Bayesian pixel classification using spatially variant finite mixtures and the generalized EM algorithm

Abstract

A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).

A Spatially Correlated Mixture Model for Image Segmentation

“…The main difference lies in the updating of {π cv } in its M-step. In [3], this updating is done using the gradient projection method [6]. On the other hand, in [4], it is done by finding the solutions of the equations ∂Q MAP ∂π cv = 0 and then solving linearly constrained quadratic programming problems to ensure that {π cv } satisfy the constraints…”

“…The spatially variant finite mixture model (SVFMM) has been proposed to incorporate the spatial correlation of the pixels effectively [3] and its learning algorithm has been improved in [4].…”

“…In the previous work [3], the spatially variant finite mixture model (SVFMM) has been proposed. In this model, a set of finite mixture models corresponding pixels whose mixing proportions can vary individually is introduced.…”

Gaussian Mixture Model and RJMCMC Based Rs Image Segmentation

“…Many MRF variants functions are proposed. Such as, Sanjay-Gopal (1998) proposed spatially variant finite mixture model, called SVFMM. Nikou (2007) proposed directional class adaptive spatially variant finite mixture model, called DCA-SVFMM.…”

Tissue Mixture Characterization In The Presence of Mri Inhomogeneity by the Em Algorithm

“…This hard segmentation ignores partial volume (PV) effect and, therefore, losses both the detail of the tissue structure and the accuracy in quantifying the tissue volume. An alternative approach has been attempted to find the probability of a specific tissue type inside each voxel [1][2][3][4][5]. While this soft segmentation is theoretically attractive in dealing the PV effect, it usually either has a very complicated model of numerically intractable or an approximated model of less numerical accuracy.…”