Order Markov Random Field Research Articles

A spatio-temporal model to reveal oscillator phenotypes in molecular clocks: Parameter estimation elucidates circadian gene transcription dynamics in single-cells.

We propose a stochastic distributed delay model together with a Markov random field prior and a measurement model for bioluminescence-reporting to analyse spatio-temporal gene expression in intact networks of cells. The model describes the oscillating time evolution of molecular mRNA counts through a negative transcriptional-translational feedback loop encoded in a chemical Langevin equation with a probabilistic delay distribution. The model is extended spatially by means of a multiplicative random effects model with a first order Markov random field prior distribution. Our methodology effectively separates intrinsic molecular noise, measurement noise, and extrinsic noise and phenotypic variation driving cell heterogeneity, while being amenable to parameter identification and inference. Based on the single-cell model we propose a novel computational stability analysis that allows us to infer two key characteristics, namely the robustness of the oscillations, i.e. whether the reaction network exhibits sustained or damped oscillations, and the profile of the regulation, i.e. whether the inhibition occurs over time in a more distributed versus a more direct manner, which affects the cells’ ability to phase-shift to new schedules. We show how insight into the spatio-temporal characteristics of the circadian feedback loop in the suprachiasmatic nucleus (SCN) can be gained by applying the methodology to bioluminescence-reported expression of the circadian core clock gene Cry1 across mouse SCN tissue. We find that while (almost) all SCN neurons exhibit robust cell-autonomous oscillations, the parameters that are associated with the regulatory transcription profile give rise to a spatial division of the tissue between the central region whose oscillations are resilient to perturbation in the sense that they maintain a high degree of synchronicity, and the dorsal region which appears to phase shift in a more diversified way as a response to large perturbations and thus could be more amenable to entrainment.

Semantic Labeling of Mobile LiDAR Point Clouds via Active Learning and Higher Order MRF

Using mobile Light Detection and Ranging point clouds to accomplish road scene labeling tasks shows promise for a variety of applications. Most existing methods for semantic labeling of point clouds require a huge number of fully supervised point cloud scenes, where each point needs to be manually annotated with a specific category. Manually annotating each point in point cloud scenes is labor intensive and hinders practical usage of those methods. To alleviate such a huge burden of manual annotation, in this paper, we introduce an active learning method that avoids annotating the whole point cloud scenes by iteratively annotating a small portion of unlabeled supervoxels and creating a minimal manually annotated training set. In order to avoid the biased sampling existing in traditional active learning methods, a neighbor-consistency prior is exploited to select the potentially misclassified samples into the training set to improve the accuracy of the statistical model. Furthermore, lots of methods only consider short-range contextual information to conduct semantic labeling tasks, but ignore the long-range contexts among local variables. In this paper, we use a higher order Markov random field model to take into account more contexts for refining the labeling results, despite of lacking fully supervised scenes. Evaluations on three data sets show that our proposed framework achieves a high accuracy in labeling point clouds although only a small portion of labels is provided. Moreover, comparative experiments demonstrate that our proposed framework is superior to traditional sampling methods and exhibits comparable performance to those fully supervised models.

Semi-supervised learning and graph cuts for consensus based medical image segmentation

Medical image segmentation requires consensus ground truth segmentations to be derived from multiple expert annotations. A novel approach is proposed that obtains consensus segmentations from experts using graph cuts (GC) and semi supervised learning (SSL). Popular approaches use iterative Expectation Maximization (EM) to estimate the final annotation and quantify annotator's performance. Such techniques pose the risk of getting trapped in local minima. We propose a self consistency (SC) score to quantify annotator consistency using low level image features. SSL is used to predict missing annotations by considering global features and local image consistency. The SC score also serves as the penalty cost in a second order Markov random field (MRF) cost function optimized using graph cuts to derive the final consensus label. Graph cut obtains a global maximum without an iterative procedure. Experimental results on synthetic images, real data of Crohn's disease patients and retinal images show our final segmentation to be accurate and more consistent than competing methods.

Combining multiple expert annotations using semi-supervised learning and graph cuts for medical image segmentation

Generating consensus ground truth segmentation from multiple experts is important in medical imaging applications such as segmentation. We propose a novel approach to combine multiple expert annotations using graph cuts (GC) and semi supervised learning (SSL). Current methods use iterative Expectation–Maximization (EM) based approaches to estimate the final annotation and quantify annotator’s performance. This poses the risk of getting trapped in local minimum and providing inaccurate estimates of annotator performance. A novel self consistency (SC) score quantifies annotator performance based on the consistency of their annotations in terms of low level image features. The missing annotations are predicted using SSL techniques that consider global features and local image consistency. The self consistency score also serves as the penalty cost in a second order Markov random field (MRF) cost function which is optimized using graph cuts to obtain the final consensus label. Graph cut optimization gives a global maximum and is non-iterative, thus speeding up the process. Experimental results on synthetic images, real data of Crohn’s disease patients and retinal images show our final segmentation to be accurate and more consistent than those obtained by competing methods. It also highlights the effectiveness of self consistency in quantifying expert reliability and accuracy of SSL in predicting missing labels.

