This paper extends previous work on the assessment of boar sperm cells in order to discriminate amongst intact or reacted acrosomes for fertility purposes. The aim of the study reported is twofold. On one hand to assess the quality of a different set of classifiers. On the other, to assess the feasibility of applying dimension-reduction techniques in order to simplify the classification process. The supervised classification techniques used are Extremely Randomized Trees, Random Forest, Support Vector Machines and Gaussian Naive Bayes. The data sets used describe the local maximum gradient, the local mean gray levels and the local standard deviation along the inner contours of the sperm cells. The procedure to obtain these features is explained along as their mathematical nature. The first experiment reported uses each of the three data sets for performing a grid search with 50-fold cross validation in order to evaluate the scores of each classifier. The second experiment reported integrates the three previous data sets into a single one. After performing a recursive feature elimination stage to this data set the results show that only 5 of 840 features suffice in order to provide satisfactory results according to veterinary experts.