Fractal Characterization of Nuclear Texture in Breast Cytology: Frequency and Spatial Domain Approaches
Andrew Jeffrey Einstein, H.-S. Wu, J. Gil · Birkhäuser Basel eBooks · 1998
The diagnosis of breast epithelial cell lesions in cytology is subject to considerable inter-observer variability, and therefore the need for adjuvant diagnostic modalities such as image analysis is acute. Chromatin appearance is among the most important of the criteria used by cytologists in the diagnosis of neoplasia, and its effective quantitative description is of great importance for the automation of cytological screening and diagnosis using image analysis procedures. This study explores the possibility that fractal dimension may be used to characterize chromatin texture. The digitized light microscopic image of a nucleus is viewed as a surface by plotting intensity as a function of position in the image. The fractal nature of this putative statistically self-affine surface can then be characterized both in the spatial domain, with a Minkowski-Bouligand dimension, and in the frequency domain, with a spectral exponent. Since conventional frequency domain approaches assume a rectangular image, a new iterative approach is suggested for determining the spectral exponent of a nuclear image, called the iterative spectral dimension method. These methods were applied to describe chromatin appearance in fine needle aspiration biopsies of the breast from eight patients with benign epithelial cell lesions and 11 with carcinomas. Chromatin appearance is shown to be statistically self-affine in breast epithelial cell nuclear images. While the mean Minkowski dimension did not differ significantly between the benign and malignant patients, the average mean spectral fractal dimension differed significantly (p = 0.0057) between benign (D S = 2.844) and malignant (D S = 2.799) cases. Using logistic regression to classify patients based on their mean fractal texture dimensions and nuclear areas, 16 of the 19 cases were diagnosed correctly. Fractals are an appropriate paradigm for describing chromatin appearance and they provide important diagnostic information.