Parallel Relaxation Algorithms For The Statistical Analysis Of Visual Motion

This paper presents a novel texture segmentation method using neural networks and a Markov random field (MRF) model. Multi-scale wavelet coefficients are used as input for the neural networks. The output of the neural network is modeled as a posterior probability. Initially, the multi-scale texture segmentation is performed by the posterior probabilities from the neural networks and MAP (maximum a posterior) classification. Then the MAP segmentation maps are produced at all scales. In order to obtain the more improved segmentation result at the finest scale, our proposed method fuses the multi-scale MAP segmentations sequentially from coarse to fine scales. This is done by computing the MAP segmentation given the segmentation map at one scale and a priori knowledge regarding contextual information which is extracted from the adjacent coarser scale segmentation. In this fusion process, the MRF prior distribution and Gibbs sampler are used, where the MRF model serves as the smoothness constraint and the Gibbs sampler acts as the MAP classifier.

A valid multiscale classification method of synthetic aperture radar (SAR) imagery is proposed based on multiscale technology and Markov random field (MRF) mode. Firstly, we employ multiscale autoregressive model for extracting the feature of SAR image. which is modeled by Markov random field (MRF) Model that relies on the Gaussian distribution. Secondly, using the joint probability distribution in terms of an energy function, estimation of parameters can be performed by the stochastic relaxation algorithm. Then the maximum posteriori (MAP) is designed as the optimal criterion and the final labels are obtained by the simulated annealing algorithm. Experimental results show that this method is accurate, efficient and robust.

For decades, Markov random fields (MRF) have been used by statistical physicists to explain various phenomena occurring among neighboring particles because of their ability to describe local interactions between them. In Winkler (1995) and Bremaud (1999), an MRF model is used to explain why neighboring particles are more likely to rotate in the same direction (clockwise or counterclockwise) or why intensity values of adjacent pixels of an image are more likely to be the same than different values. This model is called the Ising model. There are a large number of problems that can be modeled using the Ising model and where an MRF model can be used. Basically, an MRF model is a spatial-domain extension of a temporal Markov chain where an event at the current time instant depends only on events of a few previous time instants. In MRF, the statistical dependence is defined over the neighborhood system, a collection of neighbors, rather than past events as in the Markov chain model. It is obvious that this type of spatial dependence is a common phenomenon in various signal types including images. In general, images are smooth and, therefore, the intensity values of neighboring pixels are highly dependent on each other. Because of its highly theoretical and complex nature, and intensive computational requirements, practical uses of MRF were extremely limited until recently. Due to the dramatic improvements in computer technologies, MRF modeling has become more feasible for numerous applications, for example, image analysis because many image properties, such as texture, seem to fit an MRF model, i.e., intensity values of neighboring pixels of images are known to be highly correlated with each other. The Markovian nature of these textural properties has long been recognized in the image processing community, and has widely been used in a variety of applications (e.g. image compression and image noise removal). However, these applications were limited to empirical studies and were not based on a statistical model such as the MRF model.

Markov Random Field (MRF) theory has a significant potential role in image segmentation field. It uses (pixels, regions, edges)-based on MRF models to detect objects, boundaries and other relevant information in an image. This paper proposes an extension of Unified Markov Random Field (UMRF) model to include edge-based features. Firstly, the proposed technique employs the likelihood function to combine the advantages of the pixel-based, region-based and edge-based MRF model, by computing the product of the pixel likelihood function, regional likelihood function and edge likelihood function. Secondly, the region-based macro texture features are extracted using the UMRF model. Then the edge-based features are extracted using the maximum gradient method to recover any significant lost information. A principled probabilistic inference is implemented to integrate various types of likelihood information and spatial constraints by iteratively updating the posterior probability of the proposed model. The segmentation process is completed when the iterations converge. The proposed enhanced UMRF technique which combines pixel-based, region-based and edge-based features achieved a higher skin lesion segmentation accuracy than MRF model which combines pixel-based and region-based only.

