Linear Combination Of Discrete Gaussians Research Articles

Accurate Segmentation of Cerebrovasculature From TOF-MRA Images Using Appearance Descriptors

Analyzing cerebrovascular changes can significantly lead to not only detecting the presence of serious diseases e.g., hypertension and dementia, but also tracking their progress. Such analysis could be better performed using Time-of-Flight Magnetic Resonance Angiography (ToF–MRA) images, but this requires accurate segmentation of the cerebral vasculature from the surroundings. To achieve this goal, we propose a fully automated cerebral vasculature segmentation approach based on extracting both prior and current appearance features that have the ability to capture the appearance of macro and micro-vessels in ToF–MRA. The appearance prior is modeled with a novel translation and rotation invariant Markov-Gibbs Random Field (MGRF) of voxel intensities with pairwise interaction analytically identified from a set of training data sets. The appearance of the cerebral vasculature is also represented with a marginal probability distribution of voxel intensities by using a Linear Combination of Discrete Gaussians (LCDG) that its parameters are estimated by using a modified Expectation-Maximization (EM) algorithm. The extracted appearance features are separable and can be classified by any classifier, as demonstrated by our segmentation results. To validate the accuracy of our algorithm, we tested the proposed approach on in-vivo data using 270 data sets, which were qualitatively validated by a neuroradiology expert. The results were quantitatively validated using the three commonly used metrics for segmentation evaluation: the Dice coefficient, the modified Hausdorff distance, and the absolute volume difference. The proposed approach showed a higher accuracy compared to two of the existing segmentation approaches.

Automated framework for accurate segmentation of leaf images for plant health assessment.

Leaf segmentation is significantly important in assisting ecologists to automatically detect symptoms of disease and other stressors affecting trees. This paper employs state-of-the-art techniques in image processing to introduce an accurate framework for segmenting leaves and diseased leaf spots from images. The proposed framework integrates an appearance model that visually represents the current input image with the color prior information generated from RGB color images that were formerly saved in our database. Our framework consists of four main steps: (1) Enhancing the accuracy of the segmentation at minimum time by making use of contrast changes to automatically identify the region of interest (ROI) of the entire leaf, where the pixel-wise intensity relations are described by an electric field energy model. (2) Modeling the visual appearance of the input image using a linear combination of discrete Gaussians (LCDG) to predict the marginal probability distributions of the grayscale ROI main three classes. (3) Calculating the pixel-wise probabilities of these three classes for the color ROI based on the color prior information of database images that are segmented manually, where the current and prior pixel-wise probabilities are used to find the initial labels. (4) Refining the labels with the generalized Gauss-Markov random field model (GGMRF), which maintains the continuity. The proposed segmentation approach was applied to the leaves of mangrove trees in Abu Dhabi in the United Arab Emirates. Experimental validation showed high accuracy, with a Dice similarity coefficient 90% for distinguishing leaf spot from healthy leaf area.

A fast stochastic framework for automatic MR brain images segmentation

This paper introduces a new framework for the segmentation of different brain structures (white matter, gray matter, and cerebrospinal fluid) from 3D MR brain images at different life stages. The proposed segmentation framework is based on a shape prior built using a subset of co-aligned training images that is adapted during the segmentation process based on first- and second-order visual appearance characteristics of MR images. These characteristics are described using voxel-wise image intensities and their spatial interaction features. To more accurately model the empirical grey level distribution of the brain signals, we use a linear combination of discrete Gaussians (LCDG) model having positive and negative components. To accurately account for the large inhomogeneity in infant MRIs, a higher-order Markov-Gibbs Random Field (MGRF) spatial interaction model that integrates third- and fourth- order families with a traditional second-order model is proposed. The proposed approach was tested and evaluated on 102 3D MR brain scans using three metrics: the Dice coefficient, the 95-percentile modified Hausdorff distance, and the absolute brain volume difference. Experimental results show better segmentation of MR brain images compared to current open source segmentation tools.

Automated framework for accurate segmentation of pressure ulcer images

Ulcer tissue segmentation is of immense importance in helping medical personnel to assess wounds. This paper introduces a new computational framework employing state-of-the-art image processing techniques to segment pressure ulcer tissue structures from color images. The framework integrates a visual appearance model of an observed input image with prior color information from an available database of previously stored color RGB images. The following four processing steps are performed. First, to minimize the execution time and enhance the segmentation accuracy, a region-of-interest (ROI) of the whole ulcer area is automatically identified based on contrast changes. This step exploits synthetic frequencies of pixelwise intensities, which are calculated by using an electric field energy model to describe relations between the pixelwise intensities. Secondly, visual appearance of the observed image is modeled by a linear combination of discrete Gaussians (LCDG) model in order to estimate marginal probability distributions of three main tissue classes for the grayscale ROI image. Next, the pixel-wise probabilities of these classes for the color ROI image are calculated using the available prior information about the RGB colors on manually segmented database images. Initial labeling is obtained based on both the observed and prior probabilities of pixelwise colors. Finally, to preserve continuity, the labels are refined and normalized using the generalized Gauss-Markov random field (GGMRF) model. Experimental validation on 24 clinical images of pressure ulcers, provided by the Centre IGURCO, showed the high segmentation accuracy of 90.4%.

