带H1正则项的C-V模型

C-V模型(CHAN T F, VESE L A. Active contours without edges. IEEE Transactions on Image Processing, 2001, 10(2): 266-277)是一个著名的基于区域的图像分割模型。它对活动轮廓的初始化和噪声不敏感,但分割的图像的范围不够广泛。因此,运用理论分析与实验相结合的方法,在C-V模型中添加H1正则项,对其进行了改进,提出了一个新颖的图像分割的能量泛函,并推导出了以偏微分方程形式表示的基于区域的自适应插值拟合的活动轮廓模型。实验表明：该模型能够分割某些原来C-V模型不适用的图像,它对初始轮廓的大小、位置的敏感性较小,抗噪性较强。     

Segmentation of Vectorial Image Features Using Shape Gradients and Information Measures

In this paper, we propose to focus on the segmentation of vectorial features (e.g. vector fields or color intensity) using region-based active contours. We search for a domain that minimizes a criterion based on homogeneity measures of the vectorial features. We choose to evaluate, within each region to be segmented, the average quantity of information carried out by the vectorial features, namely the joint entropy of vector components. We do not make any assumption on the underlying distribution of joint probability density functions of vector components, and so we evaluate the entropy using non parametric probability density functions. A local shape minimizer is then obtained through the evolution of a deformable domain in the direction of the shape gradient. The first contribution of this paper lies in the methodological approach used to differentiate such a criterion. This approach is mainly based on shape optimization tools. The second one is the extension of this method to vectorial data. We apply this segmentation method on color images for the segmentation of color homogeneous regions. We then focus on the segmentation of synthetic vector fields and show interesting results where motion vector fields may be separated using both their length and their direction. Then, optical flow is estimated in real video sequences and segmented using the proposed technique. This leads to promising results for the segmentation of moving video objects. Ariane Herbulot received the M. Engineering degree in computer science from the Ecole Superieure en Sciences Informatiques (ESSI), Sophia Antipolis,France in 2001, and the M.S. degree in computer vision from the University of Nice-Sophia Antipolis (UNSA) in 2003. She is currently a Ph.D. student in image processing with the I3S laboratory, CNRS-UNSA. Her research interests focus on nonparametric methods for image and video segmentation. Stéphanie Jehan-Besson received the engineering degree from Ecole Centrale Nantes and a Ph.D. in computer vision from the University of Nice Sophia Antipolis. She is currently associate professor at ENSICAEN, engineering school of Caen. Her research interests include variational methods for image segmentation, geometric PDEs (Partial Differential Equations), video object detection for MPEG-4/7, medical image segmentation, motion estimation and tracking. Stefan Duffner was born in Schorndorf, Germany in 1978. He received the Bachelor's degree in Computer Science from the University of Applied Sciences Konstanz, Germany in 2002 and the Master's degree in Applied Computer Science from the University of Freiburg, Germany in 2004. He's currently pursuing a Ph.D. degree in Computer Science at the Research Laboratory of France Telecom in Rennes, France. His research interests include machine learning, neural networks and their application to object detection and recognition in images. Michel Barlaud received his These d'Etat from the University of Paris XII and Agregation de Physique. He is currently a Professor of Image Processing at the University of Nice-Sophia Antipolis, and the leader of the Image Processing group of I3S. His research topics are: Image and Video coding using Wavelet Transform, Inverse problem using Half Quadratic Regularization and, Region Based Image and Video Segmentation using Shape Gradient and Active Contours. He is a regular reviewer for several journals, a member of the technical committees of several scientific conferences. He leads several national research and development projects with French industries, and participates in several international academic collaborations: European Network of Excellence SCHEMA and SIMILAR (Louvain La Neuve (Belgium), ITI Greece, Imperial College ...) and NSF-CNRS Funding (Universities of Stanford and Boston). He is the author of a large number of publications in the area of image and video processing, and the Editor of the book “Wavelets and Image Communication” Elsevier, 1994. Gilles Aubert received the These d'Etat es-Sciences Mathematiques from the Univesity of Paris 6, France, in 1986. He is currently professor of mathematics at the University of Nice-Sophia Antipolis and member of the J.A. Dieudonne Laboratory at Nice, France. His research interests are calculus of variations, nonlinear partial differential equations. Fields of applications include image processing and, in particular, restoration, segmentation, decomposition models and optical flow.     

Variational Segmentation of Image Sequences Using Region-Based Active Contours and Deformable Shape Priors

In this paper we address the problem of segmentation in image sequences using region-based active contours and level set methods. We propose a novel method for variational segmentation of image sequences containing nonrigid, moving objects. The method is based on the classical Chan-Vese model augmented with a novel frame-to-frame interaction term, which allow us to update the segmentation result from one image frame to the next using the previous segmentation result as a shape prior. The interaction term is constructed to be pose-invariant and to allow moderate deformations in shape. It is expected to handle the appearance of occlusions which otherwise can make segmentation fail. The performance of the model is illustrated with experiments on synthetic and real image sequences.     

