Most benign breast tumors possess well-defined, sharp boundaries that delineate them from surrounding tissues, as opposed to malignant tumors. Computer techniques proposed to date for tumor analysis have concentrated on shape factors of tumor regions and texture measures. While shape measures based on contours of tumor regions can indicate differences in shape complexities between circumscribed and spiculated tumors, they are not designed to characterize the density variations across the boundary of a tumor. In this paper we propose a region-based measure of image edge profile acutance which characterizes the transition in density of a region of interest (ROI) along normals to the ROI at every boundary pixel. We investigate the potential of acutance in quantifying the sharpness of the boundaries of tumors, and propose its application to discriminate between benign and malignant mammographic tumors. In addition, we study the complementary use of various shape factors based upon the shape of the ROI, such as compactness, Fourier descriptors, moments, and chord-length statistics to distinguish between circumscribed and spiculated tumors. Thirty-nine images from the Mammographic Image Analysis Society (MIAS) database and an additional set of 15 local cases were selected for this study. The cases included 16 circumscribed benign, seven circumscribed malignant, 12 spiculated benign, and 19 spiculated malignant lesions. All diagnoses were proven by pathologic examinations of resected tissue. The contours of the lesions were first marked by an expert radiologist using X-Paint and X-Windows on a SUN-SPARCstation 2 Workstation. For computation of acutance, the ROI boundaries were iteratively approximated using a split/merge and end-point adjustment technique to obtain the best-fitting polygonal approximation. The jackknife method using the Mahalanobis distance measure in the BMDP (Biomedical Programs) package was used for classification of the lesions using acutance and the shape factors as features in various combinations. Acutance alone resulted in a benign/malignant classification accuracy of 95% the MIAS cases. Compactness alone gave a circumscribed/spiculated classification rate of 92.3% with the MIAS cases. Acutance in combination with a moment-based shape measure and a Fourier descriptor-based measure gave four-group classification rate of 95% with the MIAS cases. The results indicate the importance of including lesion edge definition with shape information for classification of tumors, and that the proposed measure of acutance fills this need.