Classification of spatial textures in benign and cancerous glandular tissues by stereology and stochastic geometry using artificial neural networks


Professor Dr T. Mattfeldt Department of Pathology, Oberer Eselsberg M23, D-89081 Ulm, Germany. Fax: +49 731 58738; e-mail:


Stereology and stochastic geometry can be used as auxiliary tools for diagnostic purposes in tumour pathology. Whether first-order parameters or stochastic-geometric functions are more important for the classification of the texture of biological tissues is not known. In the present study, volume and surface area per unit reference volume, the pair correlation function and the centred quadratic contact density function of epithelium were estimated in three case series of benign and malignant lesions of glandular tissues. The information provided by the latter functions was summarized by the total absolute areas between the estimated curves and their horizontal reference lines. These areas are considered as indicators of deviation of the tissue texture from a completely uncorrelated volume process and from the Boolean model with convex grains, respectively. We used both areas and the first-order parameters for the classification of cases using artificial neural networks (ANNs). Learning vector quantization and multilayer feedforward networks with backpropagation were applied as neural paradigms. Applications included distinction between mastopathy and mammary cancer (40 cases), between benign prostatic hyperplasia and prostatic cancer (70 cases) and between chronic pancreatitis and pancreatic cancer (60 cases). The same data sets were also classified with linear discriminant analysis. The stereological estimates in combination with ANNs or discriminant analysis provided high accuracy in the classification of individual cases. The question of which category of estimator is the most informative cannot be answered globally, but must be explored empirically for each specific data set. Using learning vector quantization, better results could often be obtained than by multilayer feedforward networks with backpropagation.