Markov-Gibbs Random Field Model Research Articles

Segmentation of Infant Brain Using Nonnegative Matrix Factorization

This study develops an atlas-based automated framework for segmenting infants’ brains from magnetic resonance imaging (MRI). For the accurate segmentation of different structures of an infant’s brain at the isointense age (6–12 months), our framework integrates features of diffusion tensor imaging (DTI) (e.g., the fractional anisotropy (FA)). A brain diffusion tensor (DT) image and its region map are considered samples of a Markov–Gibbs random field (MGRF) that jointly models visual appearance, shape, and spatial homogeneity of a goal structure. The visual appearance is modeled with an empirical distribution of the probability of the DTI features, fused by their nonnegative matrix factorization (NMF) and allocation to data clusters. Projecting an initial high-dimensional feature space onto a low-dimensional space of the significant fused features with the NMF allows for better separation of the goal structure and its background. The cluster centers in the latter space are determined at the training stage by the K-means clustering. In order to adapt to large infant brain inhomogeneities and segment the brain images more accurately, appearance descriptors of both the first-order and second-order are taken into account in the fused NMF feature space. Additionally, a second-order MGRF model is used to describe the appearance based on the voxel intensities and their pairwise spatial dependencies. An adaptive shape prior that is spatially variant is constructed from a training set of co-aligned images, forming an atlas database. Moreover, the spatial homogeneity of the shape is described with a spatially uniform 3D MGRF of the second-order for region labels. In vivo experiments on nine infant datasets showed promising results in terms of the accuracy, which was computed using three metrics: the 95-percentile modified Hausdorff distance (MHD), the Dice similarity coefficient (DSC), and the absolute volume difference (AVD). Both the quantitative and visual assessments confirm that integrating the proposed NMF-fused DTI feature and intensity MGRF models of visual appearance, the adaptive shape prior, and the shape homogeneity MGRF model is promising in segmenting the infant brain DTI.

The Role of 3D CT Imaging in the Accurate Diagnosis of Lung Function in Coronavirus Patients.

Early grading of coronavirus disease 2019 (COVID-19), as well as ventilator support machines, are prime ways to help the world fight this virus and reduce the mortality rate. To reduce the burden on physicians, we developed an automatic Computer-Aided Diagnostic (CAD) system to grade COVID-19 from Computed Tomography (CT) images. This system segments the lung region from chest CT scans using an unsupervised approach based on an appearance model, followed by 3D rotation invariant Markov–Gibbs Random Field (MGRF)-based morphological constraints. This system analyzes the segmented lung and generates precise, analytical imaging markers by estimating the MGRF-based analytical potentials. Three Gibbs energy markers were extracted from each CT scan by tuning the MGRF parameters on each lesion separately. The latter were healthy/mild, moderate, and severe lesions. To represent these markers more reliably, a Cumulative Distribution Function (CDF) was generated, then statistical markers were extracted from it, namely, 10th through 90th CDF percentiles with 10% increments. Subsequently, the three extracted markers were combined together and fed into a backpropagation neural network to make the diagnosis. The developed system was assessed on 76 COVID-19-infected patients using two metrics, namely, accuracy and Kappa. In this paper, the proposed system was trained and tested by three approaches. In the first approach, the MGRF model was trained and tested on the lungs. This approach achieved % accuracy and % kappa. In the second approach, we trained the MGRF model on the lesions and tested it on the lungs. This approach achieved % accuracy and % kappa. Finally, we trained and tested the MGRF model on lesions. It achieved 100% accuracy and 100% kappa. The results reported in this paper show the ability of the developed system to accurately grade COVID-19 lesions compared to other machine learning classifiers, such as k-Nearest Neighbor (KNN), decision tree, naïve Bayes, and random forest.

