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The author considers a practical algorithm for estimating an unknown parameter of the mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the stochastic quasi-gradient method to the maximum likelihood function, which is constructed from the observations of the realizations of the Gibbs field. The obtained results have a wide application scope in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR] more...

The author considers a practical algorithm for estimating an unknown parameter of the mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the stochastic quasi-gradient method to the maximum likelihood function, which is constructed from the observations of the realizations of the Gibbs field. The obtained results have a wide application scope in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR] more...

The author considers a practical algorithm for estimating an unknown parameter of a mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the method of stochastic quasi-gradients to the maximum likelihood function, which is constructed from the observations of the implementations of the Gibbs field. The obtained results have a wide application in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR] more...

Markov random fields (MRFs) are well studied during the past 50 years. Their success are mainly due to their flexibility and to the fact that they gives raise to stochastic image models. In this work, we will consider a stochastic differential equation (SDE) driven by Lévy noise. We will show that the solution $ X_v $ of the SDE is a MRF satisfying the Markov property. We will prove that the Gibbs distribution of the process $ X_v $ can be represented graphically through Feynman graphs, which are defined as a set of cliques, then we will provide applications of MRFs in image processing where the image intensity at a particular location depends only on a neighborhood of pixels. more...

The authors consider an algorithm for estimating the unknown parameters of the infection spread model based on the Markov field tools using the maximum likelihood method. It is assumed that each state of the Markov chain represents some configuration of a finite random Markov field, and the probability distribution of the chain states is the same as general probability distribution of the states of elements of the Gibbs random field. [ABSTRACT FROM AUTHOR] more...

In image classification, deriving robust image representations is a key process that determines the performance of vision systems. Numerous image features and descriptors have been developed manually over the years. As an alternative, however, deep neural networks, in particular convolutional neural networks (CNNs), have become popular for learning image features or representations from data and have demonstrated remarkable performance in many real-world applications. But CNNs often require huge amount of labelled data, which may be prohibitive in many applications, as well as long training times. This paper considers an alternative, data-independent means of obtaining features for CNNs. The proposed framework makes use of the Markov random field (MRF) and self-organising map (SOM) to generate basic features and model both intra- and inter-image dependencies. Various MRF textures are synthesized first, and are then clustered by a convolutional translation-invariant SOM, to form generic image features. These features can be directly applied as early convolutional filters of the CNN, leading to a new way of deriving effective features for image classification. The MRF framework also offers a theoretical and transparent way to examine and determine the influence of image features on performance of CNNs. Comprehensive experiments on the MNIST, rotated MNIST, CIFAR-10 and CIFAR-100 datasets were conducted with results outperforming most state-of-the-art models of similar complexity. [ABSTRACT FROM AUTHOR] more...

Segmentation is one of the most complicated procedures in the image processing that has important role in the image analysis. In this paper, an improved pixon-based method for image segmentation is proposed. In proposed algorithm, complex partial differential equations (PDEs) is used as a kernel function to make pixonal image. Using this kernel function causes noise on images to reduce and an image not to be over-segment when the pixon-based method is used. Utilising the PDE-based method leads to elimination of some unnecessary details and results in a fewer pixon number, faster performance and more robustness against unwanted environmental noises. As the next step, the appropriate pixons are extracted and eventually, we segment the image with the use of a Markov random field. The experimental results indicate that the proposed pixon-based approach has a reduced computational load and a better accuracy compared to the other existing pixon-image segmentation techniques. To evaluate the proposed algorithm and compare it with the last best algorithms, many experiments on standard images were performed. The results indicate that the proposed algorithm is faster than other methods, with the most segmentation accuracy. [ABSTRACT FROM AUTHOR] more...

Medical image segmentation is one of the difficult tasks in image processing since the accuracy of segmentation determines the eventual success or failure of proper diagnosis. In medical imaging identification of each pixel in a region has vital importance since it can increase the standard of evaluation criteria. In this respect segmentation of brain MR images has become more significant in research and medical applications related to diagnosis of abnormality and diseases appearing in human brain. Segmentation initiates the process of extraction of various cortical tissues which is a key issue in neuroscience, to detect early neural disorders. The aim of present study is to comprehensively evaluate intensity based fuzzy C-means and Markov random field approaches, both stochastic and deterministic, for the segmentation of brain MR images into three different cortical tissues-gray matter, white matter and cerebrospinal fluid. Along with the analytical assessment of the segmentation techniques including efficiency and user interaction, this work is concentrated on empirical evaluation based on area based matrix. The results illustrate that in all respects, Markov Random field based approaches are showing better performance as compared to fuzzy C-means. Further, the Markov random field approaches are compared to find out which segmentation technique will suit which initial conditions. [ABSTRACT FROM AUTHOR] more...

Abstract: A statistical clustering approach is proposed, based on Markov random field models. A discrete field derived from the raw data set is considered as a field of measures. A hidden field, computed using a new potential function, is used to detect the modes that correspond to domains of high local concentrations of observations. Results obtained on artificially generated and real data sets demonstrate the efficiency of this new approach for unsupervised pattern classification. [Copyright &y& Elsevier] more...

