Simultaneous vector-valued image segmentation and intensity nonuniformity correction using variational level set combined with Markov random field modeling

Object quantification requires an image segmentation to make measurements about size, material composition and morphology of the object. In vector-valued or multispectral images, each image channel has its signal characteristics and provides special information that may improve the results of image segmentation method. This paper presents a region-based active contour model for vector-valued image segmentation with a variational level set formulation. In this model, the local image intensities are characterized using Gaussian distributions with different means and variances. Furthermore, by utilizing Markov random field, the spatial correlation between neighboring pixels and voxels is modeled. With incorporation of intensity nonuniformity model, our method is able to deal with brain tissue segmentation from multispectral magnetic resonance (MR) images. Our experiments on synthetic images and multispectral cerebral MR images with different noise and bias level show the advantages of the proposed method.     

Fuzzy local Gaussian mixture model for brain MR image segmentation

Accurate brain tissue segmentation from magnetic resonance (MR) images is an essential step in quantitative brain image analysis. However, due to the existence of noise and intensity inhomogeneity in brain MR images, many segmentation algorithms suffer from limited accuracy. In this paper, we assume that the local image data within each voxel's neighborhood satisfy the Gaussian mixture model (GMM), and thus propose the fuzzy local GMM (FLGMM) algorithm for automated brain MR image segmentation. This algorithm estimates the segmentation result that maximizes the posterior probability by minimizing an objective energy function, in which a truncated Gaussian kernel function is used to impose the spatial constraint and fuzzy memberships are employed to balance the contribution of each GMM. We compared our algorithm to state-of-the-art segmentation approaches in both synthetic and clinical data. Our results show that the proposed algorithm can largely overcome the difficulties raised by noise, low contrast, and bias field, and substantially improve the accuracy of brain MR image segmentation.     

An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation

An adaptive spatial fuzzy c-means clustering algorithm is presented in this paper for the segmentation of three-dimensional (3-D) magnetic resonance (MR) images. The input images may be corrupted by noise and intensity nonuniformity (INU) artifact. The proposed algorithm takes into account the spatial continuity constraints by using a dissimilarity index that allows spatial interactions between image voxels. The local spatial continuity constraint reduces the noise effect and the classification ambiguity. The INU artifact is formulated as a multiplicative bias field affecting the true MR imaging signal. By modeling the log bias field as a stack of smoothing B-spline surfaces, with continuity enforced across slices, the computation of the 3-D bias field reduces to that of finding the B-spline coefficients, which can be obtained using a computationally efficient two-stage algorithm. The efficacy of the proposed algorithm is demonstrated by extensive segmentation experiments using both simulated and real MR images and by comparison with other published algorithms.     

Minimization of region-scalable fitting energy for image segmentation

Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function. Experimental results for synthetic and real images show desirable performances of our method.     

Statistical approach to segmentation of single-channel cerebral MRimages

A statistical model is presented that represents the distributions of major tissue classes in single-channel magnetic resonance (MR) cerebral images. Using the model, cerebral images are segmented into gray matter, white matter, and cerebrospinal fluid (CSF). The model accounts for random noise, magnetic field inhomogeneities, and biological variations of the tissues. Intensity measurements are modeled by a finite Gaussian mixture. Smoothness and piecewise contiguous nature of the tissue regions are modeled by a three-dimensional (3-D) Markov random field (MRF). A segmentation algorithm, based on the statistical model, approximately finds the maximum a posteriori (MAP) estimation of the segmentation and estimates the model parameters from the image data. The proposed scheme for segmentation is based on the iterative conditional modes (ICM) algorithm in which measurement model parameters are estimated using local information at each site, and the prior model parameters are estimated using the segmentation after each cycle of iterations. Application of the algorithm to a sample of clinical MR brain scans, comparisons of the algorithm with other statistical methods, and a validation study with a phantom are presented. The algorithm constitutes a significant step toward a complete data driven unsupervised approach to segmentation of MR images in the presence of the random noise and intensity inhomogeneities     

