A Hermite polynomial algorithm for detection of lesions in lymphoma images
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ORIGINAL ARTICLE
A Hermite polynomial algorithm for detection of lesions in lymphoma images Alessandro S. Martins1 · Leandro A. Neves2 · Paulo R. de Faria3 · Thaína A. A. Tosta4 · Leonardo C. Longo2 · Adriano B. Silva5 · Guilherme Freire Roberto5 · Marcelo Z. do Nascimento5 Received: 4 February 2020 / Accepted: 27 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract There are different types of lesions that can be investigated with the hematoxylin–eosin staining protocol. Lymphoma is a type of malignant disease which affects one of the highest white blood cell populations responsible for the immunological defence system. There are lymphoma sub-types that can have similar features, which make their diagnoses a difficult task. In this study, we investigated algorithms based on multiscale and multidimensional fractal geometry with colour models for classification of lymphoma images. Fractal features were extracted from the colour models and separate channels from these models. These features were concatenated to form feature vectors. Finally, we investigated the Hermite polynomial classifier and machine learning algorithms in order to evaluate the performance of the proposed approach. We employed the tenfold cross-validation method and evaluated the lesion sub-types with the binary and multiclass classifications. The separated colour channels obtained from histological images achieved relevant values for the binary and multiclass classifications, with an accuracy rating between 91 and 97%. These results can contribute to the detection and classification of the lesions by supporting specialists in clinical practices. Keywords Colour fractal · Colour spaces · Hermite polynomial · Classification · Lymphoma
1 Introduction Lymphoma is a type of malignant disease that affects one of the highest white blood cell populations responsible for the immunological defence system of the body [14]. This * Alessandro S. Martins [email protected] Leandro A. Neves [email protected] Paulo R. de Faria [email protected] Thaína A. A. Tosta [email protected] Leonardo C. Longo [email protected] Adriano B. Silva [email protected] Guilherme Freire Roberto [email protected]
type of malignant disease develops in cellular components called lymphocytes [30]. It can be diagnosed as a Hodgkin lymphoma (HL) or non-Hodgkin lymphoma (NHL) based on the information from morphological, genetic and clinical features [22]. According to published statistics, nearly 2530 1
Federal Institute of Triângulo Mineiro (IFTM), Rua Belarmino Vilela Junqueira sn, Ituiutaba, Minas Gerais 38305‑200, Brazil
2
Department of Computer Science and Statistics (DCCE), São Paulo State University (UNESP), Rua Cristóvão Colombo, 2265, São José do Rio Preto, São Paulo 15054‑000, Brazil
3
Department of Histology and Morphology, Institute of Biomedical Science, Federal University of Uberlândia, Uberlândia, Minas Gerais, Brazil
4
Science and Technology Institute, Federal University of São Paulo
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