We present a new approach for the discriminative training of continuous-valued Markov Random Field (MRF) model parameters. In our approach we train the MRF model by optimizing the parameters so that the minimum energy solution of the model is as similar as possible to the ground-truth. This leads to parameters which are directly optimized to increase the quality of the MAP estimates during inference. Our proposed technique allows us to develop a framework that is flexible and intuitively easy to understand and implement, which makes it an attractive alternative to learn the parameters of a continuous-valued MRF model. We demonstrate the effectiveness of our technique by applying it to the problems of image denoising and in-painting using the Field of Experts model. In our experiments, the performance of our system compares favourably to the Field of Experts model trained using contrastive divergence when applied to the denoising and in-painting tasks.

In this paper, we propose a sequence labeling method by using SVM posterior probabilities with a Markov Random Field (MRF) model for colorectal Narrow Band Imaging (NBI) zoom-videoendoscope. Classifying each frame of a video sequence by SVM classifiers independently leads to an output sequence which is unstable and hard to understand by endoscopists. To make it more stable and readable, we use an MRF model to label the sequence of posterior probabilities. In addition, we introduce class asymmetry for the NBI images in order to keep and enhance frames where there is a possibility that cancers might have been detected. Experimental results with NBI video sequences demonstrate that the proposed MRF model with class asymmetry performs much better than a model without asymmetry.

In order to overcome the poor anti-noise performance of traditional fuzzy C-Means (FCM) algorithm in image segmentation, a novel improved FCM algorithm was proposed in this paper based on Particle Swarm Optimization (PSO) algorithm and Markov Random Field (MRF) model, which can make full use of the global searching ability of PSO and the spatial information integrating ability of MRF for image segmentation. In this algorithm, the image segmentation is converted to a PSO optimization problem, in which the fitness function is set up to containing the spatial information based on the spectral value and the neighboring pixels modeled by MRFs. And segmentation results can be iteratively obtained during the PSO iterations according to the newly designed membership function of FCM in which the spatial information is integrated. The experiments herein reported in this paper illustrate the better performance of this algorithm than the traditional FCM algorithm and the PSO algorithm for image segmentation.

We present a new method using the Bayesian approach and a Markov random field (MRF) model of integrating several low level visual modules. Using this approach, we have shown how results from an edge based stereo module can be integrated with an intensity based stereo algorithm. In another example, results from a shape from shading module are combined with intensity based stereo. We first derive the intensity based stereo algorithm using the MRF model. The integration is then performed by coupling the results from other modules to the energy functional of the MRF associated with the intensity based stereo. The maximum a prosteriori (MAP) estimate of the resulting MRF is obtained using the mean field annealing algorithm. Results from real and artificial images show a consistent improvement in the accuracy after integration.

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.

A new image segmentation algorithm based on Markov random field (MRF) and ant colony system (ACS) is presented in this paper. Information positive feedback and heuristic search, the characters of ACS, were applied for the image segmentations with MRF model. The maximum a posterior (MAP) global best solution of segmentations will be got though MRF, which describes image data relations by local correlations instead of global image possibility distributions. Compared with the simulated annealing (AS), ACS needs less time to search the global best solution. In this paper we proposed a segmentation algorithm combined MRF with ACS, which not only applied ACS as optimization algorithm but also introduced the neighborhood pheromone interaction rules into ACS under MRF model. Especially the pheromone interaction update provided remunerative information to ants in a neighborhood instead of an ant, which could accelerate the optimizing velocity and restrain the relative blur noise. The followed image segmentations experiments proved that this novel algorithm could reach a satisfied result among the noise restraint, edges preservation and computation complexity.