Accurate Lungs Segmentation on CT Chest Images by Adaptive Appearance-Guided Shape Modeling.

To accurately segment pathological and healthy lungs for reliable computer-aided disease diagnostics, a stack of chest CT scans is modeled as a sample of a spatially inhomogeneous joint 3D Markov-Gibbs random field (MGRF) of voxel-wise lung and chest CT image signals (intensities). The proposed learnable MGRF integrates two visual appearance sub-models with an adaptive lung shape submodel. The first-order appearance submodel accounts for both the original CT image and its Gaussian scale space (GSS) filtered version to specify local and global signal properties, respectively. Each empirical marginal probability distribution of signals is closely approximated with a linear combination of discrete Gaussians (LCDG), containing two positive dominant and multiple sign-alternate subordinate DGs. The approximation is separated into two LCDGs to describe individually the lungs and their background, i.e., all other chest tissues. The second-order appearance submodel quantifies conditional pairwise intensity dependencies in the nearest voxel 26-neighborhood in both the original and GSS-filtered images. The shape submodel is built for a set of training data and is adapted during segmentation using both the lung and chest appearances. The accuracy of the proposed segmentation framework is quantitatively assessed using two public databases (ISBI VESSEL12 challenge and MICCAI LOLA11 challenge) and our own database with, respectively, 20, 55, and 30 CT images of various lung pathologies acquired with different scanners and protocols. Quantitative assessment of our framework in terms of Dice similarity coefficients, 95-percentile bidirectional Hausdorff distances, and percentage volume differences confirms the high accuracy of our model on both our database (98.4±1.0%, 2.2±1.0 mm, 0.42±0.10%) and the VESSEL12 database (99.0±0.5%, 2.1±1.6 mm, 0.39±0.20%), respectively. Similarly, the accuracy of our approach is further verified via a blind evaluation by the organizers of the LOLA11 competition, where an average overlap of 98.0% with the expert's segmentation is yielded on all 55 subjects with our framework being ranked first among all the state-of-the-art techniques compared.

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.

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.

Myocardial borders segmentation from cine MR images using bidirectional coupled parametric deformable models

The authors propose 3D (2D + time) novel, fast, robust, bidirectional coupled parametric deformable models that are capable of segmenting left ventricle (LV) wall borders using first- and second-order visual appearance features. The authors examine the effect of the proposed segmentation method on the estimation of global cardiac performance indexes. First-order visual appearance of the cine cardiac magnetic resonance (CMR) signals (inside and outside the boundary of the deformable model) is modeled with an adaptive linear combination of discrete Gaussians (LCDG). Second-order visual appearance of the LV wall is accurately modeled with a translational and rotation-invariant second-order Markov-Gibbs random field (MGRF). The LCDG parameters are estimated using our previously proposed modification of the EM algorithm, and the potentials of rotationally invariant MGRF are computed analytically. The authors tested the proposed segmentation approach on 15 cine CMR data sets using the Dice similarity coefficient (DSC) and the average distance (AD) between the ground truth and automated segmentation contours. The authors documented an average DSC value of 0.926 ± 0.022 and an average AD value of 2.16 ± 0.60 mm compared to two other level set methods that achieve an average DSC values of 0.904 ± 0.033 and 0.885 ± 0.02; and an average AD values of 2.86 ± 1.35 mm and 5.72 ± 4.70 mm, respectively. The proposed segmentation approach demonstrated superior performance over other methods. Specifically, the comparative results on the publicly available MICCAI 2009 Cardiac MR Left Ventricle Segmentation database documented superior performance of the proposed approach over published methods. Additionally, the high accuracy of our segmentation approach leads to accurate estimation of the global performance indexes, as evidenced by the Bland-Altman analyses of the end-systolic volume (ESV), end-diastolic volume (EDV), and the ejection fraction (EF) ratio.

Precise Segmentation of 3-D Magnetic Resonance Angiography

Accurate automatic extraction of a 3-D cerebrovascular system from images obtained by time-of-flight (TOF) or phase contrast (PC) magnetic resonance angiography (MRA) is a challenging segmentation problem due to the small size objects of interest (blood vessels) in each 2-D MRA slice and complex surrounding anatomical structures (e.g., fat, bones, or gray and white brain matter). We show that due to the multimodal nature of MRA data, blood vessels can be accurately separated from the background in each slice using a voxel-wise classification based on precisely identified probability models of voxel intensities. To identify the models, an empirical marginal probability distribution of intensities is closely approximated with a linear combination of discrete Gaussians (LCDG) with alternate signs, using our previous EM-based techniques for precise linear combination of Gaussian-approximation adapted to deal with the LCDGs. The high accuracy of the proposed approach is experimentally validated on 85 real MRA datasets (50 TOF and 35 PC) as well as on synthetic MRA data for special 3-D geometrical phantoms of known shapes.

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.