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The study of cell morphology is an important aspect of the diagnosis of some diseases, such as sickle cell disease, because red blood cell deformation is caused by these diseases. Due to the elongated shape of the erythrocyte, ellipse adjustment and concave point detection are applied widely to images of peripheral blood samples, including during the detection of cells that are partially occluded in the clusters generated by the sample preparation process. In the present study, we propose a method for the analysis of the shape of erythrocytes in peripheral blood smear samples of sickle cell disease, which uses ellipse adjustments and a new algorithm for detecting notable points. Furthermore, we apply a set of constraints that allow the elimination of significant image preprocessing steps proposed in previous studies. We used three types of images to validate our method: artificial images, which were automatically generated in a random manner using a computer code; real images from peripheral blood smear sample images that contained normal and elongated erythrocytes; and synthetic images generated from real isolated cells. Using the proposed method, the efficiency of detecting the two types of objects in the three image types exceeded 99.00%, 98.00%, and 99.35%, respectively. These efficiency levels were superior to the results obtained with previously proposed methods using the same database, which is available at http://erythrocytesidb.uib.es/. This method can be extended to clusters of several cells and it requires no user inputs.

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In this paper, the fuzzy morphological gradients from the fuzzy mathematical morphologies based on t-norms and conjunctive uninorms are deeply analyzed in order to establish which pair of conjunction and fuzzy implications are optimal, in accordance with their performance in edge detection applications. A novel three-step algorithm based on the fuzzy morphology is proposed. The comparison is performed by means of the so-called Pratt's figure of merit. In addition, a statistical analysis is carried out to study the relationship between the different configurations and to establish a classification of the conjunctions and implications considered. Both the objective measure and the statistical analysis conclude that the pairs nilpotent minimum t-norm and the KleeneDienes implication, and the idempotent uninorm obtained with the classical negation as a generator and its residual implication, are the best configurations in this approach, because they also obtain competitive results with respect to other approaches.

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