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Let us color the vertices of the grid ℤ^d or the infinite regular tree 𝕋_d, using a finite number of colors, with the constraint that some predefined pairs of colors are not allowed for adjacent vertices. The set of admissible colorings is called a nearest-neighbor subshift of finite type (SFT). We study “uniform” probability measures on SFT, with the motivation of having an insight into “typical” admissible configurations. We recall the known results on uniform measures on SFT on grids and we complete the picture by presenting some contributions to the description of uniform measures on SFT on 𝕋_d. Then we focus on the problem of uniform random sampling of configurations of SFT. We propose a first method based on probabilistic cellular automata, which is valid under some restrictive conditions. Then we concentrate on the case of SFT on ℤ for which we propose several alternative sampling methods.

A fuzzy-logic approach to the classification of multitemporal, multisensor remote-sensing images is proposed. The approach is based on a fuzzy fusion of three basic sources of information: spectral, spatial and temporal contextual information sources. It aims at improving the accuracy over that of single-time noncontextual classification. Single-time class posterior probabilities, which are used to represent spectral information, are estimated by Multilayer Perceptron neural networks trained for each single-time image, thus making the approach applicable to multisensor data. Both the spatial and temporal kinds of contextual information are derived from the single-time classification maps obtained by the neural networks. The expert's knowledge of possible transitions between classes at two different times is exploited to extract temporal contextual information. The three kinds of information are then fuzzified in order to apply a fuzzy reasoning rule for their fusion. Fuzzy reasoning is based on the "MAX" fuzzy operator and on information about class prior probabilities. Finally, the class with the largest fuzzy output value is selected for each pixel in order to provide the final classification map. Experimental results on a multitemporal data set consisting of two multisensor (Landsat TM and ERS-1 SAR) images are reported. The accuracy of the proposed fuzzy spatio-temporal contextual classifier is compared with those obtained by the Multilayer Perceptron neural networks and a reference classification approach based on Markov Random Fields (MRFs). Results show the benefit of adding spatio-temporal contextual information to the classification scheme, and suggest that the proposed approach represents an interesting alternative to the MRF-based approach, in particular, in terms of simplicity.

Rich heterogeneous data provided by social networks can be very big, which imposes considerable challenges for object extraction and image classification. Therefore, the objective of this work is to propose an unsupervised object cosegmentation method that could be notably efficient to improve image classification performance. The main goal of cosegmentation is to extract the salient common objects within each image. To this end, we propose to minimize an energy function based on the Markov Random Field using the saliency detection, while considering linear dependence of generated foreground histograms of the input image collection. In fact, the saliency detection is processed in two steps. In each image, we detect salient objects, by considering appearance similarity and spatial distributions of image pixels. Then, fuzzy quantification is used to correct the belonging of pixels to the foreground objects. Finally, an iterative optimization permits to enhance the final segmentation results. The proposed method has been validated as a preprocessing step for image classification. Indeed, to enhance cosegmentation-based classification performance, we have applied a semi-supervised object classification based on ensemble projection. Qualitative and quantitative evaluations of the proposed cosegmentation and classification techniques on the iCoseg, CDS and Oxford Flowers 17 datasets demonstrate the effectiveness of the proposed framework.

A large number of image and spatial information processing problems involves the estimation of the intrinsic image information from observed images, for instance, image restoration, image registration, image partition, depth estimation, shape reconstruction and motion estimation. These are inverse problems and generally ill-posed. Such estimation problems can be readily formulated by Bayesian models which infer the desired image information from the measured data. Bayesian paradigms have played a very important role in spatial data analysis for over three decades and have found many successful applications. In this paper, we discuss several aspects of Bayesian paradigms: uncertainty present in the observed image, prior distribution modeling, Bayesian-based estimation techniques in image processing, particularly, the maximum a posteriori estimator and the Kalman filtering theory, robustness, and Markov random fields and applications.

This paper proposes a new approach to the problem of intelligently regulating image-processing parameters of a distributed network. The proposed approach is based on two-step probabilistic process:

(a) belief updating, which consists in computing a functional cost at each node of the network and,

(b) belief maximization, which depends on maximizing this functional cost by using a stochastic optimization algorithm.

The architecture of an image processing system, consisting of three modules connected in a chain-like structure, is presented as an example showing the capabilities of the proposed approach. Each module is provided with a priori information about the set of parameters that manage a particular data transformation, and with evaluation criteria to judge data quality and to decide on the parameters to be adjusted. Experimental results obtained by using a digitally controlled camera and lens objective, are presented to show the validity of the proposed approach.

In this paper we present a system for the recognition of handwritten words on literal check amounts which advantageously combine HMMs and Markov random fields (MRFs). It operates at pixel level, in a holistic manner, on height normalized word images which are viewed as random field realizations. The HMM analyzes the image along the horizontal writing direction, in a specific state observation probability given by the column product of causal MRF-like pixel conditional probabilities. Aspects concerning definition, training and recognition via this type of model are developed throughout the paper. We report a 90.08% average word recognition rate on 2378 words and a 79.52% amount rate on 579 amounts of the SRTP^* French postal check database (7031 words, 1779 amounts, different scriptors).