MR Image Segmentation Using a Power Transformation Approach

This study proposes a segmentation method for brain MR images using a distribution transformation approach. The method extends traditional Gaussian mixtures expectation-maximization segmentation to a power transformed version of mixed intensity distributions, which includes Gaussian mixtures as a special case. As MR intensities tend to exhibit non-Gaussianity due to partial volume effects, the proposed method is designed to fit non-Gaussian tissue intensity distributions. One advantage of the method is that it is intuitively appealing and computationally simple. To avoid performance degradation caused by intensity inhomogeneity, different methods for correcting bias fields were applied prior to image segmentation, and their correction effects on the segmentation results were examined in the empirical study. The partitions of brain tissues (i.e., gray and white matter) resulting from the method were validated and evaluated against manual segmentation results based on 38 real T1-weighted image volumes from the internet brain segmentation repository, and 18 simulated image volumes from BrainWeb. The Jaccard and Dice similarity indexes were computed to evaluate the performance of the proposed approach relative to the expert segmentations. Empirical results suggested that the proposed segmentation method yielded higher similarity measures for both gray matter and white matter as compared with those based on the traditional segmentation using the Gaussian mixtures approach.      

Active contours driven by local Gaussian distribution fitting energy

This paper presents a new region-based active contour model in a variational level set formulation for image segmentation. In our model, the local image intensities are described by Gaussian distributions with different means and variances. We define a local Gaussian distribution fitting energy with a level set function and local means and variances as variables. The energy minimization is achieved by an interleaved level set evolution and estimation of local intensity means and variances in an iterative process. The means and variances of local intensities are considered as spatially varying functions to handle intensity inhomogeneities and noise of spatially varying strength (e.g. multiplicative noise). In addition, our model is able to distinguish regions with similar intensity means but different variances. This is demonstrated by applying our method on noisy and texture images in which the texture patterns of different regions can be distinguished from the local intensity variance. Comparative experiments show the advantages of the proposed method.     

Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm

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.     

一种基于多特征的距离正则化水平集快速分割方法

现有的图像分割模型存在对初始化信息敏感,分割速率慢,图像弱边界区的泄露等现象.提出了一种混合快速分割方法.该方法利用偏压场近似估计图像的局部统计信息,并结合全局信息相容性及改进的距离正则化方法建立模型,最后将模型嵌入水平集框架中,与此同时,引入双重终止准则以提高分割的速度.最后利用合成图像和真实图像进行分割实验,并与CV（Chan-Vese）模型、非线性自适应水平集方法以及局部尺度拟合模型对比,表明本方法不仅对初始化信息敏感度降低,而且分割速度提高3~5倍.     

高分三号SAR精准海陆分割的混合策略方法

高分三号（GF-3）是我国第一颗多极化雷达卫星，主要用于海洋遥感和海面监测，其中海陆分割是重要的预处理步骤.文章针对GF-3多极化合成孔径雷达（synthetic aperture radar，SAR）的精准海陆分割，提出了创新的混合策略方法，可提高分割性能对于相干斑噪声、风浪、成像等因素的稳健性.针对不同的极化通道采取三种不同的策略:1）对数混合高斯模型，用于确定海陆比，将纯陆地和纯海洋图像与海陆图像区分开，同时根据混合模型参数对海陆图像进行精细聚类；2）大津法，通过分别在对数域和复数域实现类间方差最大化，产生基于灰度信息的海陆掩膜；3）对数累积量，分析纹理信息，通过对数二阶矩与对数三阶矩之间的联系判断海陆大致分布，用作对投票机制产生的海陆掩膜进行验证与再分割，增强海陆分割精确性.针对大量GF-3数据进行实验，结果均达到理想效果，具备实际应用价值.     

基于活动轮廓模型的左心室MR图像分割

本文提出一种基于局部与全局特征的活动轮廓模型左心室MR图像分割算法.该算法融合了图像局部信息和全局信息.局部信息包含了图像局部均值和方差信息,来克服图像灰度不均匀的影响.全局信息则较好地提高模型处理图像弱边界的能力,并防止模型陷入局部最优,实验结果表明,改进算法分割出较为精确的心脏左心室MR图像.     