Early assessment of lung function in coronavirus patients using invariant markers from chest X-rays images

The primary goal of this manuscript is to develop a computer assisted diagnostic (CAD) system to assess pulmonary function and risk of mortality in patients with coronavirus disease 2019 (COVID-19). The CAD system processes chest X-ray data and provides accurate, objective imaging markers to assist in the determination of patients with a higher risk of death and thus are more likely to require mechanical ventilation and/or more intensive clinical care.To obtain an accurate stochastic model that has the ability to detect the severity of lung infection, we develop a second-order Markov-Gibbs random field (MGRF) invariant under rigid transformation (translation or rotation of the image) as well as scale (i.e., pixel size). The parameters of the MGRF model are learned automatically, given a training set of X-ray images with affected lung regions labeled. An X-ray input to the system undergoes pre-processing to correct for non-uniformity of illumination and to delimit the boundary of the lung, using either a fully-automated segmentation routine or manual delineation provided by the radiologist, prior to the diagnosis. The steps of the proposed methodology are: (i) estimate the Gibbs energy at several different radii to describe the inhomogeneity in lung infection; (ii) compute the cumulative distribution function (CDF) as a new representation to describe the local inhomogeneity in the infected region of lung; and (iii) input the CDFs to a new neural network-based fusion system to determine whether the severity of lung infection is low or high. This approach is tested on 200 clinical X-rays from 200 COVID-19 positive patients, 100 of whom died and 100 who recovered using multiple training/testing processes including leave-one-subject-out (LOSO), tenfold, fourfold, and twofold cross-validation tests. The Gibbs energy for lung pathology was estimated at three concentric rings of increasing radii. The accuracy and Dice similarity coefficient (DSC) of the system steadily improved as the radius increased. The overall CAD system combined the estimated Gibbs energy information from all radii and achieved a sensitivity, specificity, accuracy, and DSC of 100%, 97% ± 3%, 98% ± 2%, and 98% ± 2%, respectively, by twofold cross validation. Alternative classification algorithms, including support vector machine, random forest, naive Bayes classifier, K-nearest neighbors, and decision trees all produced inferior results compared to the proposed neural network used in this CAD system. The experiments demonstrate the feasibility of the proposed system as a novel tool to objectively assess disease severity and predict mortality in COVID-19 patients. The proposed tool can assist physicians to determine which patients might require more intensive clinical care, such a mechanical respiratory support.

A novel 3D segmentation approach for extracting retinal layers from optical coherence tomography images.

Accurate segmentation of retinal layers of the eye in 3D Optical Coherence Tomography (OCT) data provides relevant information for clinical diagnosis. This manuscript describes a 3D segmentation approach that uses an adaptive patient-specific retinal atlas, as well as an appearance model for 3D OCT data. To reconstruct the atlas of 3D retinal scan, the central area of the macula (macula mid-area) where the fovea could be clearly identified, was segmented initially. Markov Gibbs Random Field (MGRF) including intensity, spatial information, and shape of 12 retinal layers were used to segment the selected area of retinal fovea. A set of coregistered OCT scans that were gathered from 200 different individuals were used to build a 2D shape prior. This shape prior was adapted subsequently to the first order appearance and second order spatial interaction MGRF model. After segmenting the center of the macula "foveal area", the labels and appearances of the layers that were segmented were utilized to segment the adjacent slices. The final step was repeated recursively until a 3D OCT scan of the patient was segmented. This approach was tested in 50 patients with normal and with ocular pathological conditions. The segmentation was compared to a manually segmented ground truth. The results were verified by clinical retinal experts. Dice Similarity Coefficient (DSC), 95% bidirectional modified Hausdorff Distance (HD), Unsigned Mean Surface Position Error (MSPE), and Average Volume Difference (AVD) metrics were used to quantify the performance of the proposed approach. The proposed approach was proved to be more accurate than the current state-of-the-art 3D OCT approaches. The proposed approach has the advantage of segmenting all the 12 retinal layers rapidly and more accurately than current state-of-the-art 3D OCT approaches.

Novel stochastic framework for automatic segmentation of human thigh MRI volumes and its applications in spinal cord injured individuals.

