Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths

We introduce a novel implicit approach for single object segmentation in 3D images. The boundary surface of this object is assumed to contain two or more known curves (the constraining curves), given by an expert. The aim of our method is to find the desired surface by exploiting the information given in the supplied curves as much as possible. We use a cost potential which penalizes image regions of low interest (for example areas of low gradient). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. These paths globally minimize an energy which is defined from the cost potential. Our approach, although conceptually different, can be seen as an implicit extension to 3D of the minimal path framework already known for 2D image segmentation. As for this previous approach, and unlike other variational methods, our method is not prone to local minima traps of the energy. We present a fast implementation which has been successfully applied to 3D medical and synthetic images. Roberto Ardon graduated from the Ecole Centrale Paris in 2001 with a major in applied mathematics, obtained his master degree in image processing from the Ecole Normale Supérieure de Cachan in the same year and his Ph.D. degree in applied mathematics from the University Paris-Dauphine in 2005. Currently he is a research scientist in Philips Medical Systems Research Paris. His research interests include calculus of variations mainlly focused on medical image processing. Laurent D. Cohen was at Ecole Normale Superieure Ulm in Paris from 1981 to 1985. He received Master's and Ph.D. degrees in Applied Mathematics from Paris 6 in 1983 and 1986. From 1985 to 1987, he was member at the Computer Graphics and Image Processing group at Schlumberger Palo Alto Research, California and Schlumberger Montrouge Research, and remained consultant there for a few years afterwards. He began working with INRIA, France in 1988, mainly with the medical image understanding group Epidaure. Since 1990, he is Research Scholar (Charge then Directeur de Recherche) with CNRS in the Applied Mathematics and Image Processing group at CEREMADE, University Paris-Dauphine. His research interests and teaching at the university are applications of variational methods and Partial Differential Equations to Image Processing and Computer Vision, like deformable models, minimal paths, surface reconstruction, Image registration, Image segmentation and restoration. He obtained CS 2002 Prize for Image and Signal Processing. He has been member in program committees for boards for about 20 international conferences. Anthony Yezzi obtained his Ph.D. in 1997 through the Department of Electrical Engineering at the University of Minnesota. After completing a postdoctoral research position in the Laboratory for Information and Decision Systems (LIDS) at Massacusetts Institute of Technology, he joined the faculty of the School of Electrical and Computer Engineering at Georgia Institute of Technology in 1999 where he currently holds the position of Associate Professor. Prof. Yezzi has also consulted for a number of medical imaging companies including GE, Picker, and VTI, and has been an IEEE member since 1999. His research lies primarily within the fields of image processing and computer vision. He has worked on a variety of problems including image denoising, edge-detection, segmentation and grouping, shape analysis, multi-frame stereo reconstruction, tracking, and registration. Some central themes of his research include curve and surface evolution theory, differential geometry, and partial differential equations.     

Multiple Contour Finding and Perceptual Grouping using Minimal Paths

We address the problem of finding a set of contour curves in an image. We consider the problem of perceptual grouping and contour completion, where the data is a set of points in the image. A new method to find complete curves from a set of contours or edge points is presented. Our approach is based on a previous work on finding contours as minimal paths between two end points using the fast marching algorithm (L. D Cohen and R. Kimmel, International Journal of Computer Vision, Vol. 24, No. 1, pp. 57–78, 1997). Given a set of key points, we find the pairs of points that have to be linked and the paths that join them. We use the saddle points of the minimal action map. The paths are obtained by backpropagation from the saddle points to both points of each pair.In a second part, we propose a scheme that does not need key points for initialization. A set of key points is automatically selected from a larger set of admissible points. At the same time, saddle points between pairs of key points are extracted. Next, paths are drawn on the image and give the minimal paths between selected pairs of points. The set of minimal paths completes the initial set of contours and allows to close them. We illustrate the capability of our approach to close contours with examples on various images of sets of edge points of shapes with missing contours.     

