Non-local spatially varying finite mixture models for image segmentation

In this work, we propose a new Bayesian model for unsupervised image segmentation based on a combination of the spatially varying finite mixture models (SVFMMs) and the non-local means (NLM) framework. The probabilistic NLM weighting function is successfully integrated into a varying Gauss–Markov random field, yielding a prior density that adaptively imposes a local regularization to simultaneously preserve edges and enforce smooth constraints in homogeneous regions of the image. Two versions of our model are proposed: a pixel-based model and a patch-based model, depending on the design of the probabilistic NLM weighting function. Contrary to previous methods proposed in the literature, our approximation does not introduce new parameters to be estimated into the model, because the NLM weighting function is completely known once the neighborhood of a pixel is fixed. The proposed model can be estimated in closed-form solution via a maximum a posteriori (MAP) estimation in an expectation–maximization scheme. We have compared our model with previously proposed SVFMMs using two public datasets: the Berkeley Segmentation dataset and the BRATS 2013 dataset. The proposed model performs favorably to previous approaches in the literature, achieving better results in terms of Rand Index and Dice metrics in our experiments.