Severe spinal cord injury (SCI) leads to skeletal muscle atrophy and adipose tissue infiltration in the skeletal muscle, which can result in compromised muscle mechanical output and lead to health-related complications. In this study, we developed a novel automatic 3-D approach for volumetric segmentation and quantitative assessment of thigh Magnetic Resonance Imaging (MRI) volumes in individuals with chronic SCI as well as non-disabled individuals. In this framework, subcutaneous adipose tissue, inter-muscular adipose tissue and total muscle tissue are segmented using linear combination of discrete Gaussians algorithm. Also, three thigh muscle groups were segmented utilizing the proposed 3-D Joint Markov Gibbs Random Field model that integrates first order appearance model, spatial information, and shape model to localize the muscle groups. The accuracy of the automatic segmentation method was tested both on SCI (N = 16) and on non-disabled (N = 14) individuals, showing an overall 0.93±0.06 accuracy for adipose tissue and muscle compartments segmentation based on Dice Similarity Coefficient. The proposed framework for muscle compartment segmentation showed an overall higher accuracy compared to ANTs and STAPLE, two previously validated atlas-based segmentation methods. Also, the framework proposed in this study showed similar Dice accuracy and better Hausdorff distance measure to that obtained using DeepMedic Convolutional Neural Network structure, a well-known deep learning network for 3-D medical image segmentation. The automatic segmentation method proposed in this study can provide fast and accurate quantification of adipose and muscle tissues, which have important health and functional implications in the SCI population.

Computer-Aided Diagnostic System for Early Detection of Acute Renal Transplant Rejection Using Diffusion-Weighted MRI

Early diagnosis of acute renal transplant rejection (ARTR) is critical for accurate treatment. Although the current gold standard, diagnostic technique is renal biopsy, it is not preferred due to its invasiveness, long recovery time (1-2 weeks), and potential for complications, e.g., bleeding and/or infection. This paper presents a computer-aided diagnostic (CAD) system for early ARTR detection using (3D + b-value) diffusion-weighted (DW) magnetic resonance imaging (MRI) data. The CAD process starts from kidney tissue segmentation with an evolving geometric (level-set-based) deformable model. The evolution is guided by a voxel-wise stochastic speed function, which follows from a joint kidney-background Markov-Gibbs random field model accounting for an adaptive kidney shape prior and on-going kidney-background visual appearances. A B-spline-based three-dimensional data alignment is employed to handle local deviations due to breathing and heart beating. Then, empirical cumulative distribution functions of apparent diffusion coefficients of the segmented DW-MRI at different b-values are collected as discriminatory transplant status features. Finally, a deep-learning-based classifier with stacked nonnegative constrained autoencoders is employed to distinguish between rejected and nonrejected renal transplants. In our initial "leave-one-subject-out" experiment on 100 subjects, [Formula: see text] of the subjects were correctly classified. The subsequent four-fold and ten-fold cross-validations gave the average accuracy of [Formula: see text] and [Formula: see text], respectively. These results demonstrate the promise of this new CAD system to reliably diagnose renal transplant rejection. The technology presented here can significantly impact the quality of care of renal transplant patients since it has the potential to replace the gold standard in kidney diagnosis, biopsy.

A Generalized Deep Learning-Based Diagnostic System for Early Diagnosis of Various Types of Pulmonary Nodules.

A novel framework for the classification of lung nodules using computed tomography scans is proposed in this article. To get an accurate diagnosis of the detected lung nodules, the proposed framework integrates the following 2 groups of features: (1) appearance features modeled using the higher order Markov Gibbs random field model that has the ability to describe the spatial inhomogeneities inside the lung nodule and (2) geometric features that describe the shape geometry of the lung nodules. The novelty of this article is to accurately model the appearance of the detected lung nodules using a new developed seventh-order Markov Gibbs random field model that has the ability to model the existing spatial inhomogeneities for both small and large detected lung nodules, in addition to the integration with the extracted geometric features. Finally, a deep autoencoder classifier is fed by the above 2 feature groups to distinguish between the malignant and benign nodules. To evaluate the proposed framework, we used the publicly available data from the Lung Image Database Consortium. We used a total of 727 nodules that were collected from 467 patients. The proposed system demonstrates the promise to be a valuable tool for the detection of lung cancer evidenced by achieving a nodule classification accuracy of 91.20%.

