Near-optimal Herding

Maximum a posteriori (MAP) inference in Markov random field (MRF) lays the foundation for many computer vision tasks, which can be formulated by a binary quadratic programming (BQP) problem. Compar...

We consider general discrete Markov Random Fields(MRFs) with additional bottleneck potentials which penalize the maximum (instead of the sum) over local potential value taken by the MRF-assignment. Bottleneck potentials or analogous constructions have been considered in (i) combinatorial optimization (e.g. bottleneck shortest path problem, the minimum bottleneck spanning tree problem, bottleneck function minimization in greedoids), (ii) inverse problems with $L_{\infty}$-norm regularization and (iii) valued constraint satisfaction on the $(\min,\max)$-pre-semirings. Bottleneck potentials for general discrete MRFs are a natural generalization of the above direction of modeling work to Maximum-A-Posteriori (MAP) inference in MRFs. To this end we propose MRFs whose objective consists of two parts: terms that factorize according to (i) $(\min,+)$, i.e. potentials as in plain MRFs, and (ii) $(\min,\max)$, i.e. bottleneck potentials. To solve the ensuing inference problem, we propose high-quality relaxations and efficient algorithms for solving them. We empirically show efficacy of our approach on large scale seismic horizon tracking problems.

This paper presents a new color image analysis approach which fuses several processing maps by Graph-Cuts algorithm for Markov Random Field (MRF) in different color spaces. Recently, graph-based image analysis methods, such as Graph-Cuts, have been achieved exciting results for approximate inference in Markov Random Field. One color image can be represented in many color spaces, such as RGB, LAB and HSV, but existing Graph-Cuts approaches often compute global energy function only in one color spaces and ignore that each color space has an interesting property for certain applications respectively. This paper processes images in MRF and represents them in one MRF model firstly. Then Graph-Cuts algorithms are used to process images in each color space and generate one map. Several processing maps can be acquired from some color spaces. These maps are fused to get more reliable and accurate results. We select stereo matching which can get depth maps from multi-view images to evaluate our image analysis approach. The experiments herein reported in this paper illustrate the potential of this approach compared to existing Graph-Cuts methods from processing results.

Markov Random Fields (MRFs) are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision. Inference in MRFs is intractable in general and related work resorts to approximation algorithms. Among those techniques, semidefinite programming (SDP) relaxations have been shown to provide accurate estimates while scaling poorly with the problem size and being typically slow for practical applications. Our first contribution is to design a dual ascent method to solve standard SDP relaxations that takes advantage of the geometric structure of the problem to speed up computation. This technique, named Dual Ascent Riemannian Staircase (DARS), is able to solve large problem instances in seconds. Our second contribution is to develop a second and faster approach. The backbone of this second approach is a novel SDP relaxation combined with a fast and scalable solver based on smooth Riemannian optimization. We show that this approach, named Fast Unconstrained SEmidefinite Solver (FUSES), can solve large problems in milliseconds. Contrarily to local MRF solvers, e.g., loopy belief propagation, our approaches do not require an initial guess. Moreover, we leverage recent results from optimization theory to provide per-instance sub-optimality guarantees. We demonstrate the proposed approaches in multi-class image segmentation problems. Extensive experimental evidence shows that (i) FUSES and DARS produce near-optimal solutions, attaining an objective within 0.1% of the optimum, (ii) FUSES and DARS are remarkably faster than general-purpose SDP solvers, and FUSES is more than two orders of magnitude faster than DARS while attaining similar solution quality, (iii) FUSES is faster than local search methods while being a global solver.

Non-additive image steganographic framework based on variational inference in Markov Random Fields

Markov random field (MRF) model-based penalty is widely used in statistical iterative reconstruction (SIR) of low dose CT (LDCT) reconstruction for noise suppression and edge-preserving. In this strategy, normal dose CT scans are usually used as a priori information to further improve the LDCT quality. However, repeated CT scans are needed and registration or segmentation is usually applied first when misalignment between the low-dose and normal-dose scans exists. The study aims to propose a new MRF prior model of SIR based on the NDCT database without registration. In the proposed model, MRF weights are predicted using optimal similar patch samples from the NDCT database. The patch samples are determined by evaluating the similarity with Euclidean distance between patches from NDCT and the target patch of LDCT. The proposed prior term is incorporated into the SIR cost function, which is to be minimized for LDCT reconstruction. The proposed method is tested on an artificial LDCT data based on a high-dose patient data. Preliminary result has proved its potential performance in edge and structure detail preservation.

Hashing has been used for decades in many fields such as encryption, password verification, and pattern search. Hash systems consist mainly of three components: the hash function, the hash table, and the linked lists that are attached to the hash table. One of the major benefits of using a hash function is reduction in the runtime of the hash-based software systems. However, their linked lists are a major source of time consumption. In this paper, an innovative method is proposed to remove all the linked lists attached to the hash table and collect the necessary information in a one-dimensional array. The method can be used to create an index for the human genome. The human genome is the size of a million-page book with no index, and it is difficult to find the needed information. The proposed method transforms list search operations with linear time complexity into array searches with logarithmic time complexity. In a sample problem, finding inversions in genomic sequences, the proposed indexing system is compared with traditional hashing systems with linked lists. It is demonstrated that, in addition to time complexity reduction, the proposed method reduces the space required for the hash system to one half of what is used by linked list based methods.

