Breast cancer is the most common cancer among women. The effectiveness of treatment depends on early detection of the disease. Computer-aided diagnosis plays an increasingly important role in this field. Particularly, digital pathology has recently become of interest to a growing number of scientists. This work reports on advances in computer-aided breast cancer diagnosis based on the analysis of cytological images of fine needle biopsies. The task at hand is to classify those as either benign or malignant. We propose a robust segmentation procedure giving satisfactory nuclei separation even when they are densely clustered in the image. Firstly, we determine centers of the nuclei using conditional erosion. The erosion is performed on a binary mask obtained with the use of adaptive thresholding in grayscale and clustering in a color space. Then, we use the multi-label fast marching algorithm initialized with the centers to obtain the final segmentation. A set of 84 features extracted from the nuclei is used in the classification by three different classifiers. The approach was tested on 450 microscopic images of fine needle biopsies obtained from patients of the Regional Hospital in Zielona Góra, Poland. The classification accuracy presented in this paper reaches 100%, which shows that a medical decision support system based on our method would provide accurate diagnostic information.