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.     

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.     

Hierarchical scale-based multiobject recognition of 3-D anatomical structures

Segmentation of anatomical structures from medical images is a challenging problem, which depends on the accurate recognition (localization) of anatomical structures prior to delineation. This study generalizes anatomy segmentation problem via attacking two major challenges: 1) automatically locating anatomical structures without doing search or optimization, and 2) automatically delineating the anatomical structures based on the located model assembly. For 1), we propose intensity weighted ball-scale object extraction concept to build a hierarchical transfer function from image space to object (shape) space such that anatomical structures in 3-D medical images can be recognized without the need to perform search or optimization. For 2), we integrate the graph-cut (GC) segmentation algorithm with prior shape model. This integrated segmentation framework is evaluated on clinical 3-D images consisting of a set of 20 abdominal CT scans. In addition, we use a set of 11 foot MR images to test the generalizability of our method to the different imaging modalities as well as robustness and accuracy of the proposed methodology. Since MR image intensities do not possess a tissue specific numeric meaning, we also explore the effects of intensity nonstandardness on anatomical object recognition. Experimental results indicate that: 1) effective recognition can make the delineation more accurate; 2) incorporating a large number of anatomical structures via a model assembly in the shape model improves the recognition and delineation accuracy dramatically; 3) ball-scale yields useful information about the relationship between the objects and the image; 4) intensity variation among scenes in an ensemble degrades object recognition performance.     

Segmentation of stochastic images with a stochastic random walker method

We present an extension of the random walker segmentation to images with uncertain gray values. Such gray-value uncertainty may result from noise or other imaging artifacts or more general from measurement errors in the image acquisition process. The purpose is to quantify the influence of the gray-value uncertainty onto the result when using random walker segmentation. In random walker segmentation, a weighted graph is built from the image, where the edge weights depend on the image gradient between the pixels. For given seed regions, the probability is evaluated for a random walk on this graph starting at a pixel to end in one of the seed regions. Here, we extend this method to images with uncertain gray values. To this end, we consider the pixel values to be random variables (RVs), thus introducing the notion of stochastic images. We end up with stochastic weights for the graph in random walker segmentation and a stochastic partial differential equation (PDE) that has to be solved. We discretize the RVs and the stochastic PDE by the method of generalized polynomial chaos, combining the recent developments in numerical methods for the discretization of stochastic PDEs and an interactive segmentation algorithm. The resulting algorithm allows for the detection of regions where the segmentation result is highly influenced by the uncertain pixel values. Thus, it gives a reliability estimate for the resulting segmentation, and it furthermore allows determining the probability density function of the segmented object volume.     

Segmentation of ultrasound B-mode images with intensity inhomogeneity correction

Displayed ultrasound (US) B-mode images often exhibit tissue intensity inhomogeneities dominated by nonuniform beam attenuation within the body. This is a major problem for intensity-based, automatic segmentation of video-intensity images because conventional threshold-based or intensity-statistic-based approaches do not work well in the presence of such image distortions. Time gain compensation (TGC) is typically used in standard US machines in an attempt to overcome this. However this compensation method is position-dependent which means that different tissues in the same TGC time-range (or corresponding depth range) will be, incorrectly, compensated by the same amount. Compensation should really be tissue-type dependent but automating this step is difficult. The main contribution of this paper is to develop a method for simultaneous estimation of video-intensity inhomogeities and segmentation of US image tissue regions. The method uses a combination of the maximum a posteriori (MAP) and Markov random field (MRF) methods to estimate the US image distortion field assuming it follows a multiplicative model while at the same time labeling image regions based on the corrected intensity statistics. The MAP step is used to estimate the intensity model parameters while the MRF step provides a novel way of incorporating the distributions of image tissue classes as a spatial smoothness constraint. We explain how this multiplicative model can be related to the ultrasonic physics of image formation to justify our approach. Experiments are presented on synthetic images and a gelatin phantom to evaluate quantitatively the accuracy of the method. We also discuss qualitatively the application of the method to clinical breast and cardiac US images. Limitations of the method and potential clinical applications are outlined in the conclusion.     

Reconstruction of the human cerebral cortex from magnetic resonanceimages

Reconstructing the geometry of the human cerebral cortex from MR images is an important step in both brain mapping and surgical path planning applications. Difficulties with imaging noise, partial volume averaging, image intensity inhomogeneities, convoluted cortical structures, and the requirement to preserve anatomical topology make the development of accurate automated algorithms particularly challenging. In this paper we address each of these problems and describe a systematic method for obtaining a surface representation of the geometric central layer of the human cerebral cortex. Using fuzzy segmentation, an isosurface algorithm, and a deformable surface model, the method reconstructs the entire cortex with the correct topology, including deep convoluted sulci and gyri. The method is largely automated and its results are robust to imaging noise, partial volume averaging, and image intensity inhomogeneities. The performance of this method is demonstrated, both qualitatively and quantitatively, and the results of its application to six subjects and one simulated MR brain volume are presented.     

