Semi-blind image restoration via Mumford-Shah regularization.

Image restoration and segmentation are both classical problems, that are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved together. Mutual support of image restoration and segmentation processes within a joint variational framework is theoretically motivated, and validated by successful experimental results. The proposed variational method integrates semi-blind image deconvolution (parametric blur-kernel), and Mumford-Shah segmentation. The functional is formulated using the T-convergence approximation and is iteratively optimized via the alternate minimization method. While the major novelty of this work is in the unified treatment of the semi-blind restoration and segmentation problems, the important special case of known blur is also considered and promising results are obtained.     

Shape statistics variational approach for the outer contour segmentation of left ventricle MR images.

Segmentation of left ventricles is one of the important research topics in cardiac magnetic resonance (MR) imaging. The segmentation precision influences the authenticity of ventricular motion reconstruction. In left ventricle MR images, the weak and broken boundary increases the difficulty of segmenting the outer contour precisely. In this paper, we present an improved shape statistics variational approach for the outer contour segmentation of left ventricle MR images. We use the Mumford-Shah model in an object feature space and incorporate the shape statistics and an edge image to the variational framework. The introduction of shape statistics can improve the segmentation with broken boundaries. The edge image can enhance the weak boundary and thus improve the segmentation precision. The generation of the object feature image, which has homogenous "intensities" in the left ventricle, facilitates the application of the Mumford-Shah model. A comparison of mean absolute distance analysis between different contours generated with our algorithm and that generated by hand demonstrated that our method can achieve a higher segmentation precision and a better stability than various approaches. It is a semiautomatic way for the segmentation of the outer contour of the left ventricle in clinical applications.     

Space-time segmentation using level set active contours applied to myocardial gated SPECT

This paper presents a new variational method for the segmentation of a moving object against a still background, over a sequence of [two-dimensional or three-dimensional (3-D)] image frames. The method is illustrated in application to myocardial gated single photon emission computed tomography (SPECT) data, and incorporates a level set framework to handle topological changes while providing closed boundaries. The key innovation is the introduction of a geometrical constraint into the derivation of the Euler-Lagrange equations, such that the segmentation of each individual frame can be interpreted as a closed boundary of an object (an isolevel of a set of hyper-surfaces) while integrating information over the entire sequence. This results in the definition of an evolution velocity normal to the object boundary. Applying this method to 3-D myocardial gated SPECT sequences, the left ventricle endocardial and epicardial limits can be computed in each frame. This space-time segmentation method was tested on simulated and clinical 3-D myocardial gated SPECT sequences and the corresponding ejection fractions were computed.     

Variational level set method for image segmentation with simplex constraint of landmarks

Landmarks are prior image features for a variety of computer vision tasks. In the image processing domain, research on image segmentation methods has always been a significant topic. Due to the image characteristics of heterogeneous nature, lack of clear boundaries, noise and so on, accurate segmentation of the image is still a challenge. In this paper, utilizing a level set framework and the simplex constraint, preferred image point landmarks are combined into a variational segmentation model to enforce the contour evolve with prior points. Then the alternating minimization algorithm of the proposed model is designed, meanwhile the landmarks constraints are doubled ensured with simplex projection. Finally, experiments on many synthetic and real-world images were implemented. Comparing with other state-of-the-art segmentation variational models, the most striking result to emerge from the data is that the proposed method has higher segmentation performance. Benefiting from appropriate point landmarks, the proposed segmentation method can tackle noisy, weak edges and corrupted area images effectively and robustly.     

一种基于变分水平集的红外图像分割算法

红外图像大都存在边缘模糊或离散状边缘的特点,并且图像的先验知识较少,因此红外图像的分割是比较困难的。针对这种情况,该文提出了一种基于图像全局信息并且不需要重新初始化的变分水平集红外图像分割方法,不考虑图像边缘梯度的影响,将图像全局信息作为外部能量项,在很大程度上克服了边缘模糊时过分割的情况。同时通过引入内部变形能量约束水平集函数逼近符号距离函数,省去了重新初始化水平集函数的过程,简化了计算,减小了因重新初始化水平集函数带来的误差。将算法应用在红外图像的分割中,验证了算法的有效性。     

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.     