Based on the computer texture analysis method, a new noncontact surface roughness measurement technique is proposed. The method is inspired by the nonredundant directional selectivity and highly discriminative nature of the wavelet representation and the capability of the Markov random field (MRF) model to capture statistical regularities. Surface roughness information contained in the texture features may be extracted based on an MRF stochastic model of textures in the wavelet feature domain. The model captures significant intrascale and interscale statistical dependencies between wavelet coefficients. To investigate the relationship between the texture features and surface roughness Ra, a simple research setup, which consists of a charge-coupled diode camera without a lens and a diode laser, was established, and the laser speckle texture patterns are acquired from some standard grinding surfaces. The research results have illustrated that surface roughness Ra has a good monotonic relationship with the texture features of the laser speckle pattern. If this measuring system is calibrated with the surface standard samples roughness beforehand, the surface roughness actual value Ra can be deduced in the case of the same material surfaces ground at the same manufacture conditions.

This paper presents an effective Bayesian wavelet shrinkage approach, in which a new Markov random field (MRF) model is used to improve the noise suppression performance. It is known that relatively few large wavelet coefficients carry the essential information of an image. These coefficients tend to cluster around the location of important feature in the image, such as edge discontinuities, peaks, and corners. This spatial clustering property is expressed in a prior model in the Bayesian framework. This paper proposes a novel prior model that models the configurations of the wavelet coefficients as a MRF. This model is adaptive to the wavelet transform character of two-dimension images that significant coefficients form clusters with predominantly the horizontal, vertical, or diagonal direction in each orientation subband. This prior model consequently effects the manipulation of the coefficients and a spatially adaptive Bayesian shrinkage function is obtained. Experimental results demonstrate this method can effectively suppress additive Gaussian white noise and preserve the details of the image. The performance surpasses related earlier methods quantitatively and qualitatively.

The problem of clutter region identification based on Markov random field (MRF) models is addressed. Observations inside each clutter region are assumed homogenous, i.e., observations follow a single probability distribution. Our goal is to partition clutter scenes into homogenous regions and to determine this underlying probability distribution. Metropolis-Hasting and reversible jump Markov chain (RJMC) algorithms are used to search for solutions based on the maximum a posteriori (MAP) criterion. Several examples illustrate the performance of our algorithm.

Super-resolution technology is considered as an efficient approach to promote the image quality of forward-looking imaging radar. However, super-resolution technology is inherently an ill-conditioned issue, whose solution is quite susceptible to noise. Bayesian method can efficiently alleviate this issue through utilizing prior knowledge of the imaging process, in which the scene prior information plays a pretty significant role in ensuring the imaging accuracy. In this paper, we proposed a novel Bayesian super-resolution method on the basis of Markov random field (MRF) model. Compared with the traditional super-resolution method which is focused on one-dimensional (1-D) echo processing, the MRF model adopted in this study strives to exploit the two-dimensional (2-D) prior information of the scene. By using the MRF model, the 2-D spatial structural characteristics of the imaging scene can be well described and utilized by the nth-order neighborhood system. Then, the imaging objective function can be constructed through the maximum a posterior (MAP) framework. Finally, an accelerated iterative threshold/shrinkage method is utilized to cope with the objective function. Validation experiments using both synthetic echo and measured data are designed, and results demonstrate that the new MAP-MRF method exceeds other benchmarking approaches in terms of artifacts suppression and contour recovery.

A general framework is presented to realize 3D object recognition, invariant to object scaling, deformation, rotation, occlusion, and viewpoint change. This framework utilizes densely sampled grids, with different resolutions, to represent the local information of the input image. A Markov random field (MRF) model is then created to model the geometric distribution of the object key nodes. Flexible matching, which is aimed at finding the accurate correspondence map between the key points of two images, is performed by combining the local similarities and the geometric relations together using the highest confidence first (HCF) method. Afterwards, a global similarity is calculated for object recognition. Experimental results on the Coil-100 object database are presented. The excellent recognition rates achieved in all the experiments indicate that our approach is well-suited for appearance-based recognition.