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.

We take the point of view that a Markov random field is a collection of so-called full conditional mutual independencies. Using the theory of I-measure, we have obtained a number of fundamental characterizations related to conditional mutual independence and Markov random fields. We show that many aspects of conditional mutual independence and Markov random fields have very simple set-theoretic descriptions. New insights into the structure of conditional mutual independence and Markov random fields are obtained. Our results have immediate applications in the implication problem of probabilistic conditional independency and relational database. We obtain a hypergraph characterization of a Markov random field which makes it legitimate to view a Markov random field as a hypergraph. Based on this result, we naturally employ the Graham reduction, a tool from relational database theory, to recognize a Markov forest. This connection between Markov random fields and hypergraph sheds some light on the possible role of hypergraph theory in the study of Markov random fields.

In this study, a Markov Random Field (MRF) approach is used to locate source boundary positions which are difficult to identify from Bouguer gravity and magnetic maps. As a generalized form of Markov Chains, the MRF approach is an unsupervised statistical model based algorithm and is applied to the analysis of images, particularly in the detection of visual patterns or textures. Here, we present a dynamic programming based on the MRF approach for boundary detection of noisy and super-positioned potential anomalies, which are produced by various geological structures. In the MRF method, gravity and magnetic maps are considered as two-dimensional (2-D) images with a matrix composed of N1 × N2 pixels. Each pixel value of the matrix is optimized in real time with no a priori processing by using two parameter sets; average steering vector (θ) and quantization level (M). They carry information about the correlation of neighboring pixels and the locality of their connections. We have chosen MRF as a processing approach for geophysical data since it is an unsupervised, efficient model for image enhancement, border detection and separation of 2-D potential anomalies. The main benefit of MRF is that an average steering vector and a quantization level are enough in evaluation of the potential anomaly maps. We have compared the MRF method to noise implemented synthetic potential field anomalies. After satisfactory results were found, the method has been applied to gravity and magnetic anomaly maps of Gelibolu Peninsula in Western Turkey. Here, we have observed Anafartalar thrust fault and another parallel fault northwest of Anafartalar thrust fault. We have modeled a geological structure including a lateral fault, which results in a higher susceptibility and anomaly amplitude increment. We have shown that the MRF method is effective to detect the broad-scale geological structures in the Gelibolu Peninsula, and thus to delineate the complex tectonic structure of Gelibolu Peninsula.

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.

This paper proposes a Markov Random Field (MRF) model used for denoising to preserve the edge. This model combines both gray distinction and edge detection results to determine the weight between adjacent pixels. On the basis of MMRF (Membrane MRF), it imports the weight coefficient to build EPMRF (Edge Preserving MRF) model. This model can describe edge characteristics effectively and reduce impact between adjacent pixels to achieve preserving the edge. The experimental results show that denoising based on EPMRF model have a better performance compared with the traditional MMRF and GMRF (Gaussian MRF) models in removing the image noise, especially in edge preserving.

This study formulates the IR target detection as a binary classification problem of each pixel. Each pixel is associated with a label which indicates whether it is a target or background pixel. The optimal label set for all the pixels of an image maximizes a posterior distribution of label configuration given the pixel intensities. The posterior probability is factored into (or proportional to) a conditional likelihood of the intensity values and a prior probability of label configuration. Each of these two probabilities are computed assuming a Markov Random Field (MRF) on both pixel intensities and their labels. In particular, this study enforces neighborhood dependency on both intensity values, by a Simultaneous Auto Regressive (SAR) modle, and on labels, by an Auto-Logistic model. The parameters of these MRF models are learned from labeled examples. During testing, an MRF inference technique, namely Iterated Conditional Mode (ICM), produces the optimal label for each pixel. High performances on benchmark datasets demonstrate effectiveness of this method for IR target detection.

Message-passing-based inference algorithms have immense importance in real-world applications. In this paper, error resiliency of a message passing based Markov random field (MRF) stereo matching hardware is explored and enhanced through the application of statistical error compensation. Error resiliency is of particular interest for subnanometer and postsilicon devices. The inherent robustness of iteration-based MRF inference algorithms is explored and shows that small errors are tolerable, while large errors degrade the performance significantly. Based on these error characteristics, algorithmic noise tolerance (ANT) has been applied at the arithmetic, iteration, and system levels. Introducing timing errors via voltage overscaling, at the arithmetic level, results show that the ANT-based hardware can tolerate an error rate of 21.3%, with performance degradation of only 3.5% at an overhead of 97.4%, compared with an error-free hardware with an energy savings of 39.7%. To reduce compensation complexity, iteration and system-level compensation was explored. Results show that, compared with arithmetic level, system-level compensation reduces overhead to 59%, while maintaining stereo matching performance with only 2.5% degradation with 16% additional power savings. These results are verified via FPGA emulation with timing errors induced within the message passing unit via relaxed synthesis.

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.