非局部加权模糊C均值聚类图像分割

去除噪声与保持图像细节特征是含噪声图像分割中面临的一对矛盾。为此,提出一种改进的模糊C均值算法,通过引入非局部加权距离以抑制噪声影响。其中,权值通过局部图像块距离的指数形式计算,并利用半局部统计特性自适应调整其光滑参数。实验结果表明,新方法具有较强的抗噪声能力,同时能够保持较多地细节特征。     

基于元胞自动机模型的图像分割算法

针对图像处理中的图像分割任务,我们提出了一个基于模糊元胞自动机模型的图像分割算法.将元胞自动机原理中的演化规则换为模糊规则建立模糊元胞自动机模型,使图像中灰度水平介于目标和背景之间的像素得以更好地归类,从而得到较好的图像分割结果.     

Maximizing a Sum Related to Image Segmentation Evaluation

Consider the set S of points in the plane consisting of the ordered pairs (i, j ), where 1 \leqslant i \leqslant m1 \leqslant i \leqslant m and 1 \leqslant j \leqslant n1 \leqslant j \leqslant n. A problem related to the study of segmentation evaluation of visual images concerns finding a permutation σ of the points of S for which the sum

基于随机谱聚类的图像分割算法

图像分割就是把感兴趣的区域从背景中分割、提取出来,为了使分割出来的图像特征信息完整,根据图像的灰度值和空间距离构造了一种相似度函数,得到基于图的灰度值的相似度矩阵,将图像分割转化为图论最小割问题,然后运用谱聚类算法进行分割.针对谱聚类算法运行所需的内存空间和运算量大的特点,提出一种考虑概率因素的随机抽样谱聚类算法.在具体实施时,为了减少背景噪声对分割结果的影响,对图像进行了滤波预处理.结果表明,算法稳定性好,相对现有算法,分割效果得到改善.     

利用模拟退火遗传算法实现图像阈值分割

本文提出了一种利用模拟退火算法和遗传算法相结合的图像阈值分割算法,试验结果表明该算法增强了算法的全局收敛性,加快了算法的收敛速度,提高了图像阈值分割的效率.     

改进的水平集方法及其在图像分割中的应用

为了稳定水平集函数的演化过程,提出了一种改进的距离规则化水平集方法,新方法与传统的距离规则化方法相比,能更好地维持水平集函数的符号距离函数特性.为了检验新方法的性能,首先将其应用到基于边缘的主动轮廓模型中并用于图像分割,实验结果表明新方法能有效提高分割效率和精度.同时,还将新方法应用到一种改进的基于区域的主动轮廓模型中,实验结果不仅进一步验证了新方法的有效性,还表明新方法能改善初始位置的鲁棒性.     

求解分段常数图象分割模型的一个快速算法

针对Xue-ChengTai等提出的分段常数图象分割模型,我们提出了一个新的快速求解算法。通过引进一个函数来选择模型中的正则化参数β的值,并判断在迭代过程中何时求解不含惩罚项的泛函F。此函数的引入有效地加速了算法的收敛速度。结合原始-对偶Newton方法来求解总变差最小化问题。数值试验表明新算法具有很快的收敛速度与良好的分割效果,且算法对初始值的要求不高。     

快速均值漂移图像分割算法研究

Mean shift算法是一种搜索与样本点分布最接近模式的非参数统计方法.但它是一种迭代统计方法,要保证较高的数值计算精度需要较多的迭代次数,耗费较长的计算时间.为克服这一缺点,提出快速均值漂移图像分割算法.该算法在每次迭代时以前一次的聚类中心集合T动态地更新样本集S,并通过使用直方图缩小样本点的搜索范围进一步加快算法的收敛速度.实验结果表明该方法在保证图像分割质量的同时具有较快的收敛速度.     

一种新型的四相水平集图像分割方法

水平集方法在图像分割和计算机视觉领域有很广泛的应用,在传统的水平集方法中,水平集函数需要保持符号距离函数.现有的活动轮廓模型、GAC模型、M-S模型、C-V模型等在演化过程中均需要对水平集函数进行重新初始化,使其保持符号距离函数,然而这样会引起数值计算的错误,最终破坏演化的稳定性,另外这些模型只适用于灰度值较为均匀的图像,对灰度值不均匀的图像不能进行理想的分割·针对这些问题,结合C-V模型的思想,提出了一种带有正则项的四相水平集分割模型,其中正则项被定义为一个势函数,具有向前向后扩散的作用,使水平集函数在演化过程中保持为符号距离函数,避免了水平集函数重新初始化的过程.最后对该模型进行数值实现,实验表明了新模型的可行性和有效性.     

