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.     

A model-based, semi-global segmentation approach for automatic 3-D point landmark localization in neuroimages

The existing differential approaches for localization of 3-D anatomic point landmarks in 3-D images are sensitive to noise and usually extract numerous spurious landmarks. The parametric model-based approaches are not practically usable for localization of landmarks that can not be modeled by simple parametric forms. Some dedicated methods using anatomic knowledge to identify particular landmarks are not general enough to cope with other landmarks. In this paper, we propose a model-based, semi-global segmentation approach to automatically localize 3-D point landmarks in neuroimages. To localize a landmark, the semi-global segmentation (meaning the segmentation of a part of the studied structure in a certain neighborhood of the landmark) is first achieved by an active surface model, and then the landmark is localized by analyzing the segmented part only. The joint use of global model-to-image registration, semi-global structure registration, active surface-based segmentation, and point-anchored surface registration makes our method robust to noise and shape variation. To evaluate the method, we apply it to the localization of ventricular landmarks including curvature extrema, centerline intersections, and terminal points. Experiments with 48 clinical and 18 simulated magnetic resonance (MR) volumetric images show that the proposed approach is able to localize these landmarks with an average accuracy of 1 mm (i.e., at the level of image resolution). We also illustrate the use of the proposed approach to cortical landmark identification and discuss its potential applications ranging from computer-aided radiology and surgery to atlas registration with scans.      

一种新的基于水平集方法的SAR图像分割算法

本文基于Aubert-Aujol（AA）模型和变分水平集方法提出一个新的SAR图像分割模型;在反应-扩散框架下,将各项同性扩散算子加入到该模型的水平集演化方程中,并提出一个两步分裂水平集演化算法,该算法不需要周期性地更新水平集函数。通过对合成图像和Envisat SAR图像的分割实验,表明本文提出的算法具有较准确的边缘定位能力和噪声抑制能力。     

Combining strings and necklaces for interactive three-dimensional segmentation of spinal images using an integral deformable spine model

Segmentation of the spine directly from three-dimensional (3-D) image data is desirable to accurately capture its morphological properties. We describe a method that allows true 3-D spinal image segmentation using a deformable integral spine model. The method learns the appearance of vertebrae from multiple continuous features recorded along vertebra boundaries in a given training set of images. Important summarizing statistics are encoded into a necklace model on which landmarks are differentiated on their free dimensions. The landmarks are used within a priority segmentation scheme to reduce the complexity of the segmentation problem. Necklace models are coupled by string models. The string models describe in detail the biological variability in the appearance of spinal curvatures from multiple continuous features recorded in the training set. In the segmentation phase, the necklace and string models are used to interactively detect vertebral structures in new image data via elastic deformation reminiscent of a marionette with strings allowing for movement between interrelated structures. Strings constrain the deformation of the spine model within feasible solutions. The driving application in this work is analysis of computed tomography scans of the human lumbar spine. An illustration of the segmentation process shows that the method is promising for segmentation of the spine and for assessment of its morphological properties.     

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.     

基于Mumford-Shah模型的参数估计和两阶段图像分割方法

Mumford-Shah两相分片常数模型是一个有效的图像分割模型,但当模型用于带有噪声的图像时,其水平集解法存在对初始解和长度参数敏感这两个问题.文中给出一种两阶段分割方法,首先利用传统的简单分割方法获得一个粗分割,再将其作为变分模型的初始解,从而实现自动选取初始解.文中还给出一个有效的自适应长度参数估计模型,该模型依据图像中噪声方差大小来确定参数.两阶段分割方法和自适应参数估计结合起来使得算法大大减弱了对参量的敏感性,而且可以正确、快速地分割.针对一些计算机生成图像和实际图像的实验结果验证了算法是有效的.     

