Compound Markov Random Field Model Research Articles

Color and Texture Segmentation Using an Unified MRF Model

The color image segmentation problem has two main issues to be solved. The proper choice of a color model and the choice of an appropriate image model are the key issues in color image segmentation. In this work, Ohta (I1, I2, I3) is taken as the color model and different variants of Markov Random Field (MRF) models are proposed. In this regard, a Compound Markov Random Field (COMRF) model is porposed to take care of inter-color-plane and intra-color-plane interactions as well. In continuation to this model, a Constrained Compound Markov Random Field Model (CCOMRF) has been proposed to model the color images. The color image segmentation problem has been formulated in an unsupervised framework. The performance of the above proposed models has been compared with the standard MRF model and some of the state-of-the-art methods, and found to exhibit improved performance.

A Joint Markov Model for Communities, Connectivity and Signals Defined Over Graphs

Real-world networks are typically described in terms of nodes, links, and communities, having signal values often associated with them. The aim of this letter is to introduce a novel Compound Markov random field model (Compound MRF, or CMRF) for signals defined over graphs, encompassing jointly signal values at nodes, edge weights, and community labels. The proposed CMRF generalizes Markovian models previously proposed in the literature, since it accounts for different kinds of interactions between communities and signal smoothness constraints. Finally, the proposed approach is applied to (joint) graph learning and signal recovery. Numerical results on synthetic and real data illustrate the competitive performance of our method with respect to other state-of-the-art approaches.

Posterior-Mean Super-Resolution With a Causal Gaussian Markov Random Field Prior

We propose a Bayesian image super-resolution (SR) method with a causal Gaussian Markov random field (MRF) prior. SR is a technique to estimate a spatially high-resolution image from given multiple low-resolution images. An MRF model with the line process supplies a preferable prior for natural images with edges. We improve the existing image transformation model, the compound MRF model, and its hyperparameter prior model. We also derive the optimal estimator--not the joint maximum a posteriori (MAP) or the marginalized maximum likelihood (ML) but the posterior mean (PM)--from the objective function of the L2-norm-based (mean square error) peak signal-to-noise ratio. Point estimates such as MAP and ML are generally not stable in ill-posed high-dimensional problems because of overfitting, whereas PM is a stable estimator because all the parameters in the model are evaluated as distributions. The estimator is numerically determined by using the variational Bayesian method. The variational Bayesian method is a widely used method that approximately determines a complicated posterior distribution, but it is generally hard to use because it needs the conjugate prior. We solve this problem with simple Taylor approximations. Experimental results have shown that the proposed method is more accurate or comparable to existing methods.

Constrained Compound Markov Random Field Model with Graduated Penalty Function for Color Image Segmentation

In this paper, an unsupervised color image segmentation scheme has been proposed for preserving strong and weak edges as well. A Constrained Compound Markov Random Field (MRF) has been proposed as the a priori model for the color labels. We have used Ohta (I1, I2, I3) color model and a controlled correlation of the color space has been accomplished by the proposed compound MRF model. The Constrained Compound MRF (CCMRF) is found to possess the unifying property of modeling scenes as well as color textures. In unsupervised scheme, the associated model parameters and the image labels are estimated recursively. The model parameters are the Maximum Conditional Pseudo Likelihood (MCPL) estimates and the labels are the Maximum a Posteriori (MAP) estimates. The performance of the proposed scheme has been compared with that of Yu’s method and has been found to exhibit improved performance in the context of misclassification error.

A Change Information Based Fast Algorithm for Video Object Detection and Tracking

In this paper, we present a novel algorithm for moving object detection and tracking. The proposed algorithm includes two schemes: one for spatio-temporal spatial segmentation and the other for temporal segmentation. A combination of these schemes is used to identify moving objects and to track them. A compound Markov random field (MRF) model is used as the prior image attribute model, which takes care of the spatial distribution of color, temporal color coherence and edge map in the temporal frames to obtain a spatio-temporal spatial segmentation. In this scheme, segmentation is considered as a pixel labeling problem and is solved using the maximum a posteriori probability (MAP) estimation technique. The MRF-MAP framework is computation intensive due to random initialization. To reduce this burden, we propose a change information based heuristic initialization technique. The scheme requires an initially segmented frame. For initial frame segmentation, compound MRF model is used to model attributes and MAP estimate is obtained by a hybrid algorithm [combination of both simulated annealing (SA) and iterative conditional mode (ICM)] that converges fast. For temporal segmentation, instead of using a gray level difference based change detection mask (CDM), we propose a CDM based on label difference of two frames. The proposed scheme resulted in less effect of silhouette. Further, a combination of both spatial and temporal segmentation process is used to detect the moving objects. Results of the proposed spatial segmentation approach are compared with those of JSEG method, and edgeless and edgebased approaches of segmentation. It is noticed that the proposed approach provides a better spatial segmentation compared to the other three methods.