We describe here a computational morphology-based approach to the investigation of possible causes of chromatin alterations in sperm. A comprehensive set of state-of-the-art and geometric measures are computationally extracted from toluidine blue stained images and analyzed to infer the possible processes leading to normal and abnormal chromatin formation while seeking a possible taxonomy of chromatin alterations and their influence on sperm head morphology. Using this methodology, we have identified higher chromatin fragility at some specific points of the sperm head. Despite the lack of correlation between morphologies of sperm head and chromatin structure, four main morphological types of chromatin alterations in bull spermatozoa have been identified and their possible causes discussed.