An Efficient Variational Method for Restoring Images with Combined Additive and Multiplicative Noise

This paper proposes a novel variational model to remove either independent additive or multiplicative noise from synthetic and natural digital images via the fractional-order derivative operator. The non-local characteristics of fractional derivatives can help preserve textures and eliminate the “blocky effect”. The proposed strategy uses the fractional-order total variation (FOTV)-norm, combined with the fields of experts-image prior model, a filter-based higher-order Markov Random Fields (MRF) method which is effective for image restoration. The present model combines advantages of both FOTV and higher order MRF and results in good restoration. In this study, a fast alternating minimization algorithm is also employed to solve minimization problem. Compared with the other well-established methods, experimental results show the effectiveness of the proposed method for de-noising images contaminated by combined additive and multiplicative noises. In addition, we also discuss parameter dependency and computational analysis in details.

Automatic quantification of normal cortical folding patterns from fetal brain MRI

We automatically quantify patterns of normal cortical folding in the developing fetus from in utero MR images (N=80) over a wide gestational age (GA) range (21.7 to 38.9weeks). This work on data from healthy subjects represents a first step towards characterising abnormal folding that may be related to pathology, facilitating earlier diagnosis and intervention. The cortical boundary was delineated by automatically segmenting the brain MR image into a number of key structures. This utilised a spatio-temporal atlas as tissue priors in an expectation–maximization approach with second order Markov random field (MRF) regularization to improve the accuracy of the cortical boundary estimate. An implicit high resolution surface was then used to compute cortical folding measures. We validated the automated segmentations with manual delineations and the average surface discrepancy was of the order of 1mm. Eight curvature-based folding measures were computed for each fetal cortex and used to give summary shape descriptors. These were strongly correlated with GA (R2=0.99) confirming the close link between neurological development and cortical convolution. This allowed an age-dependent non-linear model to be accurately fitted to the folding measures. The model supports visual observations that, after a slow initial start, cortical folding increases rapidly between 25 and 30weeks and subsequently slows near birth. The model allows the accurate prediction of fetal age from an observed folding measure with a smaller error where growth is fastest. We also analysed regional patterns in folding by parcellating each fetal cortex using a nine-region anatomical atlas and found that Gompertz models fitted the change in lobar regions. Regional differences in growth rate were detected, with the parietal and posterior temporal lobes exhibiting the fastest growth, while the cingulate, frontal and medial temporal lobes developed more slowly.

Compressed Vision Information Restoration Based on Cloud Prior and Local Prior

In wireless communication, compressed vision information may suffer from kinds of degradation, which dramatically influences the final visual quality. In this paper, a compressed vision information restoration method is proposed based on two explored vision priors: 1) the cloud prior and 2) the local prior. The cloud prior can be obtained from the nature images set in the cloud, and fields of experts is used to formulate the statistical character of the nature image contents as a high order Markov random field. The local prior is achieved from the degraded image itself, and K-SVD is adopted to model the sparse and redundant representation characters of nature images. These priors are effectively comprised in the proposed vision information restoration method. The relation between the quantization parameter and the optimal configuration of the prior models is further analyzed. In addition, an enhanced quantization constrained projection algorithm is proposed to refine the high frequency components. We extend this paper to compressed video restoration for H.264/AVC and the experiment results demonstrate that the proposed scheme can reproduce higher quality images compared with conventional H.264/AVC.

영상 복원을 위한 MRF 기반 적응적 노이즈 탐지 알고리즘

In this paper, we presents a spatially adaptive noise detection and removal algorithm. Under the assumption that an observed image and the additive noise have Gaussian distribution, the noise parameters are estimated with local statistics, and the parameters are used to define the constraints on the noise detection process, where the first order Markov Random Field (MRF) is used. In addition, an adaptive low-pass filter having a variable window sizes defined by the constraints on noise detection is used to control the degree of smoothness of the reconstructed image. Experimental results demonstrate the capability of the proposed algorithm.

Simultaneous Cast Shadows, Illumination and Geometry Inference Using Hypergraphs

The cast shadows in an image provide important information about illumination and geometry. In this paper, we utilize this information in a novel framework in order to jointly recover the illumination environment, a set of geometry parameters, and an estimate of the cast shadows in the scene given a single image and coarse initial 3D geometry. We model the interaction of illumination and geometry in the scene and associate it with image evidence for cast shadows using a higher order Markov Random Field (MRF) illumination model, while we also introduce a method to obtain approximate image evidence for cast shadows. Capturing the interaction between light sources and geometry in the proposed graphical model necessitates higher order cliques and continuous-valued variables, which make inference challenging. Taking advantage of domain knowledge, we provide a two-stage minimization technique for the MRF energy of our model. We evaluate our method in different datasets, both synthetic and real. Our model is robust to rough knowledge of geometry and inaccurate initial shadow estimates, allowing a generic coarse 3D model to represent a whole class of objects for the task of illumination estimation, or the estimation of geometry parameters to refine our initial knowledge of scene geometry, simultaneously with illumination estimation.

