Polygonal Modeling of Contours Using the Turning Angle Function

Several types of signatures have been defined to facilitate the analysis of contours of objects. The turning angle function of a given contour may be used as a signature to analyze the contour. We propose a method to use the turning angle function to derive a polygonal model of the given contour in such a manner as to preserve the important details in the contour. We demonstrate the usefulness of the resulting polygonal model in deriving efficient shape factors, and illustrate its application in the classification of breast masses. Most malignant breast tumors, as seen in mammograms, have rough and spiculated contours; on the contrary, benign masses usually have smooth, round, or oval contours. An index of spiculation derived from the proposed polygonal model was tested with a set of 111 contours of which 65 are related to benign masses and 46 are related to malignant tumors. A high classification accuracy of 0.92 was obtained, in terms of the area under the receiver operating characteristics curve, with a data compression of 0.025 on average.