Bayesian Non-parametric Image Segmentation with Markov Random Field Prior
In this paper, a Bayesian framework for non-parametric density estimation with spatial smoothness constraints is presented for image segmentation. Unlike common parametric methods such as mixtures of Gaussians, the proposed method does not make strict assumptions about the shape of the density functions and thus, can handle complex structures. The multiclass kernel density estimation is considered as an unsupervised learning problem. A Dirichlet compound multinomial (DCM) prior is used to model the class label prior probabilities and a Markov random field (MRF) is exploited to impose the spatial smoothness and control the confidence on the Dirichlet hyper-parameters, as well. The proposed model results in a closed form solution using an expectation-maximization (EM) algorithm for maximum a posteriori (MAP) estimation. This provides a huge advantage over other models which utilize more complex and time consuming methods such as Markov chain Monte Carlo (MCMC) or variational approximation methods. Several experiments on natural images are performed to present the performance of the proposed model compared to other parametric approaches.
KeywordsMulticlass kernel density estimation Dirichlet compound multinomial distribution Markov random field prior Image segmentation
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