Abstract—The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogram-based model, the FM has an intrinsic limitation—no spatial information is taken into account. This causes the FM model to work only on well-defined images with low levels of noise; unfortunately, this is often not the the case due to artifacts such as partial volume effect and bias field distortion. Under these conditions, FM model-based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown that the FM model is a degenerate version of the HMRF model. The advantage of the HMRF model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites. Although MRF modeling has been employed in MR image segmentation by other researchers, most reported methods are limited to using MRF as a general prior in an FM model-based approach. To fit the HMRF model, an EM algorithm is used. We show that by incorporating both the HMRF model and the EM algorithm into a HMRF-EM framework, an accurate and robust segmentation can be achieved. More importantly, the HMRF-EM framework can easily be combined with other techniques. As an example, we show how the bias field correction algorithm of Guillemaud and Brady (1997) can be incorporated into this framework to achieve a three-dimensional fully automated approach for brain MR image segmentation. Index Terms—Bias field correction, expectation-maximization, hidden Markov random field, MRI, segmentation. I.

We describe a fully automated method for model-based tissue classification of Magnetic Resonance (MR) images of the brain. The method interleaves classification with estimation of the model parameters, improving the classification at each iteration. The algorithm is able to segment single- and multi-spectral MR images, corrects for MR signal inhomogeneities and incorporates contextual information by means of Markov Random Fields. A digital brain atlas containing prior expectations about the spatial location of tissue classes is used to initialize the algorithm. This makes the method fully automated and therefore provides objective and reproducible segmentations. We have validated the technique on simulated as well as on real MR images of the brain.

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A method is presented for segmentation of anatomical structures that incorporates prior information about the intensity and curvature pro le of the structure from a training set of images and boundaries. Specifically, we model the intensity distribution as a function of signed distance from the object boundary, instead of modeling only the intensity of the object as a whole. A curvature pro le acts as a boundary regularization term specific to the shape being extracted, as opposed to simply penalizing high curvature. Using the prior model, the segmentation process estimates a maximum a posteriori higher dimensional surface whose zero level set converges on the boundary of the object to be segmented. Segmentation results are demonstrated on synthetic data and magnetic resonance imagery.

A novel, fully automatic, adaptive, robust procedure for brain tissue classification from 3D magnetic resonance head images (MRI) is described in this paper. The procedure is adaptive in that it customizes a training set, by using a "pruning" strategy, such that the classification is robust against anatomical variability and pathology. Starting from a set of samples generated from prior tissue probability maps (a "model") in a standard, brain-based coordinate system ("stereotaxic space"), the method first reduces the fraction of incorrectly labeled samples in this set by using a minimum spanning tree graph-theoretic approach. Then, the corrected set of samples is used by a supervised kNN classifier for classifying the entire 3D image. The classification procedure is robust against variability in the image quality through a non-parametric implementation: no assumptions are made about the tissue intensity distributions. The performance of this brain tissue classification procedure is demonstrated through quantitative and qualitative validation experiments on both simulated MRI data (10 subjects) and real MRI data (43 subjects). A significant improvement in output quality was observed on subjects who exhibit morphological deviations from the model due to aging and pathology.

This paper proposes a new framework for image segmentation based on the integration of MRFs and deformable models using graphical models. We first construct a graphical model to represent the relationship of the observed image pixels, the true region labels and the underlying object contour. We then formulate the problem of image segmentation as the one of joint regioncontour inference and learning in the graphical model. The graphical model representation allows us to use an approximate structured variational inference technique to solve this otherwise intractable joint inference problem. Using this technique, the MAP solution to the original model is obtained by finding the MAP solutions of two simpler models, an extended MRF model and a probabilistic deformable model, iteratively and incrementally. In the extended MRF model, the true region labels are estimated using the BP algorithm in a band area around the estimated contour from the probabilistic deformable model, and the result in turn guides the probabilistic deformable model to an improved estimation of the contour. Experimental results show that our new hybrid method outperforms both the MRF-based and the deformable model-based methods. 1.

Abstract. A framework is proposed for the segmentation of brain tumors from MRI. Instead of training on pathology, the proposed method trains exclusively on healthy tissue. The algorithm attempts to recognize deviations from normalcy in order to compute a fitness map over the image associated with the presence of pathology. The resulting fitness map may then be used by conventional image segmentation techniques for honing in on boundary delineation. Such an approach is applicable to structures that are too irregular, in both shape and texture, to permit construction of comprehensive training sets. The technique is an extension of EM segmentation that considers information on five layers: voxel intensities, neighborhood coherence, intra-structure properties, inter-structure relationships, and user input. Information flows between the layers via multi-level Markov random fields and Bayesian classification. A simple instantiation of the framework has been implemented to perform preliminary experiments on synthetic and MRI data. 1

This paper is an attempt to review the state-of-the-art cortical segmentation techniques in 2-D and 3-D using brain magnetic resonance imaging (MRI), their applications and new challenges

Virtual colonoscopy provides a safe, minimal-invasive approach to detect colonic polyps using medical imaging and computer graphics technologies. Residual stool and fluid are problematic for optimal viewing of the colonic mucosa. Electronic cleansing techniques combining bowel preparation, oral contrast agents, and image segmentation were developed to extract the colon lumen from computed tomography (CT) images of the colon. In this paper, we present a new electronic colon cleansing technology, which employs a hidden Markov random filed (MRF) model to integrate the neighborhood information for overcoming the non-uniformity problems within the tagged stool/fluid region. Prior to obtaining CT images, the patient undergoes a bowel preparation. A statistical method for maximum a posterior probability (MAP) was developed to identify the enhanced regions of residual stool/fluid. The method utilizes a hidden MRF Gibbs model to integrate the spatial information into the Expectation Maximization (EM) model-fitting MAP algorithm. The algorithm estimates the model parameters and segments the voxels iteratively in an interleaved manner, converging to a solution where the model parameters and voxel labels are stabilized within a specified criterion. Experimental results are promising.

Abstract. Markov Random Fields (MRFs) are a popular and wellmotivated model for many medical image processing tasks such as segmentation. Discriminative Random Fields (DRFs), a discriminative alternative to the traditionally generative MRFs, allow tractable computation with less restrictive simplifying assumptions, and achieve better performance in many tasks. In this paper, we investigate the tumor segmentation performance of a recent variant of DRF models that takes advantage of the powerful Support Vector Machine (SVM) classification method. Combined with a powerful Magnetic Resonance (MR) preprocessing pipeline and a set of ‘alignment-based ’ features, we evaluate the use of SVMs, MRFs, and two types of DRFs as classifiers for three segmentation tasks related to radiation therapy target planning for brain tumors, two of which do not rely on ‘contrast agent ’ enhancement. Our results indicate that the SVM-based DRFs offer a significant advantage over the other approaches. 1