Unsupervised Segmentation of Multi-Modal Images by a Precise Approximation of Individual Modes with Linear Combinations of Discrete Gaussians

Many important applications of image analysis deal with multi-modal images such that each object of interest relates to an individual mode in the marginal signal distribution collected over the image. Segmentation of such seemingly simple images is nonetheless a challenging problem because each meaningful boundary between the objects is rarely formed by easily detectable signal differences (or "edges"). Most commonly, the signals have very close values across the boundary and relate to intersecting tails of distributions describing individual objects. To accurately segment such images, not only the main body but also the tails of each such distribution have to be precisely recovered from the available mixture. We present a re.ned version of our novel EM-based algorithm for accurate unsupervised segmentation of multi-modal grayscale images. It has a considerably improved convergence to a local maximum of the image likelihood and provides a very close approximation of each distribution related to the mode with a linear combination of sign-alternate discrete Gaussian kernels. Experiments with medical images show the proposed segmentation is more accurate than several other known alternatives.