Efficient image labeling based on markov random field and error backpropagation network

The authors investigate a method of efficiently labeling images using the Markov random field (MRF). The MRF model is defined on the region adjacency graph and the labeling is then optimally determined using simulated annealing. The MRF model parameters are automatically estimated using an error backpropagation network. The proposed method is analyzed through experiments using real natural scene images. >

The Markov random field (MRF) formation allows independence over small pixel neighborhoods suitable for SIMD implementation. The equivalence between the Gibbs distribution over global configurations and MRF allows description of the problem as maximizing a probability or, equivalently, minimizing an energy function (EF). The EF is a convenient device for integrating 'votes' from disparate, preprocessed features--mean intensity, variance, moments, etc. Contributions from each feature are simply weighted and summed. The EF is flexible and can be easily modified to capture a priori beliefs about the distribution of the configuration space, and still remain theoretically sound. A unique formulation of the EF is given. Notably, a deterministic edge finder contributes to the EF. Weights are independently assigned to each feature's report (indicators). Simulated annealing is the theoretical mechanism which guarantees convergence in distribution to a global minimum. Because the number of iterations is an exponential function of time, the authors depart from theory and implement a fast, heuristic 'cooling' schedule. A videotape of results on simulated FLIR imagery demonstrates real-time update over the entire image. Actual convergence is still too slow for real-time use (O(1 min.)), but the quality of results compares favorably with other region labeling schemes.

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.

This paper deals with the problem of depth recovery and image restoration from sparse and noisy image data. The image is modeled as a Markov random field and a new energy function is developed to effectively detect discontinuities in highly sparse and noisy images. The model provides an alternative to the use of a line process. Interpolation over missing data sites is first done using local characteristics to obtain initial estimates and then simulated annealing is used to compute the maximum a posteriori (MAP) estimate. A threshold on energy reduction per iteration is used to speed up simulated annealing by avoiding computation that contributes little to the energy minimization. Moreover, a minor modification of the posterior energy function gives improved results for random as well as structured sparsing problems. Results of simulations carried out on real range and intensity images along with details of the simulations are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Improving the runtime of MRF based method for MRI brain segmentation

One of the major factors plaguing the performance of synthetic aperture radar (SAR) imagery is the presence of signal-dependent speckle noise. Grainy in appearance, speckle noise is primarily due to the phase fluctuations of the electromagnetic return signals. Since inherent spatial-correlation characteristics of speckle in SAR images are not exploited in existing multiplicative models for speckle noise, a new approach is proposed here that provides a new mathematical framework for modeling and reduction of speckle noise. The contribution of this paper is twofold. First, a novel model for speckled SAR imagery is introduced based on Markov random fields (MRFs) in conjunction with statistical optics. Second, utilizing the model, a global energy-minimization algorithm, based on simulated annealing (SA), is introduced for speckle reduction. In particular, the joint conditional probability density function (cpdf) of the intensity of any two points in the speckled image and the associated correlation function are used to derive the cpdf of any center pixel intensity given its four neighbors. The Hammersley- Clifford theorem is then used to derive the energy function associated with the MRF. The SA, built on the Metropolis sampler, is employed for speckle reduction. Four metrics are used to assess the quality of the speckle reduction: the mean-square error, SNR, an edge-preservation parameter and the equivalent number of looks. A comparative study using both simulated speckled images as well as real SAR images indicates that the proposed approach performs favorably in comparison to existing filtering techniques such as the modified-Lee and the enhanced Frost-algorithms.

This paper introduces a multimodal approach for reranking of image retrieval results based on relevance feedback. We consider the problem of reordering the ranked list of images returned by an image retrieval system, in such a way that relevant images to a query are moved to the first positions of the list. We propose a Markov random field (MRF) model that aims at classifying the images in the initial retrieval-result list as relevant or irrelevant; the output of the MRF is used to generate a new list of ranked images. The MRF takes into account (1) the rank information provided by the initial retrieval system, (2) similarities among images in the list, and (3) relevance feedback information. Hence, the problem of image reranking is reduced to that of minimizing an energy function that represents a trade-off between image relevance and interimage similarity. The proposed MRF is a multimodal as it can take advantage of both visual and textual information by which images are described with. We report experimental results in the IAPR TC12 collection using visual and textual features to represent images. Experimental results show that our method is able to improve the ranking provided by the base retrieval system. Also, the multimodal MRF outperforms unimodal (i.e., either text-based or image-based) MRFs that we have developed in previous work. Furthermore, the proposed MRF outperforms baseline multimodal methods that combine information from unimodal MRFs.