一种二维网格中最小路径区的构建模型

矩形故障块模型可用来解决二维网格中的容错路由问题.本文基于最小路径区(RMP)概念,提出了一种最小路径区的分布式构建模型.该模型首先将带有矩形故障块的网格划分成若干个不同大小的矩形块,通过矩形块的不同组合来构成相应两点之间的最小路径区.最后对该构建模型进行了扩展讨论,指出其在特殊二维网格和容错路由算法中的应用.     

二维网格中基于最小通路区的自适应和最小容错路由算法

网格结构是并行与分布式处理中最流行的一种网络拓扑结构。在存在故障的情况下，如何设计具有最优性的容错路由算法一直是研究的热，点问题。本文研究了采用故障块模型的二维网格的最小路由问题，提出存在最小通路的一个充分必要条件。基于最小通路区（RMP）的概念，提出一种自适应的最小容错路由算法。如果源节点和目的节点之间存在最小通路区，则在最小通路区中进行自适应最小容错路由；反之，则采用多阶段最小容错路由。主要思想就是在存在故障的情况下，尽量保证路由算法能走最短路径。因为只要求知道每个节点的局部信息，故算法是分布式的。     

A moving object segmentation algorithm for static camera via active contours and GMM

Moving object segmentation is one of the most challenging issues in computer vision. In this paper, we propose a new algorithm for static camera foreground segmentation. It combines Gaussian mixture model (GMM) and active contours method, and produces much better results than conventional background subtraction methods. It formulates foreground segmentation as an energy minimization problem and minimizes the energy function using curve evolution method. Our algorithm integrates the GMM background model, shadow elimination term and curve evolution edge stopping term into energy function. It achieves more accurate segmentation than existing methods of the same type. Promising results on real images demonstrate the potential of the presented method. Supported by National Basic Research Program of China (Grant No. 2006CB303105), the Chinese Ministry of Education Innovation Team Fund Project (Grant No. IRT0707), the National Natural Science Foundation of China (Grant Nos. 60673109 and 60801053), Beijing Excellent Doctoral Thesis Program (Grant No. YB20081000401), Beijing Municipal Natural Science Foundation (Grant No. 4082025), and Doctoral Foundation of China (Grant No. 20070004037)     

最小通路法在通信保密装备可靠性建模中的应用

针对通信保密装备可靠性建模难度大的问题,提出了一种新的适用于复杂系统的可靠性建模方法一最小通路法。通过在系统拓扑结构图上搜索出所有能够使系统正常工作的最小通路,建立系统的可靠性模型。该方法基于广义的网络拓扑结构,因此网络的源节点和目标节点不必局限于严格的定义,可以随意指定,具有很大的灵活性。实例证明,该方法可行有效。     

基于中轴线约束的最短路径的血管提取算法

血管分割对于血管精确可视化、心血管疾病诊断和血管疾病定量至关重要。本文提出了基于中轴线约束的最短路径的血管提取算法。该算法包括了两次最短路径搜索过程,第一次搜索过程使用了回溯累加技术来提取血管的中轴线,然后结合中轴线信息将其作为血管搜索的能量约束进行第二次搜索过程来提取血管。本文的方法只需要为血管提取设置一个起点,并不需要为血管树复杂的分支结构设置另外的端点。本文使用三维冠状动脉CT血管造影数据来验证本文的算法的可行性和有效性。     

采用测地线活动轮廓模型检测与跟踪运动目标

水平集几何活动轮廓模型能较好地适应曲线的拓扑变化.为了跟踪和获取刚体和非刚体运动目标的轮廓信息,提出了一种基于改进测地线活动轮廓(GAC)模型和Kalman滤波相结合的算法以检测和跟踪运动目标.该算法首先采用高斯混合模型和背景差分获取目标的运动区域,在运动区域内采用引入距离规则化项的GAC模型进行曲线演化,使改进GAC模型在运动目标的真实轮廓处收敛;然后通过结合Kalman滤波预测目标下一帧的位置,实现对目标轮廓跟踪.实验结果表明,该方法适用于刚体和非刚体目标,在部分遮挡的情况下也能保持良好的检测和跟踪效果.     