A variational approach for Bayesian blind image deconvolution

In this paper, the blind image deconvolution (BID) problem is addressed using the Bayesian framework. In order to solve for the proposed Bayesian model, we present a new methodology based on a variational approximation, which has been recently introduced for several machine learning problems, and can be viewed as a generalization of the expectation maximization (EM) algorithm. This methodology reaps all the benefits of a "full Bayesian model" while bypassing some of its difficulties. We present three algorithms that solve the proposed Bayesian problem in closed form and can be implemented in the discrete Fourier domain. This makes them very cost effective even for very large images. We demonstrate with numerical experiments that these algorithms yield promising improvements as compared to previous BID algorithms. Furthermore, the proposed methodology is quite general with potential application to other Bayesian models for this and other imaging problems.     

Expectation–maximization algorithm with total variation regularization for vector-valued image segmentation

We integrate the total variation (TV) minimization into the expectation–maximization (EM) algorithm to perform the task of image segmentation for general vector-valued images. We first propose a unified variational method to bring together the EM and the TV regularization and to take advantages from both approaches. The idea is based on operator interchange and constraint optimization. In the second part of the paper we propose a simple two-phase approach by splitting the above functional into two steps. In the first phase, a typical EM method can classify pixels into different classes based on the similarity in their measurements. However, since no local geometric information of the image has yet been incorporated into the process, such classification in practice gives unsatisfactory segmentation results. In the second phase, the TV-step obtains the segmentation of the image by applying a TV regularization directly to the clustering result from EM.     

Centered pyramids

Quadtree-like pyramids have the advantage of re-suiting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous (L(2)) and the discrete (l(2)) norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.     

Space-time image sequence analysis: object tunnels and occlusion volumes.

We address the issue of image sequence analysis jointly in space and time. While typical approaches to such an analysis consider two image frames at a time, we propose to perform this analysis jointly over multiple frames. We concentrate on spatiotemporal segmentation of image sequences and on analysis of occlusion effects therein. The segmentation process is three-dimensional (3-D); we search for a volume carved out by each moving object in the image sequence domain, or "object tunnel," a new space-time concept. We pose the problem in variational framework by using only motion information (no intensity edges). The resulting formulation can be viewed as volume competition, a 3-D generalization of region competition. We parameterize the unknown surface to be estimated, but rather than using an active-surface approach, we embed it into a higher dimensional function and apply the level-set methodology. We first develop simple models for the detection of moving objects over static background; no motion models are needed. Then, in order to improve segmentation accuracy, we incorporate motion models for objects and background. We further extend the method by including explicit models for occluded and newly exposed areas that lead to "occlusion volumes," another new space-time concept. Since, in this case, multiple volumes are sought, we apply a multiphase variant of the level-set method. We present various experimental results for synthetic and natural image sequences.     

New insight at level set & Gaussian mixture model for natural image segmentation

Level set method and Gaussian Mixture model (GMM) are two very valuable tools for natural image segmentation. The former aims to acquire good geometrical continuity of segmentation boundaries, while the latter focuses on analyzing statistical properties of image feature data. Some studies on the integration between them have been reported due to their complementarity in the last 10 years. However, these studies generally supposed that the image-featured data density distribution of every segmented domain is independent with each other and can be separately approximated by Gaussian model or GMM, which conflicts with the fundamental idea of GMM clustering-based image segmentation. To remedy this problem, we give a new insight at image segmentation objective under the combined framework between Bayesian theory and GMM density approximation. Thereby, a novel level set image segmentation method integrated with GMM (GMMLS) is proposed. Then, the theoretical analysis on GMMLS is given, in which some valuable results are demonstrated. At last, several types of natural image segmentation experiments are reported and the corresponding results indicate that GMMLS can obtain better or at least equivalent performance compared with existing relevant methods in almost all cases.     