A novel fuzzy clustering algorithm with non local adaptive spatial constraint for image segmentation

Generalized fuzzy c-means clustering algorithm with improved fuzzy partitions (GIFP_FCM) is a novel fuzzy clustering algorithm. However when GIFP_FCM is applied to image segmentation, it is sensitive to noise in the image because of ignoring the spatial information contained in the pixels. In order to solve this problem, a novel fuzzy clustering algorithm with non local adaptive spatial constraint (FCA_NLASC) is proposed in this paper. In the proposed method, a novel non local adaptive spatial constraint term is introduced to modify the objective function of GIFP_FCM. The characteristic of this technique is that the adaptive spatial parameter for each pixel is designed to make the non local spatial information of each pixel playing a different role in guiding the noisy image segmentation. Segmentation experiments on synthetic and real images, especially magnetic resonance (MR) images, are performed to assess the performance of an FCA_NLASC in comparison with GIFP_FCM and fuzzy c-means clustering algorithms with local spatial constraint. Experimental results show that the proposed method is robust to noise in the image and more effective than the comparative algorithms.     

A segmentation-based regularization term for image deconvolution.

This paper proposes a new and original inhomogeneous restoration (deconvolution) model under the Bayesian framework for observed images degraded by space-invariant blur and additive Gaussian noise. In this model, regularization is achieved during the iterative restoration process with a segmentation-based a priori term. This adaptive edge-preserving regularization term applies a local smoothness constraint to pre-estimated constant-valued regions of the target image. These constant-valued regions (the segmentation map) of the target image are obtained from a preliminary Wiener deconvolution estimate. In order to estimate reliable segmentation maps, we have also adopted a Bayesian Markovian framework in which the regularized segmentations are estimated in the maximum a posteriori (MAP) sense with the joint use of local Potts prior and appropriate Gaussian conditional luminance distributions. In order to make these segmentations unsupervised, these likelihood distributions are estimated in the maximum likelihood sense. To compute the MAP estimate associated to the restoration, we use a simple steepest descent procedure resulting in an efficient iterative process converging to a globally optimal restoration. The experiments reported in this paper demonstrate that the discussed method performs competitively and sometimes better than the best existing state-of-the-art methods in benchmark tests.     

Automated brain structure segmentation based on atlas registration and appearance models

Accurate automated brain structure segmentation methods facilitate the analysis of large-scale neuroimaging studies. This work describes a novel method for brain structure segmentation in magnetic resonance images that combines information about a structure's location and appearance. The spatial model is implemented by registering multiple atlas images to the target image and creating a spatial probability map. The structure's appearance is modeled by a classifier based on Gaussian scale-space features. These components are combined with a regularization term in a Bayesian framework that is globally optimized using graph cuts. The incorporation of the appearance model enables the method to segment structures with complex intensity distributions and increases its robustness against errors in the spatial model. The method is tested in cross-validation experiments on two datasets acquired with different magnetic resonance sequences, in which the hippocampus and cerebellum were segmented by an expert. Furthermore, the method is compared to two other segmentation techniques that were applied to the same data. Results show that the atlas- and appearance-based method produces accurate results with mean Dice similarity indices of 0.95 for the cerebellum, and 0.87 for the hippocampus. This was comparable to or better than the other methods, whereas the proposed technique is more widely applicable and robust.     

Constrained Gaussian mixture model framework for automatic segmentation of MR brain images

An automated algorithm for tissue segmentation of noisy, low-contrast magnetic resonance (MR) images of the brain is presented. A mixture model composed of a large number of Gaussians is used to represent the brain image. Each tissue is represented by a large number of Gaussian components to capture the complex tissue spatial layout. The intensity of a tissue is considered a global feature and is incorporated into the model through tying of all the related Gaussian parameters. The expectation-maximization (EM) algorithm is utilized to learn the parameter-tied, constrained Gaussian mixture model. An elaborate initialization scheme is suggested to link the set of Gaussians per tissue type, such that each Gaussian in the set has similar intensity characteristics with minimal overlapping spatial supports. Segmentation of the brain image is achieved by the affiliation of each voxel to the component of the model that maximized the a posteriori probability. The presented algorithm is used to segment three-dimensional, T1-weighted, simulated and real MR images of the brain into three different tissues, under varying noise conditions. Results are compared with state-of-the-art algorithms in the literature. The algorithm does not use an atlas for initialization or parameter learning. Registration processes are therefore not required and the applicability of the framework can be extended to diseased brains and neonatal brains.     

