改进的几何活动轮廓模型图像分割算法

针对C-V模型不能有效地分割多灰度级图像以及抗噪性不强的问题,分别引入了一个以高斯函数为核函数的局部二值拟合能量项和一个边缘停止函数。利用局部窗函数内的加权均值取代C-V模型的全局均值,并加入了距离函数补偿项,避免了水平集函数的重新初始化,同时将图像的边缘信息融入到C-V模型中,克服了传统的C-V模型无法利用图像梯度信息的不足。实验证明,改进的模型和LBF模型在血管图的分割的效果明显好于C-V模型,在分割时间上,改进的模型也少于LBF模型和C-V模型;对于灰度分布不均匀以及含有噪声的图像,无论是在分割的速度还是分割的效果上,改进的模型均明显优于C-V模型和LBF模型。     

结合梯度和区域信息的多尺度水平集图像分割

提出了一种结合梯度和区域信息的多尺度水平集图像分割算法。该算法结合梯度和区域信息构造能量函数,在梯度约束项中,构建了一个基于小波高频分量的边缘检测函数,在区域约束项中,运用经典C-V模型的区域项,得到混合C-V模型,采用变分法求解,并消除了水平集的重初始化。利用小波变换首先在逼近图像中运用混合C-V模型得到粗分辨图像的一个粗尺度分割,再对当前粗尺度下的最终轮廓线作内插操作,将得到的近似轮廓曲线作为初始水平集函数在原图像中运用消除重初始化的C-V模型演化得到最终的分割。实验结果表明,在同样的模型参数条件下,该方法具有比传统方法更高的演化效率和分割质量。     

基于水平集方法的航拍图像运动分割

针对航拍图像由于受噪声和光照影响导致分割精度差问题,将一种改进的C-V水平集方法引入到航拍图像运动分割中.首先对C-V模型作了改进,通过引入新的能量项使改进方法无需重新初始化符号距离函数,在保证分割精度的同时提高了分割速度;其次对水平集函数的偏微分方程进行改进,消除了原始C-V方法对远离实际边缘的轮廓曲线进化的抑制作用.实验结果显示,改进方法能有效地分割出航拍图像中的运动目标,在初始轮廓线远离目标实际轮廓时也能够正确分割,并能更好地满足实时性的要求.改进方法具有分割精度高,耗时少的优点,可用于航拍图像运动目标检测跟踪系统.     

基于边缘检测函数尺度变换的水平集图像分割

针对Chan-Vese模型（C-V模型）存在收敛缓慢等缺陷,给出一种基于边缘检测函数尺度变换的水平集图像分割算法。引入边缘检测函数对C-V模型进行改进,在不降低分割质量的前提下,提高图像分割的速度。为了增强改进模型的灵活性,提出对边缘检测函数进行尺度变换的方法。实验结果表明,改进模型有良好的分割效果,尺度变换能有效加快改进模型的演化速度,保持分割过程的稳定性。     

基于改进的C-V模型虚拟人脑图像分割模型

C-V模型是一种较为经典的分割模型,但传统的C-V模型仅能够将图像分割成单一的目标部分与背景部分;用于彩色图像分割往往基于目标的强度信息;在曲线演化过程中需要重新初始化水平集函数保持符号距离函数。针对这些问题,使用PCA理论将颜色空间投影到新的空间中,可以扩大两者的颜色距离;使用局部信息可校正颜色强度不均匀;将距离约束项引入到模型中,使模型能够无需重新初始化,提高了演化速度。实验结果表明改进的算法能较精确地得到分割结果。     

自适应主动轮廓模型下的骨关节MRI快速分割

提出一种无须重新初始化的变分水平集自适应主动轮廓模型。该模型利用图像的局部特性自适应决定曲线的演化,同时加入局部C-V能量项,改进边界停止函数,提高对灰度分布重叠、分布不均匀及弱边界处理的鲁棒性,并加快了曲线演化的收敛速度。结合医学序列图像特点,利用Heaviside函数对当前截面分割结果进行分段常量化后投射至相邻界面作为初始化曲线,实现对序列图像的自动分割。最后,以骨关节磁共振图像中正常结构和病灶组织的分割实验对算法进行了验证。     

一种改进的快速C-V水平集红外图像分割

当红外图像中包含较强噪声时,C-V模型水平集分割方法会产生大量冗余轮廓;同时,C-V水平集采用偏微分方程(PDE)实现,存在计算量大、分割速度慢的缺点.为此,本文提出了改进的快速算法,该算法保留了C-V模型的全局优化特性,并通过窗口滤波整合图像邻域空间信息来构建曲线进化的外部速度,从而提高C-V模型的抗噪性并减少分割中产生的冗余轮廓;采用基于双链表的快速水平集算法来实现曲线的演化,去除了传统算法中的重新初始化和PDE求解的过程,减少了迭代步数,提高了分割的速度.实验结果表明,本文算法对边缘模糊、噪声较大的红外图像能实现快速而有效的分割.     

