Choice of distance function in the segmentation of regions of interest in microscopic images of breast tissues

Classification of milk duct carcinoma in the scans of diagnostic specimens is an important medical problem. Before the classification is performed, the regions of milk ducts which will be the regions of interest (ROI) should be detected. One of the approaches to such detection is to segment the image into ROIs and the remaining regions. The segmentation by clusterization with the classical K-means method was proposed in the literature. A pixel together with its square neighborhood was considered as the object. Sorted image intensities in the neighborhood with extreme values omitted were used as features, with the Euclidean distance between the objects. In this paper we investigate new distance functions: cosine distance, city block and correlation distance, in the same setting. The cosine function was found to be the best, giving smaller average error, as well as smaller scatter measure, with respect to the Euclidean function. The mean errors for the cosine, Euclidean, city block and correlation functions were 17%, 25%, 39% and 89%, respectively.