基于微分进化算法的FCM图像分割算法

为提高模糊C均值(FCM)算法的自动化程度,提出基于微分进化算法的FCM图像分割算法(DEFCM),利用微分进化算法全局性和鲁棒性的特点自动确定分类数和初始聚类中心,再将其作为模糊c均值聚类的初始聚类中心,弥补FCM算法的不足.实验表明该算法不仅能够正确地对图像分类,而且能获得较好的图像分割效果和质量.     

基于混合单纯形算法的模糊均值图像分割

针对模糊C均值算法用于图像分割时对初始值敏感、容易陷入局部极值的问题,提出基于混合单纯形算法的模糊均值图像分割算法.算法利用Nelder-Mead单纯形算法计算量小、搜索速度快和粒子群算法自适应能力强、具有较好的全局搜索能力的特点,将混合单纯形算法的结果作为模糊C均值算法的输入,并将其用于图像分割.实验结果表明:基于混合单纯形算法的模糊均值图像分割算法在改善图像分割质量的同时,提高了算法的运行速度.     

Two-Stage Image Segmentation Scheme Based on Inexact Alternating Direction Method

Image segmentation is a fundamental problem in both image processing and computer vision with numerous applications. In this paper, we propose a two-stage image segmentation scheme based on inexact alternating direction method. Specifically, we first solve the convex variant of the Mumford-Shah model to get the smooth solution, and the segmentation is then obtained by applying the K-means clustering method to the solution. Some numerical comparisons are arranged to show the effectiveness of our proposed schemes by segmenting many kinds of images such as artificial images, natural images, and brain MRI images.     

Metrics and undirected cuts

Suppose thatG is an undirected graph whose edges have nonnegative integer-valued lengthsl(e), and that {s ₁,t ₁},?, {s _m ,t _m } are pairs of its vertices. Can one assign nonnegative weights to the cuts ofG such that, for each edgee, the total weight of cuts containinge does not exceedl(e) and, for eachi, the total weight of cuts ‘separating’s _i andt _i is equal to the distance (with respect tol) betweens _i andt _i ? Using linear programming duality, it follows from Papernov's multicommodity flow theorem that the answer is affirmative if the graph induced by the pairs {s ₁,t ₁},?, {s _m ,t _m } is one of the following: (i) the complete graph with four vertices, (ii) the circuit with five vertices, (iii) a union of two stars. We prove that if, in addition, each circuit inG has an even length (with respect tol) then there exists a suitable weighting of the cuts with the weights integer-valued; moreover, an algorithm of complexity O(n ³) (n is the number of vertices ofG) is developed for solving such a problem. Also a class of metrics decomposable into a nonnegative linear combination of cut-metrics is described, and it is shown that the separation problem for cut cones isNP-hard.     

Application of the Level-Set Model with Constraints in Image Segmentation

We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper and lower constraints prescribed for the level-set function. Constraints have the same conceptual meaning as initial seeds of the popular graph-cuts based methods for image segmentation. A numerical approximation scheme is based on the complementary-finite volumes method combined with the Projected successive overrelaxation method adopted for solving constrained linear complementarity problems. The advantage of the constrained level-set method is demonstrated on several artificial images as well as on cardiac MRI data.     

基于改进遗传算法的自动阈值图像分割方法

图像分割技术在图像分析和图像识别上具有重要意义.传统自适应遗传算法有可能使问题求解陷入局部最优解,而求得错误的图像分割阈值.为了得到最优的图像分割阈值,对交叉率和变异率公式进行了重构,使得交叉率和变异率在任何情况下都不为零.同时,以最大二维熵函数作为适应度函数,采用选择、交叉变异等遗传操作作搜索最优分割阈值.仿真实验表明,该方法可以有效地提高图像分割精度和计算速度.     

Connections between Operator-Splitting Methods and Deep Neural Networks with Applications in Image Segmentation

Deep neural network is a powerful tool for many tasks. Understanding why it is so successful and providing a mathematical explanation is an important problem and has been one popular research direction in past years. In the literature of mathematical analysis of deep neural networks, a lot of works is dedicated to establishing representation theories. How to make connections between deep neural networks and mathematical algorithms is still under development. In this paper, we give an algorithmic...     

一种改进的Heaviside函数与Dirac函数的C-V图像分割研究

C-V模型中Heaviside函数和Dirac函数正则化逼近影响对目标图像的分割,根据Heaviside函数和Dirac函数的性质,提出了新的正则化Heaviside函数和Dirac函数.首先分析了C-V模型中正则化的Heaviside函数和Dirac函数在图像分割中所起的作用,在此基础上提出了新的正则化的Heaviside函数和Dirac函数,改进了C-V模型.实验结果表明,运用正则化的Heaviside函数和Dirac函数的图像分割效果较好.     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.