利用局部离散度活动轮廓模型的强度非均匀图像分割

强度非均匀现象在真实图像中普遍存在,采用常规基于强度的分割算法会导致严重的误分割。针对强度非均匀图像分割,提出了基于局部离散度的活动轮廓模型分割算法。首先定义基于类内类间距离的离散度,然后利用核函数提取局部区域信息,同时加入边缘指示函数加权的轮廓线长度项能量,建立基于局部离散度的活动轮廓模型。最后引入水平集函数惩罚项,避免水平集方法在演化求解时需要不断初始化的问题。合成图像和真实图像实验结果证明本文算法性能稳定,适应于强度非均匀图像的分割。      

基于Wasserstein距离的局部能量分割模型

 提出了一种基于Wasserstein距离和图像局部区域直方图信息的非参数活动轮廓分割模型.用该距离对图像中不同区域的直方图进行比较,提高了相似性衡量的准确性;引入高斯内核函数来获取图像局部区域直方图信息,并将信息嵌入模型指导轮廓演化,以克服由于亮度不均造成的图像分割困难;通过水平集规范项提高计算精度并避免水平集演化的重新初始化.实验结果表明,本模型能够对亮度不均的无序特征图像进行有效准确的分割.     

Adaptive fuzzy segmentation of magnetic resonance images

An algorithm is presented for the fuzzy segmentation of two-dimensional (2-D) and three-dimensional (3-D) multispectral magnetic resonance (MR) images that have been corrupted by intensity inhomogeneities, also known as shading artifacts. The algorithm is an extension of the 2-D adaptive fuzzy C-means algorithm (2-D AFCM) presented in previous work by the authors. This algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space. It iteratively adapts to the intensity inhomogeneities and is completely automated. In this paper, we fully generalize 2-D AFCM to three-dimensional (3-D) multispectral images. Because of the potential size of 3-D image data, we also describe a new faster multigrid-based algorithm for its implementation. We show, using simulated MR data, that 3-D AFCM yields lower error rates than both the standard fuzzy C-means (FCM) algorithm and two other competing methods, when segmenting corrupted images. Its efficacy is further demonstrated using real 3-D scalar and multispectral MR brain images.     

Combining learning-based intensity distributions with nonparametric shape priors for image segmentation

Integration of shape prior information into level set formulations has led to great improvements in image segmentation in the presence of missing information, occlusion, and noise. However, most shape-based segmentation techniques incorporate image intensity through simplistic data terms. A common underlying assumption of such data terms is that the foreground and the background regions in the image are homogeneous, i.e., intensities are piecewise constant or piecewise smooth. This situation makes integration of shape priors inefficient in the presence of intensity inhomogeneities. In this paper, we propose a new approach for combining information from shape priors with that from image intensities. More specifically, our approach uses shape priors learned by nonparametric density estimation and incorporates image intensity distributions learned in a supervised manner. Such a combination has not been used in previous work. Sample image patches are used to learn the intensity distributions, and segmented training shapes are used to learn the shape priors. We present an active contour algorithm that takes these learned densities into account for image segmentation. Our experiments on synthetic and real images demonstrate the robustness of the proposed approach to complicated intensity distributions, and occlusions, as well as the improvements it provides over existing methods.     

Adaptive segmentation of MRI data

Intensity-based classification of MR images has proven problematic, even when advanced techniques are used. Intrascan and interscan intensity inhomogeneities are a common source of difficulty. While reported methods have had some success in correcting intrascan inhomogeneities, such methods require supervision for the individual scan. This paper describes a new method called adaptive segmentation that uses knowledge of tissue intensity properties and intensity inhomogeneities to correct and segment MR images. Use of the expectation-maximization (EM) algorithm leads to a method that allows for more accurate segmentation of tissue types as well as better visualization of magnetic resonance imaging (MRI) data, that has proven to be effective in a study that includes more than 1000 brain scans. Implementation and results are described for segmenting the brain in the following types of images: axial (dual-echo spin-echo), coronal [three dimensional Fourier transform (3-DFT) gradient-echo T1-weighted] all using a conventional head coil, and a sagittal section acquired using a surface coil. The accuracy of adaptive segmentation was found to be comparable with manual segmentation, and closer to manual segmentation than supervised multivariant classification while segmenting gray and white matter.     

A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data

In this paper, we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic. MRI intensity inhomogeneities can be attributed to imperfections in the radio-frequency coils or to problems associated with the acquisition sequences. The result is a slowly varying shading artifact over the image that can produce errors with conventional intensity-based classification. Our algorithm is formulated by modifying the objective function of the standard fuzzy c-means (FCM) algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel (voxel) to be influenced by the labels in its immediate neighborhood. The neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings. Such a regularization is useful in segmenting scans corrupted by salt and pepper noise. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm.     