In this paper, we focus on the problem of change point detection in piecewise constant signals. This problem is central to several applications such as human activity analysis, speech or image analysis and anomaly detection in genetics. We present a novel window-sliding algorithm for an online change point detection. The proposed approach considers a local blanket of a global Markov Random Field (MRF) representing the signal and its noisy observation. For each window, we define and solve the local energy minimization problem to deduce the gradient on each edge of the MRF graph. The gradient is then processed by an activation function to filter the weak features and produce the final jumps. We demonstrate the effectiveness of our method by comparing its running time and several detection metrics with state of the art algorithms.

This paper studies the convergence of the stochastic algorithm of the modified Robbins–Monro form for a Markov random field (MRF), in which some of the nodes are clamped to be observed variables while the others are hidden ones. Based on the theory of stochastic approximation, we propose proper assumptions to guarantee the Hölder regularity of both the update function and the solution of the Poisson equation. Under these assumptions, it is proved that the control parameter sequence is almost surely bounded and accordingly the algorithm converges to the stable point of the log-likelihood function with probability $1$.

A new class of forward quantum Markov fields (FQMFs) is introduced. The structure of these quantum Markov fields is investigated in the finer structure of a quasi-local algebra of observable over a tree-like graph. We provide an effective construction of a class of FQMCs. Moreover, we show the existence of three FMRFs associated with an Ising type model on a Husimi tree.

The established approach to unsupervised protein contact prediction estimates coevolving positions using undirected graphical models. This approach trains a Potts model on a Multiple Sequence Alignment. Increasingly large Transformers are being pretrained on unlabeled, unaligned protein sequence databases and showing competitive performance on protein contact prediction. We argue that attention is a principled model of protein interactions, grounded in real properties of protein family data. We introduce an energy-based attention layer, factored attention, which, in a certain limit, recovers a Potts model, and use it to contrast Potts and Transformers. We show that the Transformer leverages hierarchical signal in protein family databases not captured by single-layer models. This raises the exciting possibility for the development of powerful structured models of protein family databases.

Over the last ten years, several model based methods have been proposed for segmentation and classification of textured images. Models based on random field representations and psychophysical/neurophysiological studies have been dominant. In this chapter, we present examples drawn from both approaches. Related issues on implementation of the various optimal/suboptimal algorithms are also addressed.

In this paper we present a system for the recognition of handwritten words on literal check amounts which advantageously combine HMMs and Markov random fields (MRFs). It operates at pixel level, in a holistic manner, on height normalized word images which are viewed as random field realizations. The HMM analyzes the image along the horizontal writing direction, in a specific state observation probability given by the column product of causal MRF-like pixel conditional probabilities. Aspects concerning definition, training and recognition via this type of model are developed throughout the paper. We report a 90.08% average word recognition rate on 2378 words and a 79.52% amount rate on 579 amounts of the SRTP* French postal check database (7031 words, 1779 amounts, different scriptors).

A large number of image and spatial information processing problems involves the estimation of the intrinsic image information from observed images, for instance, image restoration, image registration, image partition, depth estimation, shape reconstruction and motion estimation. These are inverse problems and generally ill-posed. Such estimation problems can be readily formulated by Bayesian models which infer the desired image information from the measured data. Bayesian paradigms have played a very important role in spatial data analysis for over three decades and have found many successful applications. In this paper, we discuss several aspects of Bayesian paradigms: uncertainty present in the observed image, prior distribution modeling, Bayesian-based estimation techniques in image processing, particularly, the maximum a posteriori estimator and the Kalman filtering theory, robustness, and Markov random fields and applications.

In this paper, we introduce a new algorithm for image texture synthesis from an input sample. In our approach, patch regions from a sample image are selected and copied to the output and then stitched together along optimal seams to generate a new output. In contrast to other techniques, we use min-cut/max-flow technique to determine the optimal patch region between the input and the output texture, and we use a zigzagged double direction scanning method instead of raster scan order method. This can restrain texel's imperfection and orientation of texture synthesis effectively. The results show that our method can produce a more satisfactory effect.

Over the last ten years, several model based methods have been proposed for segmentation and classification of textured images. Models based on random field representations and psychophysical/neurophysiological studies have been dominant. In this chapter, we present examples drawn from both approaches. Related issues on implementation of the various optimal/suboptimal algorithms are also addressed.

We introduce a new approach, based on the natural clique structure of diffusive networks, to both the standard and the graded weak membrane models of image reconstruction from noisy sparse data. The new clique-based formulation leads to a single discontinuity field, provides a natural solution to the long-standing localization problem concerning the gradient field construction, and yields an exact paradigm of cellular automata field. The standard weak membrane model of image reconstruction assumes weakly continuous images corrupted by white gaussian noise and operates through an iterative process of constrained anisotropic diffusion. The anisotropy is controlled by the line process I describing the discontinuity contours, while the constraint enforces closeness to the image data. The graded weak membrane model includes an extra field, the sparse processs, which computes a 0 to 1 visual significance map and excludes the less significant data from the image reconstruction scheme. In this mechanism the sparse process s couples with a local noise estimate and, in the interactive model, with the line process l. The resulting [0,1] significance hierarchy of image sites can be regarded as the membership distribution of a fuzzy minimal image.