Automatic blood vessels segmentation based on different retinal maps from OCTA scans

The retinal vascular network reflects the health of the retina, which is a useful diagnostic indicator of systemic vascular. Therefore, the segmentation of retinal blood vessels is a powerful method for diagnosing vascular diseases. This paper presents an automatic segmentation system for retinal blood vessels from Optical Coherence Tomography Angiography (OCTA) images. The system segments blood vessels from the superficial and deep retinal maps for normal and diabetic cases. Initially, we reduced the noise and improved the contrast of the OCTA images by using the Generalized Gauss-Markov random field (GGMRF) model. Secondly, we proposed a joint Markov-Gibbs random field (MGRF) model to segment the retinal blood vessels from other background tissues. It integrates both appearance and spatial models in addition to the prior probability model of OCTA images. The higher order MGRF (HO-MGRF) model in addition to the 1st-order intensity model are used to consider the spatial information in order to overcome the low contrast between vessels and other tissues. Finally, we refined the segmentation by extracting connected regions using a 2D connectivity filter. The proposed segmentation system was trained and tested on 47 data sets, which are 23 normal data sets and 24 data sets for diabetic patients. To evaluate the accuracy and robustness of the proposed segmentation framework, we used three different metrics, which are Dice similarity coefficient (DSC), absolute vessels volume difference (VVD), and area under the curve (AUC). The results on OCTA data sets (DSC=95.04±3.75%, VVD=8.51±1.49%, and AUC=95.20±1.52%) show the promise of the proposed segmentation approach.

Fuzzy-C-Means Clustering Based Segmentation and CNN-Classification for Accurate Segmentation of Lung Nodules

Objective:Accurate segmentation of abnormal and healthy lungs is very crucial for a steadfast computer-aided disease diagnostics.Methods:For this purpose a stack of chest CT scans are processed. In this paper, novel methods are proposed for segmentation of the multimodal grayscale lung CT scan. In the conventional methods using Markov–Gibbs Random Field (MGRF) model the required regions of interest (ROI) are identified.Result:The results of proposed FCM and CNN based process are compared with the results obtained from the conventional method using MGRF model. The results illustrate that the proposed method can able to segment the various kinds of complex multimodal medical images precisely.Conclusion:However, in this paper, to obtain an exact boundary of the regions, every empirical dispersion of the image is computed by Fuzzy C-Means Clustering segmentation. A classification process based on the Convolutional Neural Network (CNN) classifier is accomplished to distinguish the normal tissue and the abnormal tissue. The experimental evaluation is done using the Interstitial Lung Disease (ILD) database.

Texture modelling with nested high-order Markov–Gibbs random fields

Currently, Markov–Gibbs random field (MGRF) image models which include high-order interactions are almost always built by modelling responses of a stack of local linear filters. Actual interaction structure is specified implicitly by the filter coefficients. In contrast, we learn an explicit high-order MGRF structure by considering the learning process in terms of general exponential family distributions nested over base models, so that potentials added later can build on previous ones. We relatively rapidly add new features by skipping over the costly optimisation of parameters.We introduce the use of local binary patterns as features in MGRF texture models, and generalise them by learning offsets to the surrounding pixels. These prove effective as high-order features, and are fast to compute. Several schemes for selecting high-order features by composition or search of a small subclass are compared. Additionally we present a simple modification of the maximum likelihood as a texture modelling-specific objective function which aims to improve generalisation by local windowing of statistics.The proposed method was experimentally evaluated by learning high-order MGRF models for a broad selection of complex textures and then performing texture synthesis, and succeeded on much of the continuum from stochastic through irregularly structured to near-regular textures. Learning interaction structure is very beneficial for textures with large-scale structure, although those with complex irregular structure still provide difficulties. The texture models were also quantitatively evaluated on two tasks and found to be competitive with other works: grading of synthesised textures by a panel of observers; and comparison against several recent MGRF models by evaluation on a constrained inpainting task.