Globally convergent iterative numerical schemes for nonlinearvariational image smoothing and segmentation on a multiprocessor machine

We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than these stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported     

多源影像融合与分割的协同方法

针对现有影像融合与分割方法之间缺乏协同的问题,借鉴数据同化系统能够协同其模型算子和观测算子,并且能够自适应地优化其本身的思想,提出一个多源影像融合与分割的协同框架.在该框架下,以基于对比度金字塔变换和基于非下采样的Contourlet变换的两种融合方法分别模拟模型算子和观测算子,以评价分割效果的概率随机系数为目标函数,以带交叉算子的粒子群算法作为数据同化系统的优化算法.该框架可根据融合结果影像来调整分割算法的参数,利用分割结果来指导融合结果的优化,从而使得影像融合与分割协同工作.二组实验验证了该框架的有效性.     

Unsupervised learning of multi-task deep variational model

We propose a general deep variational model (reduced version, full version as well as the extension) via a comprehensive fusion approach in this paper. It is able to realize various image tasks in a completely unsupervised way without learning from samples. Technically, it can properly incorporate the CNN based deep image prior (DIP) architecture into the classic variational image processing models. The minimization problem solving strategy is transformed from iteratively minimizing the sub-problem for each variable to automatically minimizing the loss function by learning the generator network parameters. The proposed deep variational (DV) model contributes to the high order image edition and applications such as image restoration, inpainting, decomposition and texture segmentation. Experiments conducted have demonstrated significant advantages of the proposed deep variational model in comparison with several powerful techniques including variational methods and deep learning approaches.     

结合形状先验的图割目标分割方法

为了减少图像目标分割过程中噪声、阴影、背景复杂等因素的影响,将形状先验引入图割图像分割框架中,提出一种结合形状先验的图割目标分割方法。该方法给出了形状先验的定义,并将其转化为势函数的形式加入到能量函数中,通过能量最小化过程得到最终分割结果。同时,图像对齐过程能够适应形状模版与待分割目标之间的仿射不同。形状先验能够较好地约束目标边界,相比与传统图割算法,分割结果有了明显改善。实验结果表明,该算法具有有效性。     

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。     

结合多元信息聚类与空间约束的遥感图像分割方法

为了解决传统聚类算法对聚类表征特征量的依赖性以及定义的不完备性,结合遥感图像的数据的空间位置关系提出了一种结合多元信息聚类与空间约束的遥感图像分割方法。针对某一聚类数据,以若干数据点(多元)组合的方式遍历其所有数据点,并定义多元组合的互信息,以表征该聚类的类内相似性;通过计算类外像素对类内多元组合的互信息,刻画类间的非相似性。在此基础上建立类内相似性和类间差异性,然后结合两者之间的平衡关系建立目标函数,并将Potts模型扩展到目标函数以加入空间约束,最后通过最大化目标函数实现图像分割。对模拟及真实全色遥感影像分割结果的定性、定量分析表明:结合多元信息聚类与空间约束的遥感影像分割方法可以避免聚类表征特征量的定义,从根本上消除其对图像分割的影响,并充分考虑遥感数据的空间位置关系。      

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.     

基于统计模型的变分水平集SAR图像分割方法

针对SAR图像感兴趣区域分割问题,提出了一种基于统计模型的变分水平集分割方法。该方法在分析SAR图像特征的基础上,利用相干斑噪声的统计模型直接定义了关于水平集函数的能量泛函,不同于一般水平集方法中关于参数化曲线的能量泛函。通过极小化能量泛函,建立了水平集函数演化的偏微分方程。对水平集演化方程的数值求解,实现了对SAR图像感兴趣区域的分割。分别采用模拟和真实SAR图像对提出的方法进行了验证,试验结果表明该方法充分利用了SAR图像的特征信息,不需要相干斑噪声预处理,能够准确实现对SAR图像感兴趣区域的分割。