CADx systems have the potential to support radiologists in the difficult task of discriminating benign and malignant mammographic lesions. The segmentation of mammographic masses from the background tissue is an important module of CADx systems designed for the characterization of mass lesions. In this work, a novel approach to this task is presented. The segmentation is performed by automatically tracing the mass' contour in-between manually provided landmark points defined on the mass' margin. The performance of the proposed approach is compared to the performance of implementations of three state-of-the-art approaches based on region growing and dynamic programming. For an unbiased comparison of the different segmentation approaches, optimal parameters are selected for each approach by means of tenfold cross-validation and a genetic algorithm. Furthermore, segmentation performance is evaluated on a dataset of ROI and ground-truth pairs. The proposed method outperforms the three state-of-the-art methods. The benchmark dataset will be made available with publication of this paper and will be the first publicly available benchmark dataset for mass segmentation.