An Efficient and Effective Tool for Image Segmentation, Total Variations and Regularization

Abstract

One of the classical optimization models for image segmentation is the well known Markov Random Fields (MRF) model. MRF formulates many total variation and other optimization criteria used in image segmentation. In spite of the presence of MRF in the literature, the dominant perception has been that the model is not effective for image segmentation. We show here that the reason for the non-effectiveness is not due to the power of the model. Rather it is due to the lack of access to the optimal solution. Instead of solving optimally, heuristics have been engaged. Those heuristic methods cannot guarantee the quality of the solution nor the running time of the algorithm. We describe here an implementation of a very efficient polynomial time algorithm, which is provably fastest possible, delivering the optimal solution to the MRF problem, Hochbaum (2001). It is demonstrated here that many continuous models, common in image segmentation, have a discrete analogs to various special cases of MRF. As such they are solved optimally and efficiently, rather than with the use of continuous techniques such as PDE methods that can only guarantee convergence to a local minimum. The MRF algorithm is enhanced here demonstrating that the set of labels can be any discrete set. Other enhancements include dynamic features that permit adjustments to the input parameters and solves optimally for these changes with minimal computation time. Modifications in the set of labels (colors), for instance, are executed instantaneously. Several theoretical results on the properties of the algorithm are proved here and are demonstrated for examples in the context of medical and biological imaging.