Malignant breast tumors typically appear in mammograms with rough, spiculated, or microlobulated contours, whereas most benign masses have smooth, round, oval, or macrolobulated contours. Several studies have shown that shape factors that incorporate differences as above can provide high accuracies in distinguishing between malignant tumors and benign masses based upon their contours only. However, global measures of roughness, such as compactness, are less effective than specially designed features based upon spicularity and concavity. We propose a method to derive polygonal models of contours that preserve spicules and details of diagnostic importance. We show that an index of spiculation derived from the turning functions of the polygonal models obtained by the proposed method yields better classification accuracy than a similar measure derived using a previously published method. The methods were tested with a set of 111 contours of 65 benign masses and 46 malignant tumors. A high classification accuracy of 0.94 in terms of the area under the receiver operating characteristics curve was obtained.