Polygonal approximation of contours based on the turning angle function

Abstract

The turning angle function has been used as a signature to represent the shape of a given contour with the aim of analysis of shape and content-based image retrieval. We propose a method that uses 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. The preservation of diagnostically significant features present in the contours of breast masses in mammograms are important to discriminate between benign masses and malignant tumors. To evaluate the practical utility of the proposed polygonal modeling method in terms of the efficiency in the classification of breast masses, we derive an index of spiculation SIPMTF and a measure of fractional concavity Fcc from the models obtained and compare the results with those provided by two methods proposed in previous related works. The features SIPMTF and Fcc were tested with a set of 111 contours, of which 65 are related to benign masses and 46 are related to malignant tumors. High classification accuracies of 0.93 with SIPMTF and 0.91 with Fcc were obtained, in terms of the area under the receiver operating characteristics curve, with a data compression of 0.067 on the average.