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2 International Journal of Applied Mathematics and Computer Science

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Breast cancer nuclei segmentation and classification based on a deep learning approach

Kowal Marek, Skobel Marcin, Gramacki Artur, Korbicz Józef

International Journal of Applied Mathematics and Computer Science

2021

Vol. 31, no. 1

85--106

One of the most popular methods in the diagnosis of breast cancer is fine-needle biopsy without aspiration. Cell nuclei are the most important elements of cancer diagnostics based on cytological images. Therefore, the first step of successful classification of cytological images is effective automatic segmentation of cell nuclei. The aims of our study include (a) development of segmentation methods of cell nuclei based on deep learning techniques, (b) extraction of some morphometric, colorimetric and textural features of individual segmented nuclei, (c) based on the extracted features, construction of effective classifiers for detecting malignant or benign cases. The segmentation methods used in this paper are based on (a) fully convolutional neural networks and (b) the marker-controlled watershed algorithm. For the classification task, seven various classification methods are used. Cell nuclei segmentation achieves 90% accuracy for benign and 86% for malignant nuclei according to the F-score. The maximum accuracy of the classification reached 80.2% to 92.4%, depending on the type (malignant or benign) of cell nuclei. The classification of tumors based on cytological images is an extremely challenging task. However, the obtained results are promising, and it is possible to state that automatic diagnostic methods are competitive to manual ones.

Two-stage instrumental variables identification of polynomial Wiener systems with invertible nonlinearities

Janczak Andrzej, Korbicz Józef

International Journal of Applied Mathematics and Computer Science

2019

Vol. 29, no. 3

571--580

A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.