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.     

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.     

水平集方法与距离函数

讨论了有关水平集方法的基本问题,如保持为距离函数的方法,水平集方程解的存在性和唯一性。主要贡献是证明了,在距离函数约束下,水平集方程在初始零水平集附近有唯一解,它是关于演化界面的有向距离函数。并且用到了一些处理技巧:如注意到原始方程的任意解都是距离函数,将原始方程变化为另一简单形式。由于新的方程组不是一个经典方程组,则它被变换为一个普通形式,其中隐函数方法被采用。     

一种改进的几何活动轮廓模型

针对传统的几何活动轮廓模型在分割具有凹形边界时,演化曲线不能准确定位的缺点,提出了一种改进的几何活动轮廓模型,该模型通过在原模型的演化方程中增加一个正的常数项,使得演化曲线在未到达目标边界时,加速曲线演化,而在到达边界附近时,该加速项逐渐减小为零,从而能够很好的完成对凹形边界的分割.实验证明,该方法不仅能够分割具有凹形边界的目标,还能够使演化过程加速,提高几何活动轮廓模型的分割速度.     

图上Nordhaus-Gaddum型的符号全控制数的界

函数f:V(G)→{-1,1}称为图G的符号全控制函数,如果对每一个开邻域集上的点的函数值的和都大于等于1.符号全控制函数的权值是指图中所有点的函数值的求和.图的符号全控制数为图中所有符号全控制函数的最小权值.令G表示图G的补图.在该文中,我们研究符号全控制数的Nordhaus-Gaddum型不等式,给出了路与其补图的符号全控制数和的上界,以及图与其补图的符号全控制数和的下界.     

向量值系数Rademacher级数及其水平集

何和刘首次研究了平面上向量值系数Rademacher级数水平集的交集.他们的结果基于5个模不超过l的向量和的估计.本文继续研究高维空间Rademacher级数及其水平集.如果向量维数大于2,何和刘所用的估计方法失效.当Rademacher级数值域在全空间稠密或者等于全空间时,我们用面罩函数来研究该问题,以此考虑水平集的Hausdorff维数.     

估计单指标模型的单调联系函数

本文我们研究了联系函数单调时单指标模型的模型估计问题. 基于投影方向的相合估计, 本文提出用I-样条的办法来估计联系函数, 并建立带惩罚函数的最小二乘准则的相合性. 通过模拟与现有的方法进行了对比, 表明我们的估计方法是非常有效的.     

半监督距离度量学习的内蕴加速投影梯度算法

考虑求解一类半监督距离度量学习问题.由于样本集(数据库)的规模与复杂性的激增,在考虑距离度量学习问题时,必须考虑学习来的距离度量矩阵具有稀疏性的特点.因此,在现有的距离度量学习模型中,增加了学习矩阵的稀疏约束.为了便于模型求解,稀疏约束应用了Frobenius范数约束.进一步,通过罚函数方法将Frobenius范数约束罚到目标函数,使得具有稀疏约束的模型转化成无约束优化问题.为了求解问题,提出了正定矩阵群上加速投影梯度算法,克服了矩阵群上不能直接进行线性组合的困难,并分析了算法的收敛性.最后通过UCI数据库的分类问题的例子,进行了数值实验,数值实验的结果说明了学习矩阵的稀疏性以及加速投影梯度算法的有效性.     

半监督距离度量学习内蕴加速投影梯度算法

考虑求解一类半监督距离度量学习问题. 由于样本集(数据库)的规模与复杂性的激增, 在考虑距离度量学习问题时, 必须考虑学习来的距离度量矩阵具有稀疏性的特点. 因此, 在现有的距离度量学习模型中, 增加了学习矩阵的稀疏约束. 为了便于模型求解, 稀疏约束应用了Frobenius 范数约束. 进一步, 通过罚函数方法将Frobenius范数约束罚到目标函数, 使得具有稀疏约束的模型转化成无约束优化问题. 为了求解问题, 提出了正定矩阵群上加速投影梯度算法, 克服了矩阵群上不能直接进行线性组合的困难, 并分析了算法的收敛性. 最后通过UCI数据库的分类问题的例子, 进行了数值实验, 数值实验的结果说明了学习矩阵的稀疏性以及加速投影梯度算法的有效性.     

对称锥互补问题的一类惩罚FB函数

利用欧几里德若当代数技术,在单调的条件下,用内积的方法证明了对称锥互补问题的一类FB互补函数相应的势函数的水平集有界性. 该方法在理论和应用上相较于以往用迹不等式证明势函数水平集有界性更具普适性和推广价值. 在设计算法求解势函数的无约束极小化问题时,水平集有界性是保证下降算法收敛的重要条件,因此,对算法的设计具有理论意义.     

An improvement of level set equations via approximation of a distance function

In the classical level set method, the slope of solutions can be very small or large, and it can make it difficult to get the precise level set numerically. In this paper, we introduce an improved level set equation whose solutions are close to the signed distance function to evolving interfaces. The improved equation is derived via approximation of the evolution equation for the distance function. Applying the comparison principle, we give an upper- and lower bound near the zero level set for the viscosity solution to the initial value problem.     

