We propose techniques to analyze bilateral asymmetry in mammograms by combining directional information, morphological measures, and geometric moments related to density distributions. The procedure starts by detecting the breast boundary and the pectoral muscle edge (in mediolateral-oblique, or MLO, views). All artifacts outside the breast boundary as well as the pectoral muscle region are eliminated. A breast density model based upon a Gaussian mixture model is then used to segment the fibroglandular disks of the mammograms. Rose diagrams are used to map the magnitude and directional information related to the fibroglandular tissue filtered using multiresolution Gabor wavelets. The directional data of the left and right mammograms are aligned by using the straight lines perpendicular to the corresponding pectoral muscle edges and subtracted to obtain difference rose diagrams. Directional features are obtained from the difference rose diagrams and used to characterize the changes caused by the development of breast cancer in the form of bilateral asymmetry or architectural distortion. An additional set of features including Hu's moments, eccentricity, stretch, area, and average density are extracted from the segmented fibroglandular disks. The differences between the pairs of the features for the left and right mammograms are used as measures for the analysis of asymmetry. The techniques were applied to 88 mammograms from the Mini-MIAS database. Classification accuracies of up to 84.4% were achieved, with sensitivity and specificity rates of 82.6% and 86.4%, respectively.