局部熵驱动区域主动轮廓的局部化框架

提出一种将任意基于区域主动轮廓线模型进行局部化推广的框架.该框架的能量泛涵包含一个惩罚区域弧长的几何正则项和一个局部区域数据拟合项.根据图像像素空间排列的相关性,采用一个滑动窗函数提取图像局部熵,将图像从灰度空间转化到相应局部熵特征空间.在局部熵特征空间,采用另外的窗函数进行局部区域信息提取,从而推导出区域主动轮廓线模...     

基于图割和改进的变分水平集的图像分割方法

文章在图割理论的基础上,引入了一种新的方法将图割理论和改进的变分水平集模型结合起来,先利用图割理论对目标形成一个初始轮廓,并在得到的轮廓线上定义能量函数,通过能量函数的最小化,从而使得到的轮廓线最终收敛到目标边界,这样在保证分割精度的同时大大简化了计算量.     

基于C—V模型的目标检测与提取

在目标检测与提取中,传统的蛇模型和基于活动轮廓的局部区域检测方法受到初始条件或者自身的收敛性约束的影响,不仅时间花费多,而且不具备鲁棒性。本文提出一种基于C V模型的变分水平集的目标检测与提取方法,通过大量实验验证,在花费时间和鲁棒性上得到了显著的改善。     

基于区域活动轮廓运动目标跟踪方法研究

根据贝叶斯估计理论,首先建立了图像序列中运动目标的跟踪模型,然后用高斯分布来描述图像的区域信息,并通过对模型的分析,与区域活动轮廓模型建立对应关系,将问题的求解转化为能量最小化问题。同时为了克服目标在运动中发生的拓扑形变,采用水平集方法进行数值实现。实验结果表明,这种方法不仅可以对多个运动目标进行跟踪,并能非常好地逼近运动目标的轮廓,而且能够自然地处理运动目标的拓扑形变。     

融合区域和测地线的活动轮廓模型与图割相结合的自然图像分割

针对活动轮廓模型利用水平集函数演化来分割图像时,只能分割灰度均匀的图像 问题以及容易陷入能量泛函局部极小值的缺点,提出一种新的图像分割模型。模型将区域中的 局部和全局信息融合的活动轮廓模型与边界模型相结合,然后利用图切割进行优化。实验表明, 该方法对初始曲线不敏感,能分割灰度不均的自然图像,避免陷入局部极小,并能有效提高图 像分割的速度和精度。     

利用区域变形和背景更新实现运动对象跟踪

从时域统计的角度出发,提出了一种结合自适应混合背景更新模型的区域变形跟踪算法．该算法以模型更新得到的前景／背景二值分割掩膜作为区域特征,将跟踪问题抽象为一个水平集(Level Set)偏微分方程的数值求解问题,并分析了算法的自适应性．为了进一步提高算法的实现效率,引入了窄带跟踪方案．实验表明,该算法可以对视频序列中的指定运动对象进行快速精确的跟踪。     

Semi-Automated Extraction of Rivers from Digital Imagery

The manual production of vector maps from digital imagery can be a time consuming and costly process. Developing tools to automate this task for specific features, such as roads, has become an important research topic. The purpose of this paper was to present a technique for the semi-automatic extraction of multiple pixel width river features appearing in high resolution satellite imagery. This was accomplished using a two stage, multi-resolution procedure. Initial river extraction was performed on low resolution (SPOT multi-spectral, 20 m) imagery. The results from this low resolution extraction were then refined on higher resolution (KFA1000, panchromatic, 5 m) imagery to produce a detailed outline of the channel banks. To perform low resolution extraction a cost surface was generated to represent the combined local evidence of the presence of a river feature. The local evidence of a river was evaluated based on the results of a number of simple operators. Then, with user specified start and end points for the network, rivers were extracted by performing a least cost path search across this surface using the A* algorithm. The low resolution results were transferred to the high resolution imagery as closed contours which provided an estimate of the channel banks. These contours were then fit to the channel banks using the dynamic contours (or snakes) technique.     

