Breast cancers can be histologically categorized (graded) based upon their architectural patterns and cellular types. Inaccurate histologic grading can result in inappropriate treatment for a given patient. Computational analysis of breast cancers offers an operator-independent method for histologic grading that should enhance grading reliability. We present the initial efforts to develop computational technologies that may be used to automatically and objectively estimate the histologic grade of breast cancer tumors. The approach utilizes image processing and shape analysis of imaged histologic sections. Our work is based on the hypothesis that cellular structures found in breast cancer tumors can be transformed into distinct high-resolution shape distributions using geometric measures from stochastic geometry. The resulting shape distributions define well-populated regions of the associated high-dimensional space. Mapping an unknown breast cancer sample into this high-D space and determining to which region it belongs will allow for the automatic estimation of its histologic grade.