一种基于活动轮廓模型的PET-CT肺肿瘤分割方法

针对PET-CT肺肿瘤分割中存在的没有充分将医生临床经验融入到算法设计的问题,该文利用PET高斯分布先验,结合区域可伸缩拟合(RSF)模型和最大似然比分类(MLC)准则,提出一种基于变分水平集的混合活动轮廓模型RSF_ML。进一步,借鉴人工勾画肺肿瘤过程中融合图像的重要价值,提出了基于RSF_ML的PET-CT肺肿瘤融合图像分割方法。实验表明,所提出方法较好地实现了有代表性的非小细胞肺肿瘤(Non-Small Cell Lung Cancer, NSCLC)的精确分割,主客观结果优于对比方法,可为临床提供有效的计算机辅助分割结果。     

Restoration of speckle noise corrupted SAR images using regularization by denoising

Speckle noise removal is a well-established problem in synthetic aperture radar (SAR) image processing. Among different methods focused on the reconstruction of SAR images, variational models have achieved state-of-the-art performance. In this paper, a Rayleigh based speckle reduction algorithm is developed using the variational framework. The forward model is combined with recently proposed regularization by denoising (RED) prior. However, RED has been proposed in literature for the additive noise model. Multiplicative noise in SAR images prevents the direct application of RED to variational models. Hence, logarithm transformation is applied to change the multiplicative noise model to additive model, and the forward model from Rayleigh to Fisher–Tippett distribution. The resulting optimization problem is solved using the alternating direction method of multipliers. Further, the proof of the convergence analysis is carried out for the above framework. Simulations convey that the proposed method has better despeckling performance compared to that of state-of-the-art methods.     

Unsupervised multi class segmentation of 3D images with intensity inhomogeneities

Intensity inhomogeneities in images cause problems in gray-value based image segmentation since the varying intensity often dominates over gray-value differences of the image structures. In this paper we propose a novel biconvex variational model that includes the intensity inhomogeneities to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. In our model we assume that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of the resulting biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images serving as a motivation for our work.     

欧拉弹性正则化的图像泊松去噪

利用泊松噪声分布与图像灰度值相关这一特性,结合图像的水平集曲线对图像灰度值的刻画能力,在Bayesian-MAP框架下,提出了欧拉弹性正则与泊松似然保真的图像泊松去噪变分正则化模型.利用交替方向乘子法,将原问题转化为几个不同低阶子问题的求解.对于子问题中出现的高阶非线性项,利用滞后扩散不动点迭代进行线性化,从而得到模型的快速迭代求解算法.通过数值模拟实验,证明了当图像受不同强度泊松噪声影响时,所提出的泊松去噪方法都能够有效的抑制泊松噪声,同时具有良好的结构保持性能.     

Supervised segmentation of remote sensing images based on a tree-structured MRF model

Most remote sensing images exhibit a clear hierarchical structure which can be taken into account by defining a suitable model for the unknown segmentation map. To this end, one can resort to the tree-structured Markov random field (MRF) model, which describes a K-ary field by means of a sequence of binary MRFs, each one corresponding to a node in the tree. Here we propose to use the tree-structured MRF model for supervised segmentation. The prior knowledge on the number of classes and their statistical features allows us to generalize the model so that the binary MRFs associated with the nodes can be adapted freely, together with their local parameters, to better fit the data. In addition, it allows us to define a suitable likelihood term to be coupled with the TS-MRF prior so as to obtain a precise global model of the image. Given the complete model, a recursive supervised segmentation algorithm is easily defined. Experiments on a test SPOT image prove the superior performance of the proposed algorithm with respect to other comparable MRF-based or variational algorithms.     

Sonar image segmentation using an unsupervised hierarchical MRFmodel

This paper is concerned with hierarchical Markov random field (MRP) models and their application to sonar image segmentation. We present an original hierarchical segmentation procedure devoted to images given by a high-resolution sonar. The sonar image is segmented into two kinds of regions: shadow (corresponding to a lack of acoustic reverberation behind each object lying on the sea-bed) and sea-bottom reverberation. The proposed unsupervised scheme takes into account the variety of the laws in the distribution mixture of a sonar image, and it estimates both the parameters of noise distributions and the parameters of the Markovian prior. For the estimation step, we use an iterative technique which combines a maximum likelihood approach (for noise model parameters) with a least-squares method (for MRF-based prior). In order to model more precisely the local and global characteristics of image content at different scales, we introduce a hierarchical model involving a pyramidal label field. It combines coarse-to-fine causal interactions with a spatial neighborhood structure. This new method of segmentation, called the scale causal multigrid (SCM) algorithm, has been successfully applied to real sonar images and seems to be well suited to the segmentation of very noisy images. The experiments reported in this paper demonstrate that the discussed method performs better than other hierarchical schemes for sonar image segmentation.     