Sobolev Active Contours

All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L ²-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.     

结合全局与局部信息活动轮廓的非同质图像分割

目的 通过对现有基于区域的活动轮廓模型能量泛函的Euler-Lagrange方程进行变形,建立其与K-means方法的等价关系,提出一种新的基于K-means活动轮廓模型,该模型能有效分割灰度非同质图像。方法 结合图像全局和局部信息,根据交互熵的特性,提出新的局部自适应权重,它根据像素点所在邻域的局部统计信息自适应地确定各个像素点的分割阈值,排除灰度非同质分割目标的影响。结果 采用Jaccard相似系数-JS(Jaccard similarity)和Dice相似系数-DSC(Dice similarity coefficient)两个指标对自然以及合成图像的分割结果进行定量分析,与传统及最新经典的活动轮廓模型相比,新模型JS和DSC的值最接近1,且迭代次数不多于50次。提出的模型具有较高的计算效率和准确率。结论 通过大量实验发现,新模型结合图像全局和局部信息,利用交互熵特性得到自适应权重,对初始曲线位置具有稳定性,且对灰度非同质图像具有较好地分割效果。本文算法主要适用于分割含有噪声及灰度非同质的医学图像,而且分割结果对初始轮廓具有鲁棒性。     

改进K-means活动轮廓模型

目的 通过对C-V模型能量泛函的Euler-Lagrange方程进行变形,建立其与K-means方法的等价关系,提出一种新的基于水平集函数的改进K-means活动轮廓模型。方法 该模型包含局部自适应权重矩阵函数,它根据像素点所在邻域的局部统计信息自适应地确定各个像素点的分割阈值,排除灰度非同质对分割目标的影响,进而实现对灰度非同质图像的精确分割。结果 通过分析对合成以及自然图像的分割结果,与传统及最新经典的活动轮廓模型相比,新模型不仅能较准确地分割灰度非同质图像,而且降低了对初始曲线选取的敏感度。结论 提出了包含权重矩阵函数的新活动轮廓模型,根据分割目的和分割图像性质,制定不同的权重函数,该模型具有广泛的适用性。文中给出的一种具有局部统计特性的权重函数,对灰度非同质图像的效果较好,且对初始曲线位置具有稳定性。     

形状约束下活动轮廓模型冠脉血管图像多尺度分割

目的 由于计算机断层血管造影(CTA)图像的复杂性,临床诊断冠脉疾病往往需要经验丰富的医师对冠状动脉进行手动分割,快速、准确自动分割出冠状动脉对提高冠脉疾病诊断效率具有重要意义。针对双源CT图像特点以及传统单一基于区域或边界的活动轮廓模型的不足,研究了心脏冠脉3维分割算法,提出一种基于血管形状约束的活动轮廓模型分割方法。方法 首先,利用改进的FCM(fuzzy C-means)对心脏CT图像感兴趣区域初分割,其结果用于初始化C-V模型水平集演化曲线及控制参数,提取感兴趣区域轮廓。接着,由3维心脏图像数据获取多尺度梯度矢量信息构造边界型能量泛函,然后利用基于Hessian矩阵的多尺度血管函数对心脏感兴趣区域3维体数据增强滤波,获取血管先验形状信息用于约束能量泛函。最后融合边界、区域能量泛函并利用变分原理及水平集方法得到适合冠脉血管分割的水平集演化方程。结果 由于血管图像的灰度不均匀,血管末端区域更为细小,所以上述算法的实施是面向被划分多个子区域的血管,在缩小的范围内进行轮廓的演化。相比于传统的血管分割方法,该方法充分融合血管图像的先验信息及梯度场信息,能够从灰度及造影剂分布不均匀的冠脉血管图像中准确分割出冠状动脉,对于细小的血管结构亦能获得较好的分割效果。实验结果表明,该方法只需在给定初始轮廓前提下,有效提取3维冠脉血管。结论 对多组心脏CT图像进行分割,本文基于血管先验形状约束的活动轮廓模型可以准确分割出冠脉结构完整轮廓,并且人工交互简单。该方法在双源CT冠脉图像自动分割方面具有较好的正确率与优越性。     