The exemplar-based data clustering problem can be formulated as minimizing an energy function defined on a Markov random field (MRF). However, most algorithms for optimizing the MRF energy function cannot be directly applied to the task of clustering, as the problem has a high-order energy function. In this paper, we first show that the high-order energy function for the clustering problem can be simplified as a pairwise energy function with the metric property, and consequently it can be optimized by the α-expansion move algorithm based on graph cut. Then, the original expansion move algorithm is improved in the following two aspects: 1) Instead of solving a minimal s-t graph cut problem, we show that there is an explicit and interpretable solution for minimizing the energy function in the clustering problem. Based on this interpretation, a fast α-expansion move algorithm is proposed, which is much more efficient than the graph-cut-based algorithm. 2) The fast α-expansion move algorithm is further improved by extending its move space so that a larger energy value reduction can be achieved in each iteration. Experiments on benchmark data sets show that the enhanced expansion move algorithm has a better performance, compared to other state-of-the-art exemplar-based clustering algorithms.

In this paper we describe Neural Network based algorithms for the segmentation of textured gray level images. We for- mulate the problem as one of minimizing an energy function, derived through the representation of textures as Markov Random Fields (MRF). The texture intensity array is modelled as a Gauss Markov Random Field (GMRF) and an Ising model is used to characterize the label distribution. The resulting nonconvex energy function is minimized using a Hopfield neural network. The solution obtained is a local optimum in general and may not be satisfactory in many cases. Although stochastic algorithms like simulated annealing have a potential of finding the global optimum, they are computationally expensive. We suggest an alternate approach based on the theory of learning automata which introduces stochastic learning into the iterations of the Hopfield network. A probability distribution over the possible label configurations is defined and the probabilities are updated depending on the final stable states reached by the neural network. This iterated hill climbing algorithm combines the fast convergence of the deterministic relaxation with the sustained exploration of the stochastic algorithms. The perfor- mance of this rule in classifying some real textured images is given.

This paper presents a new optical flow estimation method using Markov Random Fields (MRFs) modelling. In the MRF framework, optical flow estimation leads to minimizing an energy function. To this end, we propose an Evolutionary Algorithm (EA) based on a Divide-and-Conquer strategy which adequately exploits the Markovian property. The image is split into small parts on which EAs are performed separately and independently. The elementary results obtained from all image parts are then combined into a final global solution. Experimental results using synthetic and real-world image sequences demonstrate the effectiveness of the method. Compared with traditional ICM and simulated annealing, results are improved. Moreover, computation cost is significantly reduced in comparison with a basic EA.

Floods can cause huge damage to society, the economy, and the environment. As a result, it is vital to determine the extent and type of land cover in flooded areas quickly and accurately in order to facilitate disaster relief and mitigation efforts. Synthetic aperture radar (SAR) is an all-weather, 24 h data source used to extract information about flood inundations, and its primary aim is to extract water body information for flood monitoring. In this study, we have studied the backscattering characteristics of water and non-water, combined the threshold segmentation method with Markov random fields (MRF), and embedded simulated annealing (SA) in the process of image noise reduction, resulting in the development of a water extraction method KI-MRF-SA with high accuracy in classification and high automation. Furthermore, object-scale adaptive convolutional neural networks (OSA-CNN) are introduced for the classification of optical images before the flood in order to provide reference data for flood inundation analysis. The method proposed in this study consists of the following three steps: (1) The Kittler and Illingworth (KI) thresholding algorithm is used for the segmentation of SAR images in order to determine the initial flood inundation extent; (2) MRF and SA algorithms are employed as a means to optimize the initial flood inundation extent, and the results are combined across multiple polarizations by using an intersection operation to determine the final flood inundation extent; and (3) As part of the flood mapping process, land cover types before the flood are classified using OSA-CNN and combined with flood inundation extents. According to the experimental results, it is evident that the proposed KI-MRF-SA method is capable of distinguishing water from non-water with significantly higher accuracy (3–5% improvement in the overall accuracy) than conventional thresholding methods. Combined with the classification method of OSA-CNN proposed in our earlier research, the overall classification accuracy of flood-affected areas could reach 92.7%.