EM image segmentation algorithm based on an inhomogeneous hidden MRF model

This paper introduces a Bayesian image segmentation algorithm that considers the label scale variability of images. An inhomogeneous hidden Markov random field is adopted in this algorithm to model the label scale variability as prior probabilities. An EM algorithm is developed to estimate parameters of the prior probabilities and likelihood probabilities. The image segmentation is established by using a MAP estimator. Different images are tested to verify the algorithm and comparisons with other segmentation algorithms are carried out. The segmentation results show the proposed algorithm has better performance than others.     

A Game-Theoretic Framework for Landmark-Based Image Segmentation

A novel game-theoretic framework for landmark-based image segmentation is presented. Landmark detection is formulated as a game, in which landmarks are players, landmark candidate points are strategies, and likelihoods that candidate points represent landmarks are payoffs, determined according to the similarity of image intensities and spatial relationships between the candidate points in the target image and their corresponding landmarks in images from the training set. The solution of the formulated game-theoretic problem is the equilibrium of candidate points that represent landmarks in the target image and is obtained by a novel iterative scheme that solves the segmentation problem in polynomial time. The object boundaries are finally extracted by applying dynamic programming to the optimal path searching problem between the obtained adjacent landmarks. The performance of the proposed framework was evaluated for segmentation of lung fields from chest radiographs and heart ventricles from cardiac magnetic resonance cross sections. The comparison to other landmark-based segmentation techniques shows that the results obtained by the proposed game-theoretic framework are highly accurate and precise in terms of mean boundary distance and area overlap. Moreover, the framework overcomes several shortcomings of the existing techniques, such as sensitivity to initialization and convergence to local optima.     

隐式曲面两相图像分割的变分水平集模型及对偶方法

本文对曲面上分段常值和分段光滑的两相图像分割的变分水平集模型及其对偶方法进行了研究.图像所在的曲面用静态的符号距离函数的零水平集表达,曲面上图像分割轮廓线用另一动态符号距离函数的零水平集与上述静态的零水平集的交线表达,借助内蕴梯度、内蕴散度的概念平面两相图像分割的变分水平集模型已被推广到隐式曲面上图像分割的变分模型.本...     

Ultrasound kidney segmentation with a global prior shape

In this paper, we focus on segmentation of ultrasound kidney images. Unlike previous work by using trained prior shapes, we employ a parametric super-ellipse as a global prior shape for a human kidney. The Fisher–Tippett distribution is employed to describe the grey level statistics. Combining the grey level statistics with a global character of a kidney shape, we propose a new active contour model to segment ultrasound kidney images. The proposed model involves two subproblems. One subproblem is to optimize the parameters of a super-ellipse. Another subproblem is to segment an ultrasound kidney image. An alternating minimization scheme is used to optimize the parameters of a super-ellipse and segment an image simultaneously. To segment an image fast, a convex relaxation method is introduced and the split Bregman method is incorporated to propose a fast segmentation algorithm. The efficiency of the proposed method is illustrated by numerical experiments on both simulated images and real ultrasound kidney images.     

A segmentation model using compound Markov random fields based on a boundary model.

Markov random field (MRF) theory has been widely applied to the challenging problem of image segmentation. In this paper, we propose a new nontexture segmentation model using compound MRFs, in which the original label MRF is coupled with a new boundary MRF to help improve the segmentation performance. The boundary model is relatively general and does not need prior training on boundary patterns. Unlike some existing related work, the proposed method offers a more compact interaction between label and boundary MRFs. Furthermore, our boundary model systematically takes into account all the possible scenarios of a single edge existing in a 3 x 3 neighborhood and, thus, incorporates sophisticated prior information about the relation between label and boundary. It is experimentally shown that the proposed model can segment objects with complex boundaries and at the same time is able to work under noise corruption. The new method has been applied to medical image segmentation. Experiments on synthetic images and real clinical datasets show that the proposed model is able to produce more accurate segmentation results and satisfactorily keep the delicate boundary. It is also less sensitive to noise in both high and low signal-to-noise ratio regions than some of the existing models in common use.     

