Convex and Nonconvex Formulations for Image Segmentation Using Hidden Fields

2 February 2016

José Bioucas-Dias Instituto de Telecomunicações/IST

Image segmentation is fundamentally a discrete problem. It consists in finding a partition of the image domain such that the pixels in each element of the partition exhibit some kind of similarity. Very often, the partitions are obtained via integer optimization, which is NP-hard, apart from a few exceptions. We sidestep the discrete nature of image segmentation by formulating the problem in the Bayesian framework and introducing a set of hidden real-valued random fields informative with respect to the probability of the partitions. Armed with this model, and assuming a supervised scenario, the original discrete optimization is converted into a convex problem, which is solved efficiently using the SALSA solver. In the semi-supervised scenario, we are lead to a nonconvex problem which is addressed with alternating optimization. The effectiveness of the proposed methodology is illustrated in simulated and real segmentation problems.



José Bioucas-Dias received the EE, MSc, PhD, and "Agregado" degrees from Instituto Superior Técnico (IST), Portugal, in 1985, 1991, 1995, and 2007, respectively, all in electrical and computer engineering. Since 1995, he has been with the Department of Electrical and Computer Engineering, IST, where he is an Associate Professor. He is also a Senior Researcher with the Pattern and Image Analysis group of the Instituto de Telecomunicações, which is a private non-profit research institution. He has introduced scientific contributions in inverse problems, signal and image processing, pattern recognition, optimization, and remote sensing. He is included in Thomson Reuters' Highly Cited Researchers 2015 list.