Learnable high-order MGRF models for contrast-invariant texture recognition

Frequent in practice spatially variant contrast/offset deviations that preserve image appearance hinder classification based on signal co-occurrence statistics. Contrast/offset-invariant descriptors of ordinal signal relations, such as local binary or ternary patterns (LBP/LTP), are popular means to overcome this drawback. This paper extends conventional LBP/LTP-based classifiers towards learning, rather than prescribing most characteristic shapes, sizes, and numbers of these patterns for semi-supervised texture classification and retrieval. The goal is to discriminate a particular texture represented by a single training or query sample from other types of textures. The proposed learning framework models images as samples from a high-order ordinal Markov–Gibbs random field (MGRF). Approximate analytical estimates of the model parameters guide selecting characteristic patterns of a given order, the higher order patterns being learned on the basis of the already found lower order ones. Comparative experiments on four texture databases confirmed that classifiers with the learned multiple LTPs from the 3rd to 8th order consistently outperform more conventional ones with the prescribed 9th-order fixed-shape LBP/LTPs or a few other filters.

Infant Brain Extraction in T1-Weighted MR Images Using BET and Refinement Using LCDG and MGRF Models.

In this paper, we propose a novel framework for the automated extraction of the brain from T1-weighted MR images. The proposed approach is primarily based on the integration of a stochastic model [a two-level Markov-Gibbs random field (MGRF)] that serves to learn the visual appearance of the brain texture, and a geometric model (the brain isosurfaces) that preserves the brain geometry during the extraction process. The proposed framework consists of three main steps: 1) Following bias correction of the brain, a new three-dimensional (3-D) MGRF having a 26-pairwise interaction model is applied to enhance the homogeneity of MR images and preserve the 3-D edges between different brain tissues. 2) The nonbrain tissue found in the MR images is initially removed using the brain extraction tool (BET), and then the brain is parceled to nested isosurfaces using a fast marching level set method. 3) Finally, a classification step is applied in order to accurately remove the remaining parts of the skull without distorting the brain geometry. The classification of each voxel found on the isosurfaces is made based on the first- and second-order visual appearance features. The first-order visual appearance is estimated using a linear combination of discrete Gaussians (LCDG) to model the intensity distribution of the brain signals. The second-order visual appearance is constructed using an MGRF model with analytically estimated parameters. The fusion of the LCDG and MGRF, along with their analytical estimation, allows the approach to be fast and accurate for use in clinical applications. The proposed approach was tested on in vivo data using 300 infant 3-D MR brain scans, which were qualitatively validated by an MR expert. In addition, it was quantitatively validated using 30 datasets based on three metrics: the Dice coefficient, the 95% modified Hausdorff distance, and absolute brain volume difference. Results showed the capability of the proposed approach, outperforming four widely used BETs: BET, BET2, brain surface extractor, and infant brain extraction and analysis toolbox. Experiments conducted also proved that the proposed framework can be generalized to adult brain extraction as well.

Intramyocardial strain estimation from cardiac cine MRI.