Abstract: In this paper the design of maximally flat linear phase finite impulse response (FIR) filters is considered. The problem with using the genetic algorithm (GA) in this kind of problems is the high cost of evaluating the fitness for each string in the population. The designing of optimum FIR filters under given constraints and required criteria includes exhaustive number of evaluations for filter coefficients, and the repetitive evaluations of objective functions that implicitly constitutes construction of the filter transfer functions. This problem is handled here with acceptable results utilizing Markov random fields (MRF''s) approach. We establish a new theoretical approach here and we apply it on the design of FIR filters. This approach allows us to construct an explicit probabilistic model of the GA fitness function forming what is called the “Ising GA” that is based on sampling from a Gibbs distribution. Ising GA avoids the exhaustive design of suggested FIR filters (solutions) for every string of coefficients in every generation and replace this by a probabilistic model of fitness every gap (period) of iterations. Experimentations done with Ising GA of probabilistic fitness models are less costly than those done with standard GA and with high quality solutions. [Copyright &y& Elsevier] more...

This paper presents a Markov random field (MRF) approach to estimating and sampling the probability distribution in populations of solutions. The approach is used to define a class of algorithms under the general heading distribution estimation using Markov random fields (DEUM). DEUM is a subclass of estimation of distribution algorithms (EDAs) where interaction between solution variables is represented as an undirected graph and the joint probability of a solution is factorized as a Gibbs distribution derived from the structure of the graph. The focus of this paper will be on describing the three main characteristics of DEUM framework, which distinguishes it from the traditional EDA. They are: 1) use of MRF models, 2) fitness modeling approach to estimating the parameter of the model and 3) Monte Carlo approach to sampling from the model. [ABSTRACT FROM AUTHOR] more...

Abstract: This paper describes how a visual system can automatically define features of interest from the observation of a large enough number of natural images. The principle complements the low-level feature extractors provided by PCA filters by analyzing their spatial interactions. This is achieved by modeling an internal representation in the system, composed with ternary variables obtained by thresholding the filters, using a Markov Random Field model. A stochastic gradient algorithm, based on statistics computed from an image database, is used to train this model. The result is a probability distribution on the internal state of the system which adjusts with its environment, under what is referred to as a principle of homeostasis. When new images enter the system, they are confronted to this internal distribution, and images which appear as salient in this regard are detected as visually relevant. A classification of these relevant images is provided, as an illustration of the model. [Copyright &y& Elsevier] more...

Abstract: Occurrence of mixed pixels in remote sensing images is a major problem particularly at coarse spatial resolutions. Therefore, sub-pixel classification is often preferred, where a pixel is resolved into various class components (also called class proportions or fractions). While, under most circumstances, land cover information in this form is more effective than crisp classification, sub-pixel classification fails to account for the spatial distribution of class proportions within the pixel. An alternative approach is to consider the spatial distribution of class proportions within and between pixels to perform super-resolution mapping (i.e. mapping land cover at a spatial resolution finer than the size of the pixel of the image). Markov random field (MRF) models are well suited to represent the spatial dependence within and between pixels. In this paper, an MRF model based approach is introduced to generate super-resolution land cover maps from remote sensing data. In the proposed MRF model based approach, the intensity values of pixels in a particular spatial structure (i.e., neighborhood) are allowed to have higher probability (i.e., weight) than others. Remote sensing images at two markedly different spatial resolutions, IKONOS MSS image at 4 m spatial resolution and Landsat ETM+ image at 30 m spatial resolution, are used to illustrate the effectiveness of the proposed MRF model based approach for super-resolution land cover mapping. The results show a significant increase in the accuracy of land cover maps at fine spatial resolution over that obtained from a recently proposed linear optimization approach suggested by Verhoeye and Wulf (2002) (Verhoeye, J., Wulf, R. D. (2002). Land Cover Mapping at Sub-pixel Scales using Linear Optimization Techniques. Remote Sensing of Environment, 79, 96–104). [Copyright &y& Elsevier] more...

Let n S‐valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag‐r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag‐r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed. [ABSTRACT FROM AUTHOR] more...

Image modeling using Gibbs priors was previously shown, based on experiments, to be effective in image reconstruction problems. This motivated us to evaluate three methods for estimating the priors. Two of them accurately recover the parameters of the priors; however, all of them are useful for binary tomography. This is demonstrated by two sets of experiments: in one the images are from a Gibbs distribution and in the other they are typical cardiac phantom images. [Copyright &y& Elsevier] more...

This paper proposes a stochastic model for continuous speech recognition that provides automatic segmentation of a spoken utterance into phonemes and facilitates the quantitative assessment of uncertainty associated with the identified utterance features. The model is specified hierarchically within the Bayesian paradigm. At the lowest level of the hierarchy, a Gibbs distribution is used to specify a probability distribution on all the possible partitions of the utterance. The number of partitioning elements which are phonemes is not specified a priori. At a higher level in the hierarchical specification, random variables representing phoneme durations and acoustic vector values are associated reported about 0.9% word error rate. The new model was experimentally compared to continuous density mixture HMM (CDHMM) on a same recognition task, and gave significantly smaller word error rates. [Copyright &y& Elsevier] more...