CLASSIFICATION OF BINARY SPATIAL TEXTURES USING STOCHASTIC GEOMETRY, NONLINEAR DETERMINISTIC ANALYSIS AND ARTIFICIAL NEURAL NETWORKS

Abstract

Stereology and stochastic geometry can be used as auxiliary tools for diagnostic purposes in tumour pathology. The role of first-order parameters and stochastic–geometric functions for the classification of the texture of biological tissues has been investigated recently. The volume fraction and surface area per unit 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. This approach was further extended by applying the Laslett test, i.e. a point process statistic computed after transformation of the convex tangent points of sectioned random sets from planar images. This method has not yet been applied to histological images so far. Also the nonlinear deterministic approach to tissue texture was applied by estimating the correlation dimension as a function of embedding dimension. We used the stochastic–geometric functions, the first-order parameters and the correlation dimensions for the classification of cases using various algorithms. Learning vector quantization was applied as neural paradigm. Applications included distinction between mastopathy and mammary cancer, between benign prostatic hyperplasia and prostatic cancer, and between chronic pancreatitis and pancreatic cancer. The same data sets were also classified with discriminant analysis and support vector machines. The stereological estimates provided high accuracy in the classification of individual cases. The question: which category of estimator is the most informative, cannot be answered globally, but must be explored empirically for each specific data set. The results obtained by the three algorithms were similar.