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In the current research in the field of analysis of mammograms by means of image processing tools the task of malignancy and spicularity assessment is investigated extensively. Early detection of malignant masses may significantly lower the risk of metastasis. It is known that malignancy is closely related to the shape of a mass (existence of spicules emanating from the center of the mass). Therefore the tasks of malignancy and spicularity analysis are very often treated jointly. In this paper we introduce a new set of features useful in performing this task. For a contour of a cancerous mass a sequence of dilations is computed, the number of pixels on the outer contour of each dilation is counted, and this number is plotted against the size of the disk-shaped structuring element. Next, the linear trend is removed, and after denoising, the proposed features are calculated. The crucial point is that the proposed features are zero iff the input contour is circular and that all the features are invariant under translation, rotation, and scaling. These distinctive properties ensure successful classification irrespective to location, orientation and scale of the mass with the Az values of the ROC curve higher than for features given in the literature. The additional advantage of our approach is the relative simplicity of the proposed features. In contrast to many traditional features, no sophisticated algorithms are employed, so reimplementation of the new features is easy.