Purpose Breast cancer is the second most common cancer in the world, being more common among women and representing 24.2% of new cases each year. Mammography is currently the best technique for early detection of non-palpable breast lesions. Due to the need to create new more computationally efficient techniques, this paper presents a methodology for mass classification from mammographic images based on their geometric and topological features. Methods For each image, two spatial feature maps named distance map and surface map are computed. These features describe the mass geometry and topology, respectively. Also, shape descriptors based on distances histograms are used to characterize the shape of the masses. The purpose of this comparison is to discriminate its malignancy and benignity patterns. The high-boost filter is applied to enhance the masses, since the difference between them and the breast tissue or other components of them is very subtle. Mammograms digitized from the Digital Database for Screening Mammography (DDSM) were used for the testing of this methodology, corresponding to 794 ROIs that were separated into groups by density, according to BI-RADS classification. Results The best results for accuracy, sensitivity, and specificity were 93.70%, 96.29%, and 91.05%, respectively, for density 2 and 90.18%, 91.01%, and 89.94% for all images. Conclusion The results obtained demonstrate that the sets of features successfully discriminate mass standards, even with the exceptions and obstacles that characterize and classify the masses through their shape.