一种鲁棒的视频分割算法

无论是在图象识别，还是在基于MPEG－4的图象压缩编码等应用领域，视频对象分割取是其中一个很重要的技术环节，为了在静止背景的情况下，能很好地解决多目标分割的问题，同时能进行单目标的分割，提出了一种鲁棒性较好的视频分割算法，该算法通过对图象序列中每连续3 帧图象进行对称差分，首先检测出目标的运动范围，然后通过对差分结构进行聚类分析来确定该帧图象中视频对象的个数，接着再利用在二值差分图象上收缩的活动轮廓，把视频对象的轮廓精确地包围起来，即得到该帧分割结果；最后利用光流法来对视频对象进行投注跟踪，修正，另外还利用多个图象序列对该方法进行了试验，实验结果表明，在静止背景下，该算法无论是对运动的单目标，还是对运动的多目标，均能较好地从静止背景中分离出来，即能得到理想的分割结果，故具有一定的鲁棒性和实用性。     

分片常值灰度图像的快速分割

PC模型是一个著名的基于区域的活动轮廓模型,它实际上是利用水平集方法解决分片常值灰度图像的分割问题。提出一个以偏微分方程形式表达的新模型,它可以看成是PC模型的一种改进。实验显示：新模型能够实现分片常值灰度图像的快速分割,同时迭代次数对初始轮廓的大小和位置不敏感。     

C-V活动轮廓模型的一个注记

Chan-Vese提出的“无边活动轮廓”模型（C-V模型）是一个著名的基于区域的图像分割模型,它是基于Mumford-Shah泛函和二值PC函数（目标区域取一个值,背景区域取另一个值）解决图像分割问题的。在C-V模型中,定义能量泛函的面积项的系数被要求为非负值,这个要求限制了模型适用的范围。实验研究表明：面积项系数取负值时,C-V模型能够分割某些原来不适用的图像。     

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。     

基于目标模糊置信度描述驱动的区域能量进化增长图像分割算法

为了克服经典区域增长算法在复杂目标与背景分布情况下, 停止条件难以确定的不足, 提出基于目标模糊置信度描述驱动的区域能量进化增长图像分割算法. 该算法结合了主动轮廓模型(Active contour model, ACM)、目标数据分布域描述与区域增长三者的优点, 首先利用分割目标的支持向量数据域描述将待分割图像转化为相对于分割目标的模糊置信度表示, 因为分割过程充分利用了有监督学习策略得到的目标特征分布情况, 使得本文提出的算法具有更高的稳定性和更加广泛的适用范围, 特别是对目标灰度分布不均或存在多纹理的目标也可以得到较好的分割结果. 在区域增长进行分割时, 引入了新的区域能量表示模型作为区域增长的结束判决条件, 分割时逐渐降低目标模糊置信度的门限, 通过对区域能量模型的动态优化来逼近最佳分割结果. 对比实验结果表明本文提出的算法具有更大的灵活性和更好的分割性能.     

ORACM: Online region-based active contour model

A new online region-based active contour model (ORACM) is proposed in this paper. The classical geodesic active contour (GAC) model has only local segmentation property, although the Chan–Vese (C–V) model possesses global. An up-to-date active contour model (ACM with SBGFRLS) proposed in Zhang, Zhang, Song, and Zhou (2010) both has the properties of global/local segmentation and incorporates the GAC and the C–V models to raise active contours’ performance on image segmentation. However it has two major disadvantages. First, it deforms the active contour model just using the gradient of current level set iteratively and so works too slowly. Second, it needs a parameter α which plays major impact on the results and to be tuned according to input images. The proposed model ORACM eliminates these two disadvantages by using a new binary level set formula and a new regularization operation such as morphological opening and closing. Without changing segmentation accuracy, ORACM requires no parameter and less time over the traditional ACMs. Experiments on synthetic and real images demonstrate that the computational cost of ORACM with the morphological operations is 3.75 times less than the traditional ACMs on average.     

Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization

This paper proposes an improved variational model, multiple piecewise constant with geodesic active contour (MPC-GAC) model, which generalizes the region-based active contour model by Chan and Vese, 2001 [11] and merges the edge-based active contour by Caselles et al., 1997 [7] to inherit the advantages of region-based and edge-based image segmentation models. We show that the new MPC-GAC energy functional can be iteratively minimized by graph cut algorithms with high computational efficiency compared with the level set framework. This iterative algorithm alternates between the piecewise constant functional learning and the foreground and background updating so that the energy value gradually decreases to the minimum of the energy functional. The k-means method is used to compute the piecewise constant values of the foreground and background of image. We use a graph cut method to detect and update the foreground and background. Numerical experiments show that the proposed interactive segmentation method based on the MPC-GAC model by graph cut optimization can effectively segment images with inhomogeneous objects and background.     