LCV模型在医学图像分割中的应用

针对C-V模型不能充分利用图像局部区域灰度变化信息从而导致难以准确分割灰度不均物体等缺陷,提出一种基于局部区域的C-V(LCV)模型。利用计算局部窗函数内的加权灰度均值来取代全局均值,并加入约束水平集函数为符号距离函数的能量项,从而避免水平集函数的重新初始化。对医学图像的分割结果证明LCV模型在分割灰度不均物体方面优于C-V模型,其分割效率高于LBF模型。     

水平集图像分割中重新初始化规避的探索

水平集方法有效地解决了图像分割中曲线演化过程中的拓扑变化问题,其实质是水平集方法与模型的结合,以水平集方法来求解模型得到的偏微分方程的方法.要想约束水平集函数在迭代过程中保持为符号距离函数,保证水平集函数的稳定收敛,就必须对SDF重新进行初始化.但是每次都对SDF重新进行初始化,大大增加了计算量,浪费了宝贵的时间,从而大幅降低了曲线的演化速度.一直以来,大家在不断地改进算法,缩短每次初始化所需的时间,但收效甚微.SDF重新初始化的规避,使图像分割时曲线演化速度加快,实验结果表明这种方法是非常有效的,并且具有很强的鲁棒性.重新初始化的规避,减少了计算量,使水平集图像分割法能满足更多的生活、工业应用中的实时性要求.     

一种改进的活动区域轮廓模型 ——无需水平集重新初始化

基于区域的活动区域模型已经成功应用在图像分割、目标跟踪等领域,较之基于梯度的活动轮廓模型具有很多优点。但是,这些水平集模型在演化过程中,为了保持为符号距离函数,必须对其重新初始化,降低了曲线演化速度,增加了实现复杂度。为了解决重新初始化问题,在测地活动区域模型的能量函数中,加入惩罚项来约束水平集保持为符号距离函数,无需再重新初始化,极大地提高了演化速度。将其运用在纹理图像、脑MR图像分割以及视频跟踪中,实验证明该模型是有效的。     

Application of spectral level set methodology in topology optimization

In this paper, two benchmark problems in structural boundary design are solved using the spectral level set methodology, which is a new approach to topology optimization of interfaces. This methodology is an extension of the level set methods, in which the interface is represented as the zero level set of a function. According to the proposed formulation, the Fourier coefficients of that function are the design variables describing the interface during the topology optimization. An advantage of the spectral level set methodology, in the case of a sufficiently regular interface, is to admit an upper bound error which is asymptotically smaller than the one for nonadaptive spacial discretizations of the level set function. Other advantages include the nucleation of holes in the interior of the interface and the avoidance of checkerboard-like designs. The theoretical framework of the methodology is presented and estimates on its convergence rate are discussed. The numerical applications consist in the design of short and long cantilevers subject to a vertical concentrated load opposite to the fixed end. The goal is to maximize the structural stiffness subject to a solid volume constraint. The zero level set of the level set function defines the structural boundary.     

Fast Path Re-planning Based on Fast Marching and Level Sets

We investigate path planning algorithms that are based on level set methods for applications in which the environment is static, but where an a priori map is inaccurate and the environment is sensed in real-time. Our principal contribution is not a new path planning algorithm, but rather a formal analysis of path planning algorithms based on level set methods. Computational costs when planning paths with level set methods are due to the creation of the level set function. Once the level set function has been computed, the optimal path is simply gradient descent down the level set function. Our approach rests on the formal analysis of how value of the level set function changes when the changes in the environment are detected. We show that in many practical cases, only a small domain of the level set function needs to be re-computed when the environment changes. Simulation examples are presented to validate the effectiveness of the proposed method.     

Moving-boundary problems solved by adaptive radial basis functions

The objective of this paper is to present an alternative approach to the conventional level set methods for solving two-dimensional moving-boundary problems known as the passive transport. Moving boundaries are associated with time-dependent problems and the position of the boundaries need to be determined as a function of time and space. The level set method has become an attractive design tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations. In the present approach, the moving interface is captured by the level set method at all time with the zero contour of a smooth function known as the level set function. A new approach is used to solve a convective transport equation for advancing the level set function in time. This new approach is based on the asymmetric meshless collocation method and the adaptive greedy algorithm for trial subspaces selection. Numerical simulations are performed to verify the accuracy and stability of the new numerical scheme which is then applied to simulate a bubble that is moving, stretching and circulating in an ambient flow to demonstrate the performance of the new meshless approach.     

前向后向扩散的距离正则模型应用于图像分割*

针对在演化过程中水平集函数震荡问题,提出前向后向扩散的距离正则模型应用于图像分割。新的距离正则项由一个势函数定义,推导的演化方程以唯一的方式前向后向扩散,即：水平集函数在其陡峭区域前向扩散,降低函数的梯度模直至为1,反之它后向扩散,提高梯度模直至1。演化结果是水平集函数收敛于符号距离函数,这是水平集函数稳定演化所希望保持的状态。为了阐述距离正则项的有效性,本文将其和基于边缘信息的外能量项相结合。实验结果表明,该模型能够好的完成图像分割,对噪声和弱目标图像鲁棒。     