Scoring matching approach: Learning high order Markov random fields

Traditional Markov Random Field (MRF) models have two inherent limitations that are low order property of pixel neighborhoods and selecting parameters by hand. In this paper, we adopted a new machine learning method of score matching and get a group of parameters of high order MRF models by learning from training image data. We demonstrated the capabilities of the learning MRF models by applying them to image denoising according to Bayesian rule. Imaging denoising experiments show that our denoising algorithm can produce excellent result in the Peak Signal-to-Noise Ratios (PSNR) and subjective visual effect. Thus, our learning method is effective.

Global optimization for first order Markov Random Fields with submodular priors

This paper copes with the global optimization of Markovian energies. Energies are defined on an arbitrary graph and pairwise interactions are considered. The label set is assumed to be linearly ordered and of finite cardinality, while each interaction term (prior) shall be a submodular function. We propose an algorithm that computes a global optimizer under these assumptions. The approach consists of mapping the original problem into a combinatorial one that is shown to be globally solvable using a maximum-flow/ s - t minimum-cut algorithm. This restatement relies on considering the level sets of the labels (seen as binary variables) instead of the label values themselves. The submodularity assumption of the priors is shown to be a necessary and sufficient condition for the applicability of the proposed approach. Finally, some numerical results are presented.

A generative framework for fast urban labeling using spatial and temporal context

This paper introduces a multi-level classification framework for the semantic annotation of urban maps as provided by a mobile robot. Environmental cues are considered for classification at different scales. The first stage considers local scene properties using a probabilistic bag-of-words classifier. The second stage incorporates contextual information across a given scene (spatial context) and across several consecutive scenes (temporal context) via a Markov Random Field (MRF). Our approach is driven by data from an onboard camera and 3D laser scanner and uses a combination of visual and geometric features. By framing the classification exercise probabilistically we take advantage of an information-theoretic bail-out policy when evaluating class-conditional likelihoods. This efficiency, combined with low order MRFs resulting from our two-stage approach, allows us to generate scene labels at speeds suitable for online deployment. We demonstrate the virtue of considering such spatial and temporal context during the classification task and analyze the performance of our technique on data gathered over almost 17 km of track through a city.

Postprocessing of Low Bit-Rate Block DCT Coded Images Based on a Fields of Experts Prior

Transform coding using the discrete cosine transform (DCT) has been widely used in image and video coding standards, but at low bit rates, the coded images suffer from severe visual distortions which prevent further bit reduction. Postprocessing can reduce these distortions and alleviate the conflict between bit rate reduction and quality preservation. Viewing postprocessing as an inverse problem, we propose to solve it by the maximum a posteriori criterion. The distortion caused by coding is modeled as additive, spatially correlated Gaussian noise, while the original image is modeled as a high order Markov random field based on the fields of experts framework. Experimental results show that the proposed method, in most cases, achieves higher PSNR gain than other methods and the processed images possess good visual quality. In addition, we examine the noise model used and its parameter setting. The noise model assumes that the DCT coefficients and their quantization errors are independent. This assumption is no longer valid when the coefficients are truncated. We explain how this problem can be rectified using the current parameter setting.

Segmentation of color images via reversible jump MCMC sampling

Reversible jump Markov chain Monte Carlo (RJMCMC) is a recent method which makes it possible to construct reversible Markov chain samplers that jump between parameter subspaces of different dimensionality. In this paper, we propose a new RJMCMC sampler for multivariate Gaussian mixture identification and we apply it to color image segmentation. For this purpose, we consider a first order Markov random field (MRF) model where the singleton energies derive from a multivariate Gaussian distribution and second order potentials favor similar classes in neighboring pixels. The proposed algorithm finds the most likely number of classes, their associated model parameters and generates a segmentation of the image by classifying the pixels into these classes. The estimation is done according to the Maximum A Posteriori (MAP) criterion. The algorithm has been validated on a database of real images with human segmented ground truth.

Exact optimization for markov random fields with convex priors

We introduce a method to solve exactly a first order Markov random field optimization problem in more generality than was previously possible. The MRF has a prior term that is convex in terms of a linearly ordered label set. The method maps the problem into a minimum-cut problem for a directed graph, for which a globally optimal solution can be found in polynomial time. The convexity of the prior function in the energy is shown to be necessary and sufficient for the applicability of the method.

Synchronous and Asynchronous Reversible Markov Systems(1)

AbstractThe relationships between synchronous and asynchronous reversible Markov systems are investigated. It is shown that the invariant measure of such systems is a second order Markov random field. The conditions under which the invariant measure is a first order Markov random field are obtained.