Concurrent 3-D motion segmentation and 3-D interpretation of temporal sequences of monocular images.

The purpose of this study is to investigate a variational method for joint multiregion three-dimensional (3-D) motion segmentation and 3-D interpretation of temporal sequences of monocular images. Interpretation consists of dense recovery of 3-D structure and motion from the image sequence spatiotemporal variations due to short-range image motion. The method is direct insomuch as it does not require prior computation of image motion. It allows movement of both viewing system and multiple independently moving objects. The problem is formulated following a variational statement with a functional containing three terms. One term measures the conformity of the interpretation within each region of 3-D motion segmentation to the image sequence spatiotemporal variations. The second term is of regularization of depth. The assumption that environmental objects are rigid accounts automatically for the regularity of 3-D motion within each region of segmentation. The third and last term is for the regularity of segmentation boundaries. Minimization of the functional follows the corresponding Euler-Lagrange equations. This results in iterated concurrent computation of 3-D motion segmentation by curve evolution, depth by gradient descent, and 3-D motion by least squares within each region of segmentation. Curve evolution is implemented via level sets for topology independence and numerical stability. This algorithm and its implementation are verified on synthetic and real image sequences. Viewers presented with anaglyphs of stereoscopic images constructed from the algorithm's output reported a strong perception of depth.     

Multiframe super-resolution based on half-quadratic prior with artifacts suppress

The multiframe super-resolution (SR) technique aims to obtain a high-resolution (HR) image by using a set of observed low-resolution (LR) images. In the reconstruction process, artifacts may be possibly produced due to the noise, especially in presence of stronger noise. In order to suppress artifacts while preserving discontinuities of images, in this paper a multiframe SR method is proposed by involving the reconstruction properties of the half-quadratic prior model together with the quadratic prior model using a convex combination. Moreover, by analyzing local features of the underlined HR image, these two prior models are combined by using an automatically calculated weight function, making both smooth and discontinuous pixels handled properly. A variational Bayesian inference (VBF) based algorithm is designed to efficiently and effectively seek the solution of the proposed method. With the VBF framework, motion parameters and hyper-parameters are all determined automatically, leading to an unsupervised SR method. The efficiency of the hybrid prior model is demonstrated theoretically and practically, which shows that our SR method can obtain better results from LR images even with stronger noise. Extensive experiments on several visual data have demonstrated the efficacy and superior performance of the proposed algorithm, which can not only preserve image details but also suppress artifacts.     

Background removal of multiview images by learning shape priors.

Image-based rendering has been successfully used to display 3-D objects for many applications. A well-known example is the object movie, which is an image-based 3-D object composed of a collection of 2-D images taken from many different viewpoints of a 3-D object. In order to integrate image-based 3-D objects into a chosen scene (e.g., a panorama), one has to meet a hard challenge--to efficiently and effectively remove the background from the foreground object. This problem is referred to as multiview images (MVIs) segmentation. Another task requires MVI segmentation is image-based 3-D reconstruction using multiview images. In this paper, we propose a new method for segmenting MVI, which integrates some useful algorithms, including the well-known graph-cut image segmentation and volumetric graph-cut. The main idea is to incorporate the shape prior into the image segmentation process. The shape prior introduced into every image of the MVI is extracted from the 3-D model reconstructed by using the volumetric graph cuts algorithm. Here, the constraint obtained from the discrete medial axis is adopted to improve the reconstruction algorithm. The proposed MVI segmentation process requires only a small amount of user intervention, which is to select a subset of acceptable segmentations of the MVI after the initial segmentation process. According to our experiments, the proposed method can provide not only good MVI segmentation, but also provide acceptable 3-D reconstructed models for certain less-demanding applications.