基于EM算法和小波多尺度边缘检测的活动轮廓模型初始化

本文研究了活动轮廓模型初始化的问题.利用EM算法和小波多尺度边缘检测的方法,获得了活动轮廓模型的外部能量函数和初始曲线,并对于具体的X射线图像给出了实验结果和该算法的有效性.     

New normalized nonlocal hybrid level set method for image segmentation

This article introduces a new normalized nonlocal hybrid level set method for image segmentation. Due to intensity overlapping, blurred edges with complex backgrounds, simple intensity and texture information, such kind of image segmentation is still a challenging task. The proposed method uses both the region and boundary information to achieve accurate segmentation results. The region information can help to identify rough region of interest and prevent the boundary leakage problem. It makes use of normalized nonlocal comparisons between pairs of patches in each region, and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation. The boundary information can help to detect the precise location of the target object, it makes use of the geodesic active contour model to obtain the target boundary. The corresponding variational segmentation problem is implemented by a level set formulation. We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function. At last, experimental results on synthetic images and real images are shown in the paper with promising results.     

Semi-implicit finite volume level set method for advective motion of interfaces in normal direction

In this paper a semi-implicit finite volume method is proposed to solve the applications with moving interfaces using the approach of level set methods. The level set advection equation with a given speed in normal direction is solved by this method. Moreover, the scheme is used for the numerical solution of eikonal equation to compute the signed distance function and for the linear advection equation to compute the so-called extension speed [1]. In both equations an extrapolation near the interface is used in our method to treat Dirichlet boundary conditions on implicitly given interfaces. No restrictive CFL stability condition is required by the semi-implicit method that is very convenient especially when using the extrapolation approach. In summary, we can apply the method for the numerical solution of level set advection equation with the initial condition given by the signed distance function and with the advection velocity in normal direction given by the extension speed. Several advantages of the proposed approach can be shown for chosen examples and application. The advected numerical level set function approximates well the property of remaining the signed distance function during whole simulation time. Sufficiently accurate numerical results can be obtained even with the time steps violating the CFL stability condition.     

Adaptive level set evolution starting with a constant function

In this paper, we propose a novel level set evolution model in a partial differential equation (PDE) formulation. According to the governing PDE, the evolution of level set function is controlled by two forces, an adaptive driving force and a total variation (TV)-based regularizing force that smoothes the level set function. Due to the adaptive driving force, the evolving level set function can adaptively move up or down in accordance with image information as the evolution proceeds forward in time. As a result, the level set function can be simply initialized to a constant function rather than the widely-used signed distance function or piecewise constant function in existing level set evolution models. Our model completely eliminates the needs of initial contours as well as re-initialization, and so avoids the problems resulted from contours initialization and re-initialization. In addition, the evolution PDE can be solved numerically via a simple explicit finite difference scheme with a significantly larger time step. The proposed model is fast enough for near real-time segmentation applications while still retaining enough accuracy; in general, only a few iterations are needed to obtain segmentation results accurately.     

Distribution Metrics and Image Segmentation

The purpose of this paper is to describe certain alternative metrics for quantifying distances between distributions, and to explain their use and relevance in visual tracking. Besides the theoretical interest, such metrics may be used to design filters for image segmentation, that is for solving the key visual task of separating an object from the background in an image. The segmenting curve is represented as the zero level set of a signed distance function. Most existing methods in the geometric active contour framework perform segmentation by maximizing the separation of intensity moments between the interior and the exterior of an evolving contour. Here one can use the given distributional metric to determine a flow which minimizes changes in the distribution inside and outside the curve.     

Level set based multi-scale methods for large deformation contact problems

We consider the numerical simulation of contact problems in elasticity with large deformations. The non-penetration condition is described by means of a signed distance function to the obstacle's boundary. Techniques from level set methods allow for an appropriate numerical approximation of the signed distance function preserving its non-smooth character. The emerging non-convex optimization problem subject to non-smooth inequality constraints is solved by a non-smooth multiscale SQP method in combination with a non-smooth multigrid method as interior solver. Several examples in three space dimensions including applications in biomechanics illustrate the capability of our methods.     

Adaptive Segmentation Model for Images with Intensity Inhomogeneity based on Local Neighborhood Contrast

Segmentation of images with intensity inhomogeneity is a significant task in the field of image processing, especially in medical image processing and analysis. Some local region-based models work well on handling intensity inhomogeneity, but they are always sensitive to contour initialization and high noise. In this paper, we present an adaptive segmentation model for images with intensity inhomogeneity in the form of partial differential equation. Firstly, a global intensity fitting term and a local intensity fitting term are constructed by employing the global and local image information, respectively. Secondly, a tradeoff function is defined to adjust adaptively the weight between two fitting terms, which is based on the neighborhood contrast of image pixel. Finally, a weighted regularization term related to local entropy is used to ensure the smoothness of evolution curve. Meanwhile, a distance regularization term is added for stable level set evolution. Experimental results show that the proposed model without initial contour can segment inhomogeneous images stably and effectively, which thereby avoiding the influence of contour initialization on segmentation results. Besides, the proposed model works better on noise images comparing with two relevant segmentation models.