基于图像分解的稀疏正则化多区域图像分割方法

针对图像具有不同特征的成分,提出一种基于图像分解的多区域图像分割模型和算法.首先将图像分解项引入到图像分割模型中,递减了纹理和噪声对分割的影响;其次使用稀疏正则化方法保持分割区域的边缘几何结构;最后基于增广Lagrange乘子法,给出一种由扩散流引导的小波迭代阈值图像分割算法.一系列实验结果表明,提出的方法抗干扰能力强,对噪声具有更好的鲁棒性.提出的方法不仅能够分割结构图像,并且能够分割较复杂的纹理图像.     

Method to correct intensity inhomogeneity in MR images for atherosclerosis characterization

We are developing methods to characterize atherosclerotic disease in human carotid arteries using multiple MR images having different contrast mechanisms (T1W, T2W, PDW). To enable the use of voxel gray values for interpretation of disease, we created a new method, local entropy minimization with a bicubic spline model (LEMS), to correct the severe (approximately 80%) intensity inhomogeneity that arises from the surface coil array. This entropy-based method does not require classification and robustly addresses some problems that are more severe than those found in brain imaging, including noise, steep bias field, sensitivity of artery wall voxels to edge artifacts, and signal voids near the artery wall. Validation studies were performed on a synthetic digital phantom with realistic intensity inhomogeneity, a physical phantom roughly mimicking the neck, and patient carotid artery images. We compared LEMS to a modified fuzzy c-means segmentation based method (mAFCM), and a linear filtering method (LINF). Following LEMS correction, skeletal muscles in patient images were relatively isointense across the field of view. In the physical phantom, LEMS reduced the variation in the image to 1.9% and across the vessel wall region to 2.5%, a value which should be sufficient to distinguish plaque tissue types, based on literature measurements. In conclusion, we believe that the correction method shows promise for aiding human and computerized tissue classification from MR signal intensities.     

基于参数化互信息的脑MR图像分割与偏移场矫正模型及快速算法

脑核磁共振(Magnetic Resonance简称MR)图像中存在灰度不均匀现象使得传统方法很难得到理想的分割与偏移场矫正结果.针对这一问题,本文首先提出Legendre基函数拟合偏移场下的参数化互信息度量,建立脑MR图像的分割与偏移场矫正的变分模型.最后,给出了基于分裂Bregman迭代方法的快速分割与偏移场矫正算...     

Comparison and validation of tissue modelization and statistical classification methods in T1-weighted MR brain images

This paper presents a validation study on statistical nonsupervised brain tissue classification techniques in magnetic resonance (MR) images. Several image models assuming different hypotheses regarding the intensity distribution model, the spatial model and the number of classes are assessed. The methods are tested on simulated data for which the classification ground truth is known. Different noise and intensity nonuniformities are added to simulate real imaging conditions. No enhancement of the image quality is considered either before or during the classification process. This way, the accuracy of the methods and their robustness against image artifacts are tested. Classification is also performed on real data where a quantitative validation compares the methods' results with an estimated ground truth from manual segmentations by experts. Validity of the various classification methods in the labeling of the image as well as in the tissue volume is estimated with different local and global measures. Results demonstrate that methods relying on both intensity and spatial information are more robust to noise and field inhomogeneities. We also demonstrate that partial volume is not perfectly modeled, even though methods that account for mixture classes outperform methods that only consider pure Gaussian classes. Finally, we show that simulated data results can also be extended to real data.     

基于低秩先验非局部匹配的高光谱图像恢复北大核心CSCD

为了实现未知退化类型条件下的图像恢复,提出了一种基于低秩先验非局部匹配的高光谱图像恢复方法。该恢复策略将结构相似性指数度量作为数据保真度项,核范数作为正则化项,从而能够使用单一算法解决延迟和信号相关的退化形式,能够处理加性高斯噪声、与信号相关的泊松噪声、混合泊松-高斯噪声,并且能够恢复被截止期和条纹损坏的高光谱图像。通过多个数据集实验结果证明了提出方法具有较好的恢复效果。