text:

PDF


DOI: 10.5566/ias.v26.p13-22

Copyright (c) 2014 Image Analysis & Stereology

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)