The contours of benign masses and malignant tumors in mammograms and other types of breast images differ substantially in their shape and complexity; the former are usually round and smooth, whereas the latter are typically spiculated and irregular. We demonstrate the usefulness of fractal analysis via a frequency domain approach applied to one-dimensional signatures of the two-dimensional contours of breast masses in mammograms. The model related to fractional Brownian motion was applied via power spectral analysis of signatures to estimate the fractal dimension. Experiments with a dataset of 111 contours, including those of 65 benign masses and 46 malignant tumors, indicated a high classification performance of 0.8962 in terms of the area under the receiver-operating characteristic curve. The method should be useful in computer-aided diagnosis of breast cancer.