Within the complex branching system of the breast, terminal duct lobular units (TDLUs) are the anatomical location where most cancer originates. With aging, TDLUs undergo physiological involution, reflected in a loss of structural components (acini) and a reduction in total number. Data suggest that women undergoing benign breast biopsies that do not show age appropriate involution are at increased risk of developing breast cancer. To date, TDLU assessments have generally been made by qualitative visual assessment, rather by objective quantitative analysis. This paper introduces a technique to automatically estimate a set of quantitative measurements and use those variables to more objectively describe and classify TDLUs. To validate the accuracy of our system, we compared the computer-based morphological properties of 51 TDLUs in breast tissues donated for research by volunteers in the Susan G. Komen Tissue Bank and compared results to those of a pathologist, demonstrating 70% agreement. Secondly, in order to show that our method is applicable to a wider range of datasets, we analyzed 52 TDLUs from biopsies performed for clinical indications in the National Cancer Institute Breast Radiology and Study of Tissues (BREAST) STAMP project and obtained 82% correlation with visual assessment. Lastly, we demonstrate the ability to uncover novel measures when researching the structural properties of the acini by applying machine learning and clustering techniques. Through our study we found that while the number of acini per TDLU increase exponentially with the TDLU diameter, the average elongation and roundness remain constant.