基于最小超球体的快速分类法

文章提出了两种快速分类的方法——基于最小超球体的平分最近点法和基于最小超球体的按比例划分法。前者只对分别包含正、负类训练点的两类超球体线性可分的情形有效,后者则适用于线性可分和近似线性可分的两类分类问题,且在确定分划超平面时融入了对训练集分布特征的考虑。两种方法皆借鉴了平分最近点法的思想,结合超球体的几何特征,用解析几何方法就可求得分划超平面,从而避免了求解二次规划,大大缩短了训练时间,减小了内存占用量,尤其在处理大规模数据集时优势更为明显。两种方法的特点及其和平分最近点法的对比在实证中都给予了分析说明。     

基于有限元方法的极小曲面造型

讨论极小曲面方程的求解。极小曲面方程是一个高度非线性的二阶椭圆偏微分方程,求解十分困难。该文基于有限元方法,使用一个简单而有效的线性化策略,将问题转化为一系列线性问题,从而大大简化了求解过程。数值结果表明该方法简单有效,能产生合理的结果。     

On the Evolution of Vector Distance Functions of Closed Curves

Inspired by the work by Gomes et al., we describe and analyze a vector distance function approach for the implicit evolution of closed curves of codimension larger than one. The approach is set up in complete generality, and then applied to the evolution of dynamic geometric active contours in (codimension three case). In order to carry this out one needs an explicit expression for the zero level set for which we propose a discrete connectivity method. This leads us to make connections with the new theory of cubical homology. We provide some explicit simulation results in order to illustrate the methodology. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users. First online version published in October, 2005     

图像局部交互熵分割模型的两步快速优化

目的 针对LCK（local correntropy-based K-means）模型收敛速度慢,提出新的基于LCK模型的两步快速分割模型。方法 两步快速分割模型包括粗分割和细分割。1）粗分割：先将待分割的原始图像下采样,减少数据量;然后使用LCK模型对采样后的粗尺度图像进行分割,得到粗分割结果及其相应的粗水平集函数。由于数据量的减少,粗分割步骤可以快速得到近似分割结果。2）细分割：在水平集函数光滑性约束下,将粗分割结果及其对应的粗水平集函数上采样到原始图像的尺度,然后将上采样后的粗水平集函数作为细分割的初始值,利用LCK模型对原始图像进行精细分割。因初始值与真实目标边界很接近,所以只需很少迭代次数就能得到最终分割结果。结果 采用F-score评价方法分析自然以及合成图像的分割结果,并与LCK模型作比较,新的模型F-score数值最大,且迭代次数不大于50。结论 粗分割步骤能在小数据量的情况下,快速分割出粗略的目标;细分割步骤在较好的初始值条件下,能够快速收敛到最终的分割结果,从而有效提高了模型的计算效率和精确性。本文算法主要适用于分割含有未知噪声及灰度非同质的医学图像,且分割效率高。     

Global and Local Active Contours for Head Boundary Extraction

Active contours are an attractive choice to extract the head boundary, for deployment within a face recognition or model-based coding scenario. However, conventional snake approaches can suffer difficulty in initialisation and parameterisation. A dual active contour configuration using dynamic programming has been developed to resolve these difficulties by using a global energy minimisation technique and a simplified parameterisation, to enable a global solution to be obtained. The merits of conventional gradient descent based snake (local) approaches, and search-based (global) approaches are discussed. In application to find head and face boundaries in front-view face images, the new technique employing dynamic programming is deployed to extract the inner face boundary, along with a conventional normal-driven contour to extract the outer (head) boundary. The extracted contours appear to offer sufficient discriminatory capability for inclusion within an automatic face recognition system.