Pre-stack seismic inversion has inherently supremacy and is a complicated problem. It is a simultaneous inversion for multi-parameters and is ill-posed and band-limited. Thus the results are of non-unique and its process is unstable. Combining the full Zoeppritz equation with both section constant V S /V P and the edge-preserving regularization can relieve these problems. Here we provided an inverted strategy constructing a new objective function based on the edge-preserving regularization and Markov random field (MRF). The method needs to gain reflectivity by the full Zoeppritz equation, and applies fast simulated annealing (FSA) to nonlinear optimization problem. Combining high- with low- orders MRF can improve the inverted results, namely utilize high-order MRF at the early stage and low-order MRF at late iterations. Moreover, to the transverse isotropy layered model, a large coefficient in horizontal direction is helpful to improve lateral continuity, and a small coefficient in vertical direction can preserve large longitudinal gradient. We test the method on field data example. The inverted results of multiple-order MRF are better than that of single-order MRF, and they match well with logging data.

The present paper is concerned with the study of parallel approaches for the relaxation algorithms associated to Markov Random Fields (MRF) models in image analysis, [2]. MRF-based relaxation algorithms are known to be intrinsically parallel and massive parallelizations by updating at once independent variables of the field have been early described, [4]. We present here a different approach based on relaxation algorithms running in parallel at different and interacting periodically. The proposed approach is based on parallel Markov chains which have been studied by Aarts et al., [l], and Graffigne, [3], for global optimization using simulated annealing. In our method, parallel Markov chains are coupled with a new multiscale exploration of the configuration space for MRF. This multiscale exploration can be implemented efficiently by considering a sequence of multiresolution MRF models whose parameters and neighborhood structures are obtained from the original MRF model. The designed algorithm is suited for MIMD computers and can be outlined as follows. First MRF models at different scales are computed from the original MRF model. The relaxations at different scales are stochastic and cooperative : every p iterations - one iteration corresponding to a full sweep on the image - a processor attempts to transfer local estimates to the processor controlling the next finer scale. With the low resolution levels of the hierarchy are associated high temperatures in the stochastic relaxation, [3]. A high temperature allows to escape from local minima of the energy function. With the intermediate resolution levels are associated lower temperatures. At these levels, the relaxation process becomes more sensitive to local minima and visits the large or medium size valleys of the energy landscape. At the finest resolution level deterministic relaxation is adopted : the estimation is ultimately refined at that level. The proposed parallelization approach is compared to sequential deterministic and stochastic relaxation in the context of optical flow estimation. The multiscale algorithm exhibits fast convergence properties, comparable to multigrid deterministic relaxation, and the obtained estimates are close to the near optimal solutions obtained by time consuming sequential stochastic methods.

In Terahertz continuous-wave laser scanning imaging system, the laser output power's fluctuation and the aperture effects of a finite focus diameter have significant influence on the image quality, which reduces the image resolution and causes the imaging noise. The most common problem of image denoising is that some interesting structures in the image will be removed from the concerned image during noise suppression. Because Markov random field (MRF) can be used to describe the spatial continuity, the structures of images can be modeled if a proper neighborhood system is selected. Therefore, MRF and simulated annealing are used to suppress the image noise and increase the image resolution. Simulation and experiment show that the method can preserve the object structures of THz images.

In the traditional processing flow of interferometric synthetic aperture radar (SAR) technique, the processing of phase is conducted via two separated and successive steps, i.e., phase denoising and phase unwrapping. That is to say, first, wrapped phases without noise are generated, and then, the true phases without 2π-ambiguities are reconstructed (here and in the rest of this paper, true phase refers to the information-induced unwrapped phase without noise). Such separated steps will inevitably bring in extra estimation error because each step has necessary approximations and presumptions which do not always hold. On the contrary, in this paper, we treat phase denoising and unwrapping as a single problem of true phase recovery from observed ones. Following this methodology, an integrated phase denoising and unwrapping algorithm based upon Markov random fields (MRFs) is proposed. Taking a priori knowledge of interferometric phases into account, MRF is used to model the relationship between the elements in the random variable set including both true phases and their observations. After the model is built up, the energy function of this MRF is defined according to the local-independence property inferred from the MRF structure and then minimized to obtain the estimate of the true phase value. In the end of this paper, experiments on simulated and true phase data are conducted, and the comparison with several commonly used unwrapping methods is proposed to verify the efficiency of the proposed MRF algorithm.