In this study, we analyze histologic human colon tissue images that we captured with a camera-mounted microscope. We propose the Augmented K-Means Clustering algorithm as a method of segmenting cell nuclei in such colon images. Then we compare the proposed algorithm to the weighted K-Means Clustering algorithm. As a result, we observe that the developed Augmented K-Means Clustering algorithm decreased the needed number of iterations and shortened the duration of the segmentation process. Moreover, the algorithm we propose appears more consistent in comparison to the weighted K-Means Clustering algorithm. We also assess the similarity of the segmented images to the original images, for which we used the Histogram-Based Similarity method. Our assessment indicates that the images segmented by the Augmented K-Means Clustering algorithm are more frequently similar to the original images than the images segmented by the Weighed K-Means Clustering algorithm.