Ring theory is most widely known as a branch of pure mathematics under the field of abstract algebra. Some of the uses of Ring Theory in the modern world involve cryptography, computer vision, and image segmentation. As of now, finite cyclic rings have been incorporated into performing image segmentations for the Mean Shift Iterative Algorithm. This paper analyzes the Mean Shift Iterative Algorithm and devises an improved algorithm and stopping criterion using finite cyclic rings and matrices in Ring Theory that perform high-quality image segmentations for images that can be used in computer vision and possibly the segmentation(s) of grayscale (d = 1), colored (d = 3), and multispectral (d ≥ 3) images.