Improving the runtime of MRF based method for MRI brain segmentation

In this study, a Markov Random Field (MRF) approach is used to locate source boundary positions which are difficult to identify from Bouguer gravity and magnetic maps. As a generalized form of Markov Chains, the MRF approach is an unsupervised statistical model based algorithm and is applied to the analysis of images, particularly in the detection of visual patterns or textures. Here, we present a dynamic programming based on the MRF approach for boundary detection of noisy and super-positioned potential anomalies, which are produced by various geological structures. In the MRF method, gravity and magnetic maps are considered as two-dimensional (2-D) images with a matrix composed of N1 × N2 pixels. Each pixel value of the matrix is optimized in real time with no a priori processing by using two parameter sets; average steering vector (θ) and quantization level (M). They carry information about the correlation of neighboring pixels and the locality of their connections. We have chosen MRF as a processing approach for geophysical data since it is an unsupervised, efficient model for image enhancement, border detection and separation of 2-D potential anomalies. The main benefit of MRF is that an average steering vector and a quantization level are enough in evaluation of the potential anomaly maps. We have compared the MRF method to noise implemented synthetic potential field anomalies. After satisfactory results were found, the method has been applied to gravity and magnetic anomaly maps of Gelibolu Peninsula in Western Turkey. Here, we have observed Anafartalar thrust fault and another parallel fault northwest of Anafartalar thrust fault. We have modeled a geological structure including a lateral fault, which results in a higher susceptibility and anomaly amplitude increment. We have shown that the MRF method is effective to detect the broad-scale geological structures in the Gelibolu Peninsula, and thus to delineate the complex tectonic structure of Gelibolu Peninsula.

Image segmentation method combined with Markov random field (MRF) model and regional growth image in this paper is proposed to achieve the accuracy of sonar image segmentation. First of all, the characteristics of field and the label field of sonar image is established through the MRF model; secondly, the further image segmentation is processed by region growing based on the initial image segmentation by ICM algorithm, and this reduced segmentation plaques caused by the MRF method on image segmentation. Finally, experimental results show that the method in this paper can obtain the image segmentation effectively.

An unsupervised segmentation method of polarimetric synthetic aperture radar (POLSAR) data is proposed in this paper. Firstly, this method performs initial classification of the POLSAR data based on polarimetric target decomposition. Then a model for the conditional distribution of the polarimetric coherency matrix is combined with a Markov random field (MRF) representation for the distribution of the region label to obtain the posterior distribution. Finally, iterated conditional modes (ICM) method is used to obtain the final segmentation results. A new MRF model with variable parameter is used in this method. Experiment results indicate that the proposed method achieves improvement over standard MRF method. (4 pages)

We present an automatic segmentation method using the Maximum a posterior (MAP)-Markov random field (MRF) framework that possesses regional adaptive capability for the segmentation of MR brain images with the presence of noise and the intensity inhomogeneity. A spatial-varying Gaussian mixture (SVGM) is used to model the conditional probability distribution of each of the three brain tissues (WM, GM and CSF), and the MRF is used to represent prior probabilities. A three-component random vector consisting of spatial and intensity information is used in SVGM such that the model can represent more complex image characteristics, such as intensity inhomogeneity. The regional adaptive capability is achieved by imposing a similarity criterion that minimizes the intensity variation of the segmented tissues in local regions. Initial parameters of SVGM are estimated from a brain atlas using either the expectation maximization (EM) algorithm or modified k-mean (MKM) algorithm, and the iterated conditional modes (ICM) algorithm is used to perform the segmentation. The parameters estimation and the ICM algorithm are alternatively operated until a stopping criterion is reached. The implement of the method is validated by quantitatively comparing with other published classification methods on fifteen simulated and twenty in vivo brain volumes using the same evaluation criteria. Our algorithm demonstrates superior performance in all cases other than two, and is especially suitable for the volumes with higher noise and inhomogeneity. The complete experiments illustrate that the incorporations of the spatial information and the regional adaptive processing into MAP-MRF framework provide better solution to the segmentation of MR brain images.

Uncertainty quantification of metallic microstructures using principal image moments

In this paper, we propose and compare two spectral angle based approaches for spatial-spectral classification. Our methods use the spectral angle to generate unary energies in a grid-structured Markov random field defined over the pixel labels of a hyperspectral image. The first approach is to use the exponential spectral angle mapper (ESAM) kernel/covariance function, a spectral angle based function, with the support vector machine and the Gaussian process classifier. The second approach is to directly use the minimum spectral angle between the test pixel and the training pixels as the unary energy. We compare the proposed methods with the state-of-the-art Markov random field methods that use support vector machines and Gaussian processes with squared exponential kernel/covariance function. In our experiments with two datasets, it is seen that using minimum spectral angle as unary energy produces better or comparable results to the existing methods at a smaller running time.

