1 3 Med Biol Eng Comput DOI 10.1007/s11517-015-1267-x ORIGINAL ARTICLE Erythrocyte shape classification using integral-geometry-based methods X. Gual-Arnau 1 · S. Herold-García 2 · A. Simó 3 Received: 2 May 2013 / Accepted: 2 March 2015 © International Federation for Medical and Biological Engineering 2015 with other deformations present in the images. A process of automatic classification, with cross-validation of errors with the proposed descriptors and with other two functions used in previous studies, was realized. Keywords Contour functions · Erythrocytes · Shape classification · Integral geometry 1 Introduction Sickle cell disease (SCD) is one of the most common genetic diseases and has been recognized as a major public health problem by international agencies, such as the World Health Organization (WHO) and the United Nations Edu- cational, Scientific and Cultural Organization (UNESCO). SCD causes the hardening or polymerization of the hemo- globin that contains the erythrocytes, leading to sickle- shaped red blood cells. Sickle-shaped means that the eryth- rocytes are shaped like a crescent. Sickle cells tend to block blood flow in the blood vessels and result in a risk of vari- ous complications, for example the risk of vaso-occlusive crisis. The patients that have this disease are classified into three types: those with a benignant form, who do not have pain crisis, those with a moderate form, who only have one crisis a year, and the seriously ill that have two or more cri- ses per year. They all have deformed cells in their blood, in lesser or greater quantity according to their condition. The treatment depends on this condition, and in general, it is a moisturizing treatment that does not cause collateral prob- lems. If the patient is seriously ill, the quantity of elongated cells is very high and he should receive anti-deforming treatments, applied periodically. Quantitative analysis of digital images has been applied previously to the study and classification of erythrocytes, Abstract Erythrocyte shape deformations are related to different important illnesses. In this paper, we focus on one of the most important: the Sickle cell disease. This disease causes the hardening or polymerization of the hemoglobin that contains the erythrocytes. The study of this process using digital images of peripheral blood smears can offer useful results in the clinical diagnosis of these illnesses. In particular, it would be very valuable to find a rapid and reproducible automatic classification method to quantify the number of deformed cells and so gauge the severity of the illness. In this paper, we show the good results obtained in the automatic classification of erythrocytes in normal cells, sickle cells, and cells with other deformations, when we use a set of functions based on integral-geometry methods, an active contour-based segmentation method, and a k-NN clas- sification algorithm. Blood specimens were obtained from patients with Sickle cell disease. Seventeen peripheral blood smears were obtained for the study, and 45 images of differ- ent fields were obtained. A specialist selected the cells to use, determining those cells which were normal, elongated, and * A. Simó simo@uji.es X. Gual-Arnau gual@uji.es S. Herold-García silena@csd.uo.edu.cu 1 Institute of New Imaging Technologies, Universitat Jaume I, 12071 Castelló, Spain 2 Departamento de Computación, Universidad de Oriente, Santiago de Cuba, Cuba 3 Institut Universitari de Matemàtiques i Aplicacions de Castelló, Universitat Jaume I, Avda. del Riu Sec s/n, 12071 Castellón, Spain