Conventional Markov Random Field Research Articles

A wavelet-based Markov random field segmentation model in segmenting microarray experiments

In the present study, an adaptation of the Markov Random Field (MRF) segmentation model, by means of the stationary wavelet transform (SWT), applied to complementary DNA (cDNA) microarray images is proposed (WMRF). A 3-level decomposition scheme of the initial microarray image was performed, followed by a soft thresholding filtering technique. With the inverse process, a Denoised image was created. In addition, by using the Amplitudes of the filtered wavelet Horizontal and Vertical images at each level, three different Magnitudes were formed. These images were combined with the Denoised one to create the proposed SMRF segmentation model. For numerical evaluation of the segmentation accuracy, the segmentation matching factor (SMF), the Coefficient of Determination ( r 2), and the concordance correlation ( p c ) were calculated on the simulated images. In addition, the SMRF performance was contrasted to the Fuzzy C Means (FCM), Gaussian Mixture Models (GMM), Fuzzy GMM (FGMM), and the conventional MRF techniques. Indirect accuracy performances were also tested on the experimental images by means of the Mean Absolute Error (MAE) and the Coefficient of Variation (CV). In the latter case, SPOT and SCANALYZE software results were also tested. In the former case, SMRF attained the best SMF, r 2, and p c (92.66%, 0.923, and 0.88, respectively) scores, whereas, in the latter case scored MAE and CV, 497 and 0.88, respectively. The results and support the performance superiority of the SMRF algorithm in segmenting cDNA images.

A new Markov random field segmentation method for breast lesion segmentation in MR images

Breast cancer is a major public health problem for women in the Iran and many other parts of the world. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) plays a pivotal role in breast cancer care, including detection, diagnosis, and treatment monitoring. But segmentation of these images which is seriously affected by intensity inhomogeneities created by radio-frequency coils is a challenging task. Markov Random Field (MRF) is used widely in medical image segmentation especially in MR images. It is because this method can model intensity inhomogeneities occurring in these images. But this method has two critical weaknesses: Computational complexity and sensitivity of the results to the models parameters. To overcome these problems, in this paper, we present Improved-Markov Random Field (I-MRF) method for breast lesion segmentation in MR images. Unlike the conventional MRF, in the proposed approach, we don't use the Iterative Conditional Mode (ICM) method or Simulated Annealing (SA) for class membership estimation of each pixel (lesion and non-lesion). The prior distribution of the class membership is modeled as a ratio of two conditional probability distributions in a neighborhood which is defined for each pixel: probability distribution of similar pixels and non-similar ones. Since our proposed approach don't use an iterative method for maximizing the posterior probability, above mentioned problems are solved. Experimental results show that performance of segmentation in this approach is higher than conventional MRF in terms of accuracy, precision, and Computational complexity.

Adaptive support vector machine and Markov random field model for classifying hyperspectral imagery

Markov random field (MRF) provides a useful model for integrating contextual information into remote sensing image classification. However, there are two limitations when using the conventional MRF model in hyperspectral image classification. First, the maximum likelihood classifier used in MRF to estimate the spectral-based probability needs accurate estimation of covariance matrix for each class, which is often hard to obtain with a small number of training samples for hyperspectral imagery. Second, a fixed spatial neighboring impact parameter for all pixels causes overcorrection of spatially high variation areas and makes class boundaries blurred. This paper presents an improved method for integrating a support vector machine (SVM) and Markov random field to classify the hyperspectral imagery. An adaptive spatial neighboring impact parameter is assigned to each pixel according to its spatial contextualcorrelation.Experimentalresultsofahyperspectralimageshowthattheclassification accuracyfromtheproposedmethodhasbeenimprovedcomparedtothosefromtheconventional MRF model and pixel-wise classifiers including the maximum likelihood classifier and SVM

Computation of Image Spatial Entropy Using Quadrilateral Markov Random Field

Shannon entropy is a powerful tool in image analysis, but its reliable computation from image data faces an inherent dimensionality problem that calls for a low-dimensional and closed form model for the pixel value distributions. The most promising such models are Markovian, however, the conventional Markov random field is hampered by noncausality and its causal versions are also not free of difficulties. For example, the Markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system. A new model, named quadrilateral Markov random field (QMRF) is introduced in this paper in order to overcome these limitations. A property of QMRF with neighboring size of 2 is then used to decompose an image prior into a product of 2-D joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption. In addition, the paper includes an extension of the introduced method to the computation of image spatial mutual information. Comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones.

Image magnification based on a blockwise adaptive Markov random field model

In this paper, an effective image magnification algorithm based on an adaptive Markov random field (MRF) model with a Bayesian framework is proposed. A low-resolution (LR) image is first magnified to form a high-resolution (HR) image using a fractal-based method, namely the multiple partitioned iterated function system (MPIFS). The quality of this magnified HR image is then improved by means of a blockwise adaptive MRF model using the Bayesian ‘maximum a posteriori’ (MAP) approach. We propose an efficient parameter estimation method for the MRF model such that the staircase artifact will be reduced in the HR image. Experimental results show that, when compared to the conventional MRF model, which uses a fixed set of parameters for a whole image, our algorithm can provide a magnified image with the well-preserved edges and texture, and can achieve a better PSNR and visual quality.

Improved VHR Urban Area Mapping Exploiting Object Boundaries

In this paper, a mapping procedure exploiting object boundaries in very high-resolution (VHR) images is proposed. After discrimination between boundary and nonboundary pixel sets, each of the two sets is separately classified. The former are labeled using a neural network (NN), and the shape of the pixel set is finely tuned by enforcing a few geometrical constraints, while the latter are classified using an adaptive Markov random field (MRF) model. The two mapping outputs are finally combined through a decision fusion process. Experimental results on hyperspectral and satellite VHR imagery show the superior performance of this method over conventional NN and MRF classifiers.

Discriminative Random Fields

In this research we address the problem of classification and labeling of regions given a single static natural image. Natural images exhibit strong spatial dependencies, and modeling these dependencies in a principled manner is crucial to achieve good classification accuracy. In this work, we present Discriminative Random Fields (DRFs) to model spatial interactions in images in a discriminative framework based on the concept of Conditional Random Fields proposed by lafferty et al.(2001). The DRFs classify image regions by incorporating neighborhood spatial interactions in the labels as well as the observed data. The DRF framework offers several advantages over the conventional Markov Random Field (MRF) framework. First, the DRFs allow to relax the strong assumption of conditional independence of the observed data generally used in the MRF framework for tractability. This assumption is too restrictive for a large number of applications in computer vision. Second, the DRFs derive their classification power by exploiting the probabilistic discriminative models instead of the generative models used for modeling observations in the MRF framework. Third, the interaction in labels in DRFs is based on the idea of pairwise discrimination of the observed data making it data-adaptive instead of being fixed a priori as in MRFs. Finally, all the parameters in the DRF model are estimated simultaneously from the training data unlike the MRF framework where the likelihood parameters are usually learned separately from the field parameters. We present preliminary experiments with man-made structure detection and binary image restoration tasks, and compare the DRF results with the MRF results.