With an estimated life-time-risk of about 10%, breast cancer is the most common cancer among women in western societies. Extensive mammography-screening programs have been implemented for diagnosis of the disease at an early stage. Several algorithms for computer-aided detection (CAD) have been proposed to help radiologists manage the increasing number of mammographic image-data and identify new cases of cancer. However, a major issue with most CAD-solutions is the fact that performance strongly depends on the structure and density of the breast tissue. Prior information about the global tissue quality in a patient would be helpful for selecting the most effective CAD-approach in order to increase the sensitivity of lesion-detection. In our study, we propose an automated method for textural evaluation of digital mammograms using the Minkowski Functionals in 2D. 80 mammograms are consensus-classified by two experienced readers as fibrosis, involution/atrophy, or normal. For each case, the topology of graylevel distribution is evaluated within a retromamillary image-section of 512 x 512 pixels. In addition, we obtain parameters from the graylevel-histogram (20th percentile, median and mean graylevel intensity). As a result, correct classification of the mammograms based on the densitometic parameters is achieved in between 38 and 48%, whereas topological analysis increases the rate to 83%. The findings demonstrate the effectiveness of the proposed algorithm. Compared to features obtained from graylevel histograms and comparable studies, we draw the conclusion that the presented method performs equally good or better. Our future work will be focused on the characterization of the mammographic tissue according to the Breast Imaging Reporting and Data System (BI-RADS). Moreover, other databases will be tested for an in-depth evaluation of the efficiency of our proposal.