Functional strain is one of the important clinical indicators for the quantification of heart performance and the early detection of cardiovascular diseases, and functional strain parameters are used to aid therapeutic decisions and follow-up evaluations after cardiac surgery. A comprehensive framework for deriving functional strain parameters at the endocardium, epicardium, and mid-wall of the left ventricle (LV) from conventional cine MRI data was developed and tested. Cine data were collected using short TR-/TE-balanced steady-state free precession acquisitions on a 1.5T Siemens Espree scanner. The LV wall borders are segmented using a level set-based deformable model guided by a stochastic force derived from a second-order Markov-Gibbs random field model that accounts for the object shape and appearance features. Then, the mid-wall of the segmented LV is determined based on estimating the centerline between the endocardium and epicardium of the LV. Finally, a geometrical Laplace-based method is proposed to track corresponding points on successive myocardial contours throughout the cardiac cycle in order to characterize the strain evolutions. The method was tested using simulated phantom images with predefined point locations of the LV wall throughout the cardiac cycle. The method was tested on 30 in vivo datasets to evaluate the feasibility of the proposed framework to index functional strain parameters. The cine MRI-based model agreed with the ground truth for functional metrics to within 0.30 % for indexing the peak systolic strain change and 0.29 % (per unit time) for indexing systolic and diastolic strain rates. The method was feasible for in vivo extraction of functional strain parameters. Strain indexes of the endocardium, mid-wall, and epicardium can be derived from routine cine images using automated techniques, thereby improving the utility of cine MRI data for characterization of myocardial function. Unlike traditional texture-based tracking, the proposed geometrical method showed the ability to track the LV wall points throughout the cardiac cycle, thus permitting more accurate strain estimation.

MAP–Based Framework for Segmentation of MR Brain Images Based on Visual Appearance and Prior Shape

We propose a new MAP-based technique for the unsupervised segmentation of different brain structures (white matter, gray matter, etc.) from T1-weighted MR brain images. In this paper, we follow a procedure like most conventional approaches, in which T1-weighted MR brain images and desired maps of regions (white matter, gray matter, etc.) are modeled by a joint Markov-Gibbs Random Field model (MGRF) of independent image signals and interdependent region labels. However, we specifically focus on the most accurate model identification that can be achieved. The proposed joint MGRF model accounts for the following three descriptors: i) a 1st-order visual appearance descriptor(empirical distribution of signal intensity), ii) a 3D probabilistic shape prior, and iii) a 3D spatially invariant 2nd-order homogeneity descriptor. To better specify the 1st-order visual appearance descriptor, each empirical distribution of signals is precisely approximated by a Linear Combination of Discrete Gaussians (LCDG) having both positive and negative components. The 3D probabilistic shape prior is learned using a subset of 3D co-aligned training T1-weighted MR brain images. The 2nd-order homogeneity descriptor is modeled by a 2nd-order translation and rotation invariant MGRF of 3D T1-weighted MR brain region labels with analytically estimated potentials. The initial segmentation, based on a 1st-order visual appearance and 3D probabilistic shape, is then iteratively refined using a 3D MGRF model with analytically estimated potentials. Experiments on twelve 3D T1-weighted MR brain images confirm the high accuracy of the proposed approach.

Dynamic Contrast-Enhanced MRI-Based Early Detection of Acute Renal Transplant Rejection

A novel framework for the classification of acute rejection versus nonrejection status of renal transplants from 2-D dynamic contrast-enhanced magnetic resonance imaging is proposed. The framework consists of four steps. First, kidney objects are segmented from adjacent structures with a level set deformable boundary guided by a stochastic speed function that accounts for a fourth-order Markov-Gibbs random field model of the kidney/background shape and appearance. Second, a Laplace-based nonrigid registration approach is used to account for local deformations caused by physiological effects. Namely, the target kidney object is deformed over closed, equispaced contours (iso-contours) to closely match the reference object. Next, the cortex is segmented as it is the functional kidney unit that is most affected by rejection. To characterize rejection, perfusion is estimated from contrast agent kinetics using empirical indexes, namely, the transient phase indexes (peak signal intensity, time-to-peak, and initial up-slope), and a steady-phase index defined as the average signal change during the slowly varying tissue phase of agent transit. We used a kn-nearest neighbor classifier to distinguish between acute rejection and nonrejection. Performance of our method was evaluated using the receiver operating characteristics (ROC). Experimental results in 50 subjects, using a combinatoric kn-classifier, correctly classified 92% of training subjects, 100% of the test subjects, and yielded an area under the ROC curve that approached the ideal value. Our proposed framework thus holds promise as a reliable noninvasive diagnostic tool.

