Red blood cell (RBC) deformation is the consequence of several diseases, including sickle cell anemia, which causes recurring episodes of pain and severe pronounced anemia. Monitoring patients with these diseases involves the observation of peripheral blood samples under a microscope, a time-consuming procedure. Moreover, a specialist is required to perform this technique, and owing to the subjective nature of the observation of isolated RBCs, the error rate is high. In this paper, we propose an automated method for differentially enumerating RBCs that uses peripheral blood smear image analysis. In this method, the objects of interest in the image are segmented using a Chan-Vese active contour model. An analysis is then performed to classify the RBCs, also called erythrocytes, as normal or elongated or having other deformations, using the basic shape analysis descriptors: circular shape factor (CSF) and elliptical shape factor (ESF). To analyze cells that become partially occluded in a cluster during sample preparation, an elliptical adjustment is performed to allow the analysis of erythrocytes with discoidal and elongated shapes. The images of patient blood samples used in the study were acquired by a clinical laboratory specialist in the Special Hematology Department of the ``Dr. Juan Bruno Zayas'' General Hospital in Santiago de Cuba. A comparison of the results obtained by the proposed method in our experiments with those obtained by some state-of-the-art methods showed that the proposed method is superior for the diagnosis of sickle cell anemia. This superiority is achieved for evidenced by the obtained F-measure value (0.97 for normal cells and 0.95 for elongated ones) and several overall multiclass performance measures. The results achieved by the proposed method are suitable for the purpose of clinical treatment and diagnostic support of sickle cell anemia.