The detection of lesions on mammography is a repetitive and fatiguing task. Thus, computer-aided detection systems have been developed to aid radiologists. The detection accuracy of current systems is much higher for clusters of microcalcifications than for spiculated masses. In this article, the authors present a new model-based framework for the detection of spiculated masses. The authors have invented a new class of linear filters, spiculated lesion filters, for the detection of converging lines or spiculations. These filters are highly specific narrowband filters, which are designed to match the expected structures of spiculated masses. As a part of this algorithm, the authors have also invented a novel technique to enhance spicules on mammograms. This entails filtering in the radon domain. They have also developed models to reduce the false positives due to normal linear structures. A key contribution of this work is that the parameters of the detection algorithm are based on measurements of physical properties of spiculated masses. The results of the detection algorithm are presented in the form of free-response receiver operating characteristic curves on images from the Mammographic Image Analysis Society and Digital Database for Screening Mammography databases.