Image segmentation and inpainting using hierarchical level set and texture mapping

Image inpainting is an artistic procedure to recover a damaged painting or picture. We propose a novel approach for image inpainting by using the Mumford-Shah (MS) model and the level set method to estimate image structure of the damaged regions. This approach has been successfully used in image segmentation problem. Compared to some other inpainting methods, the MS model approach detects and preserves edges in the inpainting areas. We propose a fast and efficient algorithm that achieves both inpainting and segmentation. In previous works on the MS model, only one or two level set functions are used to segment an image. While this approach works well on simple cases, detailed edges cannot be detected in complicated image structures. Although multi-level set functions can be used to segment an image into many regions, the traditional approach causes extensive computations and the solutions depend on the location of initial curves. Our proposed approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. Because we detect both the main structure and the detailed edges, our approach preserves edges in the inpainting area. Also, exemplar-based approach for filling textured regions is employed. Experimental results demonstrate the advantage of our method.     

Parametric estimate of intensity inhomogeneities applied to MRI

This paper presents a new approach to the correction of intensity inhomogeneities in magnetic resonance imaging (MRI) that significantly improves intensity-based tissue segmentation. The distortion of the image brightness values by a low-frequency bias field impedes visual inspection and segmentation. The new correction method called parametric bias field correction (PABIC) is based on a simplified model of the imaging process, a parametric model of tissue class statistics, and a polynomial model of the inhomogeneity field. We assume that the image is composed of pixels assigned to a small number of categories with a priori known statistics. Further we assume that the image is corrupted by noise and a low-frequency inhomogeneity field. The estimation of the parametric bias field is formulated as a nonlinear energy minimization problem using an evolution strategy (ES). The resulting bias field is independent of the image region configurations and thus overcomes limitations of methods based on homomorphic filtering. Furthermore, PABIC can correct bias distortions much larger than the image contrast. Input parameters are the intensity statistics of the classes and the degree of the polynomial function. The polynomial approach combines bias correction with histogram adjustment, making it well suited for normalizing the intensity histogram of datasets from serial studies. We present simulations and a quantitative validation with phantom and test images. A large number of MR image data acquired with breast, surface, and head coils, both in two dimensions and three dimensions, have been processed and demonstrate the versatility and robustness of this new bias correction scheme.     

A new filter for the removal of random-valued impulse noise from highly corrupted images

In this paper, we present a new two-stage filter for the removal of random-valued impulse noise. The new filter identifies noise candidates by analyzing the amount of similar pixels in intensity value, and then reconstructs them by the total variation inpainting method. The experimental results are reported which show the efficiency of our method in removing random-valued impulse noise. Further, our filter can be used for image restoration from images damaged by the superimposed artifacts.     

Kernel estimation from salient structure for robust motion deblurring

Blind image deblurring algorithms have been improving steadily in the past years. Most state-of-the-art algorithms, however, still cannot perform perfectly in challenging cases, especially in large blur setting. In this paper, we focus on how to estimate a good blur kernel from a single blurred image based on the image structure. We found that image details caused by blur could adversely affect the kernel estimation, especially when the blur kernel is large. One effective way to remove these details is to apply image denoising model based on the total variation (TV). First, we developed a novel method for computing image structures based on the TV model, such that the structures undermining the kernel estimation will be removed. Second, we applied a gradient selection method to mitigate the possible adverse effect of salient edges and improve the robustness of kernel estimation. Third, we proposed a novel kernel estimation method, which is capable of removing noise and preserving the continuity in the kernel. Finally, we developed an adaptive weighted spatial prior to preserve sharp edges in latent image restoration. Extensive experiments testify to the effectiveness of our method on various kinds of challenging examples.     

A customized low-rank prior model for structured cartoon–texture image decomposition

The mathematical characterization of the texture component plays an instrumental role in image decomposition. In this paper, we are concerned with a low-rank texture prior based cartoon–texture image decomposition model, which utilizes a total variation norm and a global nuclear norm to characterize the cartoon and texture components, respectively. It is promising that our decomposition model is not only extremely simple, but also works perfectly for globally well-patterned images in the sense that the model can recover cleaner texture (or details) than the other novel models. Moreover, such a model can be easily reformulated as a separable convex optimization problem, thereby enjoying a splitting nature so that we can employ a partially parallel splitting method (PPSM) to solve it efficiently. A series of numerical experiments on image restoration demonstrate that PPSM can recover slightly higher quality images than some existing algorithms in terms of taking less iterations or computing time in many cases.     

Brain MR image segmentation based on local Gaussian mixture model and nonlocal spatial regularization

Brain Magnetic Resonance (MR) images often suffer from the inhomogeneous intensities caused by the bias field and heavy noise. The most widely used image segmentation algorithms, which typically rely on the homogeneity of image intensities in different regions, often fail to provide accurate segmentation results due to the existence of bias field and heavy noise. This paper proposes a novel variational approach for brain image segmentation with simultaneous bias correction. We define an energy functional with a local data fitting term and a nonlocal spatial regularization term. The local data fitting term is based on the idea of local Gaussian mixture model (LGMM), which locally models the distribution of each tissue by a linear combination of Gaussian function. By the LGMM, the bias field function in an additive form is embedded to the energy functional, which is helpful for eliminating the influence of the intensity inhomogeneity. For reducing the influence of noise and getting a smooth segmentation, the nonlocal spatial regularization is drawn upon, which is good at preserving fine structures in brain images. Experiments performed on simulated as well as real MR brain data and comparisons with other related methods are given to demonstrate the effectiveness of the proposed method.     

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.     

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.