Image classification of remote sensing data is an important topic and long-term tasks in applications [1]. Markov random field (MRF) has more advantages in processing contextual information [2]. Bayesian approach enables the incorporation of prior model and likelihood distribution, this paper has formulated a Bayesian-MRF classification model based on MAP-ICM framework. It uses Potts model in label field and assume Gaussian distribution in observation field. According to maximum a posteriori (MAP) criterion, each new classified label can be obtained by the minimum of energy using Iterated Conditional Modes (ICM) algorithm. Finally, classification tasks are carried out by Bayesian-MRF classification model. Experimental results show that: (1) Clique potential parameters affect classification greatly. When it is 0.5, the classification accuracy reaches maximum with the best classification result for study area of Dali Erhai Lake basin using landsat TM data. (2) Bayesian MRF model have obvious advantages in classification for neighbourhood pixels so that it can separate Shadow class from Water class because the Shadow in mountain areas is very similar to Water in spectrum. In this case study, the best classification accuracy reaches 95.8%. The approaches and results will have important reference value for applications such as land use/cover classification, environment/ecological monitoring etc.

In this paper, we shall describe a new method for contextual classification of remotely sensed images. A compound deterministic pseudo annealing-Markov random field model that estimates the correct label for each pixel is suggested. The contextual information is used via the developed context function that depends on the probability function for the adjacent class labels. This function is then formulated as a discrete Markov Random Field (MRF). The global energy function to be minimized is made up of the adaptive a priori probability of classes and the context function. Without using the Metropolis criterion, the optimization procedure consists of selecting the new configuration that corresponds to the minimal value of the global energy function. We call such a procedure of optimization a Deterministic Pseudo Annealing (DPA). The method has been tested and evaluated on real multispectral image provided by the SPOT satellite. The results obtained have the same, or nearly the same, accuracy as those obtained with simulated annealing (SA)-based method and Iterated Conditional Modes (ICM)-based method. The convergence of the proposed DPA approach is better than SA method and very close to ICM method.

A comparative study of markovian and variational image-matching techniques in application to mammograms

Entropy based region selection for moving object detection

Features of several well-known global and local optimization methods were discussed and their robustness and efficiency were tested on several artificial test functions in Matlab environment. The tested local methods were the interior-point, the quasi-Newton method, Nelder–Mead simplex, the pattern search, the NEWUOA and the BOBYQA methods. The global methods were the genetic algorithm (GA), the simulated annealing (SA), the particle swarm optimization (PSO), and the covariance matrix adaptation evolutionary strategy (CMA-ES) methods (see subsections 2.2 and 2.3 for their details). Furthermore, a novel global optimization method, called FOCusing robusT Optimization with Uncertainty-based Sampling (FOCTOPUS), which proved to be very efficient in the optimization of constrained and highly correlated parameters of combustion kinetic models, was also tested. The test functions were selected in such a way that they had a variety of features: uni-modal and multi-modal, differentiable and non-differentiable, separable and non-separable, low dimensional and high dimensional. The following test functions were used: the 20D Alpine function, the 4D Ackley function, the Cross-in-tray 2D function, the Hartmann-6D function, the Holder table 2D function, the 5D Rastrigin function, the 5D Rosenbrock function, the 4D modified Rosenbrock function, the 20D Zakharov function and a typical 2D multi-modal function. The general conclusion here is that, the global methods performed well on the multi-modal and high-dimensional test functions while the local methods were superior in the case of low-dimensional and uni-modal test functions. For the highly multi-modal test functions, the GA was better than all the other methods. The FOCTOPUS method proved to be inferior to GA for most of the test functions, thus its application cannot be generally recommended.

GPU-accelerated MRF segmentation algorithm for SAR images

A new method for the automated extraction of pipelines and other linear objects from Synthetic Aperture Radar (SAR) scenes is presented. It combines intensity data with coherence data from an interferometric evaluation of a SAR scene pair. The fusion is based on Bayesian statistics and is part of a Markov random field (MRF) model for line extraction. Both intensity and coherence data are evaluated using rotating templates. The different statistical properties of intensity and coherence are taken into account by a multiplicative noise model and an additive noise model respectively. The MRF model introduces prior knowledge about the continuity and the narrowness of lines. Posterior odds resulting from the MRF method are input to a method based on ziplock snakes for linear object extraction. This processing step is controlled interactively which is necessary as fully automatic processing of the given noisy data does not provide sufficiently predictable results. The method is applied to data of the ERS tandem mission.

This paper presents multiresolution models for Gauss-Markov random fields (GMRFs) with applications to texture segmentation. Coarser resolution sample fields are obtained by subsampling the sample field at fine resolution. Although the Markov property is lost under such resolution transformation, coarse resolution non-Markov random fields can be effectively approximated by Markov fields. We present two techniques to estimate the GMRF parameters at coarser resolutions from the fine resolution parameters, one by minimizing the Kullback-Leibler distance and another based on local conditional distribution invariance. We also allude to the fact that different GMRF parameters at the fine resolution can result in the same probability measure after subsampling and present the results for first- and second-order cases. We apply this multiresolution model to texture segmentation. Different texture regions in an image are modeled by GMRFs and the associated parameters are assumed to be known. Parameters at lower resolutions are estimated from the fine resolution parameters. The coarsest resolution data is first segmented and the segmentation results are propagated upward to the finer resolution. We use the iterated conditional mode (ICM) minimization at all resolutions. Our experiments with synthetic, Brodatz texture, and real satellite images show that the multiresolution technique results in a better segmentation and requires lesser computation than the single resolution algorithm.

Color Image Segmentation Using Entropy of Fuzziness and Markov Random Field