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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...

Synthetic aperture radar (SAR) provides rich information about the Earth’s surface under all-weather and day-and-night conditions, and is applied in many relevant fields. SAR imagery semantic segmentation, which can be a final product for end users and a fundamental procedure to support other applications, is one of the most difficult challenges. This paper proposes an encoding-decoding network based on Deeplabv3+ to semantically segment SAR imagery. A new potential energy loss function based on the Gibbs distribution is proposed here to establish the semantic dependence among different categories through the relationship among different cliques in the neighborhood system. This paper introduces an improved channel and spatial attention module to the Mobilenetv2 backbone to improve the recognition accuracy of small object categories in SAR imagery. The experimental results show that the proposed method achieves the highest mean intersection over union (mIoU) and global accuracy (GA) with the least running time, which verifies the effectiveness of our method. more...

We propose a numerical method to learn maximum entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers, [10] and [4], which proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows one to properly handle memory effects in spike statistics, for large-sized neural networks. more...

A novel video motion object segmentation algorithm was proposed under spatial-temporal framework. First, the inter-frame image was partitioned into some regions by the improved watershed algorithm, and the initial segmentation mask was obtained after combining the spatial and temporal segmentation results. Then a model of Markov random field was built based on regions, and the corresponding Gibbs potential energy function was defined. The optimization of solution was carried out by iterated conditional mode （ICM） method. The experiment results show that the algorithm is more effective than COST 211 analysis model. more...

A novel video motion object segmentation algorithm was proposed under spatial-temporal framework. First, the inter-frame image was partitioned into some regions by the improved watershed algorithm, and the initial segmentation mask was obtained after combining the spatial and temporal segmentation results. Then a model of Markov random field was built based on regions, and the corresponding Gibbs potential energy function was defined. The optimization of solution was carried out by iterated conditional mode （ICM） method. The experiment results show that the algorithm is more effective than COST 211 analysis model. more...

Molecular dynamic simulations are performed to investigate a long-time evolution of different initial signals in nonlinear acoustic chains with realistic Exp-6 potential and with power potentials. First, in the chain with realistic potential, long-lifetime kink-shaped excitations are found in the system in thermodynamic equilibrium. They give sharp peaks on high-energy tile of Gibbs distribution. Travelling along the chain, each kink collects the energy from the background atoms, and, consequently, transfers it to small-amplitude phonons. Dynamic equilibrium is observed between the processes of growth and decay of the kinks. more...

This paper presents a reduced-complexity deterministic annealing (DA) approach for vector quantizer (VQ) design by using soft information processing with simplified assignment measures. Low-complexity distributions are designed to mimic the Gibbs distribution, where the latter is the optimal distribution used in the standard DA method. These low-complexity distributions are simple enough to facilitate fast computation, but at the same time they can closely approximate the Gibbs distribution to result in near-optimal performance. We have also derived the theoretical performance loss at a given system entropy due to using the simple soft measures instead of the optimal Gibbs measure. We use thederived result to obtain optimal annealing schedules for the simple soft measures that approximate the annealing schedule for the optimal Gibbs distribution. The proposed reduced-complexity DA algorithms have significantly improved the quality of the final codebooks compared to the generalized Lloyd algorithm and standard stochastic relaxation techniques, both with and without the pairwise nearest neighbor (PNN) codebook initialization. The proposed algorithms are able to evade the local minima and the results show that they are not sensitive to the choice of the initial codebook. Compared to the standard DA approach, the reduced-complexity DA algorithms can operate over 100 times faster with negligible performance difference. For example, for the design of a 16-dimensional vector quantizer having a rate of 0.4375 bit/sample for Gaussian source, the standard DA algorithm achieved 3.60 dB performance in 16 483 CPU seconds, whereas the reduced-complexity DA algorithm achieved the same performance in 136 CPU seconds. Other than VQ design, the DA techniques are applicable to problems such as classification, clustering, and resource allocation. more...