Semen analysis is the first step in the evaluation of an infertile couple. Within this process, an accurate and objective morphological analysis becomes more critical as it is based on the correct detection and segmentation of human sperm components. In this paper, we present an improved two-stage framework for detection and segmentation of human sperm head characteristics (including acrosome and nucleus) that uses three different color spaces. The first stage detects regions of interest that define sperm heads, using k-means, then candidate heads are refined using mathematical morphology. In the second stage, we work on each region of interest to segment accurately the sperm head as well as nucleus and acrosome, using clustering and histogram statistical analysis techniques. Our proposal is also characterized by being fully automatic, where a user intervention is not required. Our experimental evaluation shows that our proposed method outperforms the state-of-the-art. This is supported by the results of different evaluation metrics. In addition, we propose a gold-standard built with the cooperation of a referent expert in the field, aiming to compare methods for detecting and segmenting sperm cells. Our results achieve notable improvement getting above 98% in the sperm head detection process at the expense of having significantly fewer false positives obtained by the state-of-the-art method. Our results also show an accurate head, acrosome and nucleus segmentation achieving over 80% overlapping against hand-segmented gold-standard. Our method achieves higher Dice coefficient, lower Hausdorff distance and less dispersion with respect to the results achieved by the state-of-the-art method.