Multimodal imaging: modelling and segmentation with biomedical applications

The maximum a posteriori (MAP) technique, combining intensity and spatial interactions, has been a standard statistical approach for image segmentation. Crucial steps for the MAP technique are the model identification, incorporation of priors, and the optimisation approach. This paper describes an unsupervised MAP segmentation framework of N-dimensional multimodal images. The input image and its desired labelling are described by a joint Markov-Gibbs random field (MGRF) model of independent image signals and interdependent region labels. A kernel approach is used to model the joint and marginal probability densities of objects from the gray level histogram, incorporating a generalised linear combination of Gaussians (LCG). A novel maximum likelihood estimate (MLE) for the number of classes in the LCG model is introduced. An approach is devised for MGRF model identification based on region characteristics. The segmentation process employs LCG to provide an initial segmentation, then α-expansion move algorithm iteratively refines the labelled image using MGRF. The resulting MAP algorithm is studied in terms of convergence and sensitivity to initialisation, improper estimation of the number of classes, and discontinuities in the objects. The framework is modular, allowing incorporation of intensity and spatial interactions with varying complexity, and can be extended to incorporate shape priors.

Markov-Gibbs Random Field Model for Improved Full-Cardiac Cycle Strain Estimation from Tagged CMR

Background Due to the ability of MR to index systolic and diastolic non-transmural function, by strain and strain rates, with full 3-D geometric concordance, this area is of ongoing interest for regional ischemic conditions, and for conditions such as heart failure and diabetes that result in global dysfunction. Quantitative tag analysis is often hampered by noisy images, and the tag spatial profile, especially when combined with the very efficient algorithms that are based on frequency or spectral domain analysis. We herein propose a new energy minimization approach, using a 3-variable function (x-direction, ydirection, and time) based on a rotation-invariant, Markov-Gibbs Random Field (MGRF) spatial interaction model. This is intended to reduce noise within a tag line, and un-sharpen the tag edges in the spatial domain (which improves the power spectral density), and thus emphasizes the first symmetric lobes of the Fourier Transform of the images in the frequency domain, for optimized analysis by algorithms such as the Harmonic Phase (HARP) method. Methods The tag-to-background contrast is optimized by modeling the marginal distribution of MR signals for the tag grids and for the anatomic background, by a linear combination of discrete Gaussians (LCDG). The 3-variable MGRF then uses the derived parameters as inputs. This approach requires no user specification, and unique parameters are empirically calculated from the given image. The result is a processed image that is optimized for the frequency domain. We have validated our approach using commercially available HARP analysis software (Diagnosoft Inc.) on synthetic phantoms, and on full cardiac-cycle real data. Results We tested the approach on two synthetic phantoms. We corrupted the phantom images by adding noise. We then calculated the absolute strain error using the HARP technique. In the first phantom the absolute strain error was 94%, and in the second phantom the absolute error was 80%. After processing the images using our approach, the absolute strain error was reduced to 36%, and 16%, respectively. We also observed an average improvement of 230% in the power of the spectral main lobe. We have also generated strain function curves, and parametric strain maps, in patients with ischemic damage from heart attacks who are undergoing experimental myoregeneration therapy, and have documented an improvement in visualization and display of treatment effects, in initial patient data. Conclusions Our results document that Markov-Gibbs Random Field modeling of the spatial domain, for tagged MR images, leads to an improved representation in the spectral domain. This results in more efficient and robust estimation of functional parameters, using spectral domain techniques, such as HARP. Funding None.

Texture Analysis by Accurate Identification of Simple Markovian Models

A more accurate identification (estimation of parameters) of simple Markov-Gibbs random field models of images results in a better segmentation of specific multimodal images and realistic synthesis of some types of natural textures. Identification algorithms for segmentation are based in part on a novel modification of an unsupervised learning algorithm published first in "Cybernetics and Systems Analysis" ("Kibernetika i Sistemnyi Analiz") almost four decades ago. A texture synthesis algorithm uses an identified model for selecting a characteristic geometric shape of and a placement grid for texture elements sampled from a training image utilized for the identification.