A Locally Gradient-Preserving Reinitialization for Level Set Functions

The level set method commonly requires a reinitialization of the level set function due to interface motion and deformation. We extend the traditional technique for reinitializing the level set function to a method that preserves the interface gradient. The gradient of the level set function represents the stretching of the interface, which is of critical importance in many physical applications. The proposed locally gradient-preserving reinitialization (LGPR) method involves the solution of three PDEs of Hamilton–Jacobi type in succession; first the signed distance function is found using a traditional reinitialization technique, then the interface gradient is extended into the domain by a transport equation, and finally the new level set function is found by solving a generalized reinitialization equation. We prove the well-posedness of the Hamilton–Jacobi equations, with possibly discontinuous Hamiltonians, and propose numerical schemes for their solutions. A subcell resolution technique is used in the numerical solution of the transport equation to extend data away from the interface directly with high accuracy. The reinitialization technique is computationally inexpensive if the PDEs are solved only in a small band surrounding the interface. As an important application, we show how the LGPR procedure can be used to make possible the local level set approach to the Eulerian Immersed boundary method.     

曲面扩散的变分水平集方法

基于变分水平集方法提出了一种通用的曲面扩散变分模型,其数据项为演化曲面与原曲面的水平集函数Heaviside函数差的平方,规则项为基于整体曲率的通用函数,通过图像扩散模型中的总变差与该模型中的总曲率类比设计该规则项,以实现曲面扩散的任务。为了避免水平集函数的重新初始化,在本文的能量泛函中增加了水平集函数为符号距离函数的惩罚项。所得到的演化方程为4阶偏微分方程,对其对流项采用经典迎风差分格式离散,对其中的扩散项采用中心差分格式。最后通过数值算例验证了模型用于曲面光滑、边缘保持与边缘增强的可行性。     

隐式曲面上两相图像分割的变分水平集方法

在平面图像分割的Chan-Vese模型基础上,提出隐式曲面上两相图像分割模型。用静态水平集函数的零水平集表达图像所在的闭合曲面,用另一动态水平集函数的零水平集与静态水平集函数零水平集的交线表达静态曲面上图像分割的动态轮廓线。所研究模型的能量泛函的数据项即为曲面上两分割区域的图像强度与对应区域平均图像强度的差的平方,其轮廓线长度项为两水平集函数的零水平集交线的长度。为避免动态水平集函数的重新初始化,在能量泛函中引入水平集函数为符号距离函数的约束惩罚项。通过变分方法得到图像分割空间轮廓线演化的梯度降方程。通过显式差分格式对演化方程进行离散。实验结果表明,该模型能有效实现复杂封闭曲面上图像的两相分割。     

基于粗糙集和新能量公式的水平集图像分割

为了提高水平集图像分割的质量和减少水平集迭代次数,本文提出了新的能量公式和水平集函数.在粗糙集数据离散化基础上引入了针对图像数据的离散化方法,根据图像离散区域的信息对新能量函数进行直接加权并且对核函数进行间接加权,使用加权的核映射函数将原始离散图像数据映射到高维空间,从而使得该模型可以处理多种类型的图像甚至是一定信噪比的噪声图像.新的能量公式联合由它导出的区域参数能够更好地表达同质区域的灰度信息,从而能够更精确地分割图像.与传统水平集图像分割不同,在迭代过程中新的水平集函数中的水平集元素可以拥有不同的步长,步长越大水平集元素的更新速度越快并且水平集函数能够快速达到收敛状态,实现快速图像分割.人工合成图像和真实图像的分割实验表明本文方法可以获得更好的分割效果.     

Fast level set image and video segmentation using new evolution indicator operators

We propose an effective level set evolution method for robust object segmentation in real images. We construct an effective region indicator and an multiscale edge indicator, and use these two indicators to adaptively guide the evolution of the level set function. The multiscale edge indicator is defined in the gradient domain of the multiscale feature-preserving filtered image. The region indicator is built on the similarity map between image pixels and user specified interest regions, where the similarity map is computed using Gaussian Mixture Models (GMM). Then we combine these two methods to develop a new mixing edge stop function, which makes the level set method more robust to initial active contour setting, and forces the level set to evolve adaptively based on the image content. Furthermore, we apply an acceleration approach to speed up our evolution process, which yields real time segmentation performance. Finally, we extend the proposed approach to video segmentation for achieving effective target tracking results. As the results show, our approach is effective for image and video segmentation and works well to accurately detect the complex object boundaries in real-time.     

基于变分水平集的图像分割模型

基于传统的变分水平集方法的图像分割,水平集函数必须周期性地重新初始化使之保持为符号距离函数,这存在如何选择重新初始化的时间和方式的难题.Li模型通过在能量泛函中引入一个内部约束能量,去除了水平集函数在演化过程中需重新初始化的难题.通过对Li模型的分析,提出了一个新的变分水平集的分割模型.该模型通过在能量泛函中加入一个较简单的内部约束能量,同样可以实现水平集演化过程中的无需重新初始化.并且通过对边缘停止函数的重新定义,引入了新的外部能量,使得本文模型对噪声图像的分割更具鲁棒性.实验表明无论是在收敛速度上,还是在对噪声图像的分割质量上,本文模型和Li模型相比都具有一定的优势.