全局和局部拟合的活动轮廓模型

在现有的活动轮廓模型中,PC模型和RSF模型是两个著名的基于区域的模型。PC模型对活动轮廓的初始化和噪声不敏感,但不能分割灰度不均一图像。RSF模型能够分割灰度不均一图像,但对活动轮廓的初始化和噪声较为敏感。基于PC和RSF模型,提出一个以偏微分方程形式表达的基于区域的活动轮廓模型。实验表明该模型能够分割灰度不均一图像,对初始轮廓的大小和位置不敏感,抗噪性也较强。     

Segmentation of a Vector Field: Dominant Parameter and Shape Optimization

Vector field segmentation methods usually belong to either of three classes: methods which segment regions homogeneous in direction and/or norm, methods which detect discontinuities in the vector field, and region growing or classification methods. The first two classes of method do not allow segmentation of complex vector fields and control of the type of fields to be segmented, respectively. The third class does not directly allow a smooth representation of the segmentation boundaries. In the particular case where the vector field actually represents an optical flow, a fourth class of methods acts as a detector of main motion. The proposed method combines a vector field model and a theoretically founded minimization approach. Compared to existing methods following the same philosophy, it relies on an intuitive, geometric way to define the model while preserving a general point of view adapted to the segmentation of potentially complex vector fields with the condition that they can be described by a finite number of parameters. The energy to be minimized is deduced from the choice of a specific class of field lines, e.g. straight lines or circles, described by the general form of their parametric equations. In that sense, the proposed method is a principled approach for segmenting parametric vector fields. The minimization problem was rewritten into a shape optimization and implemented by spline-based active contours. The algorithm was applied to the segmentation of precomputed optical flow fields given by an external, independent algorithm. Tristan Roy graduated from Ecole Centrale de Lille, France, in 2001. He is currently a Ph.D. student in mathematics at UCLA. His current research interests are variational analysis, optimization problems and PDEs. Fields of application are image segmentation and restoration. Eric Debreuve received his Ph.D. in Image Processing from the University of Nice-Sophia Antipolis, France, in 2000. He was a postdoctoral fellow at the Medical Imaging Research Laboratory (now UCAIR), University of Utah, Salt Lake City, for two years. He is currently a research scientist of the CNRS (a national research institute of France) at Laboratory I3S, University of Nice-Sophia Antipolis, France. His current research interests are image and video segmentation using active contours. Michel Barlaud received his These d'Etat from the University of Paris XII and Agregation de Physique (ENS Cachan). He is currently a Professor of Image Processing at the University of Nice-Sophia Antipolis, and the leader of the Image Processing group of I3S. His research topics are: Image and Video coding using Scan Based Wavelet Transform, Inverse problem using Half Quadratic Regularization and, Image and Video Segmentation using Region Based Active Contours and PDE's. He is a regular reviewer for several journals, a member of the technical committees of several scientific conferences. He leads several national research and development projects with French industries, and participates in several international academic collaborations: European Network of Excellence SCHEMA and SIMILAR (Louvain La Neuve (Belgium), ITI Greece, Imperial College …) and NSF-CNRS Funding (Universities of Stanford and Boston). He is the author of a large number of publications in the area of image and video processing, and the Editor of the book “Wavelets and Image Communication” Elsevier, 1994. Gilles Aubert received the These d'Etat es-sciences Mathematiques from the University of Paris 6, France, in 1986. He is currently professor of mathematics at the University of Nice-Sophia Antipolis and member of the J.A.Dieudonne Laboratory at Nice, France. His research interests are calculus of variations, nonlinear partial differential equations and numerical analysis; fields of application including image processing and, in particular, restoration, segmentation, optical flow and reconstruction in medical imaging.     

扩展无边活动轮廓模型

灰度变化对图像分割是至关重要的。然而,一个著名的基于区域的活动轮廓模型——无边活动轮廓模型（通常称CV模型）完全忽略了这种灰度变化。提出了一个扩展CV模型（ECV）,它利用了图像的灰度变化信息。实验表明：（1）ECV模型能分割CV模型不适用的某些类型的图像;（2）ECV模型也能分割CV模型适用的图像,且对噪声的鲁棒性强于CV模型。     

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。     

双层水平集描述眼底图像视杯视盘分割

目的 青光眼是一种可导致视力严重减弱甚至失明的高发眼部疾病。在眼底图像中,视杯和视盘的检测是青光眼临床诊断的重要步骤之一。然而,眼底图像普遍是灰度不均匀的,眼底结构复杂,不同结构之间的灰度重叠较多,受到血管和病变的干扰较为严重。这些都给视盘与视杯的分割带来很大挑战。因此,为了更准确地提取眼底图像中的视杯和视盘区域,提出一种基于双层水平集描述的眼底图像视杯视盘分割方法。方法 通过水平集函数的不同层级分别表示视杯轮廓和视盘轮廓,依据视杯与视盘间的位置关系建立距离约束,应用图像的局部信息驱动活动轮廓演化,克服图像的灰度不均匀性。根据视杯与视盘的几何形状特征,引入视杯与视盘形状的先验信息约束活动轮廓的演化,从而实现视杯与视盘的准确分割。结果 本文使用印度Aravind眼科医院提供的具有视杯和视盘真实轮廓注释的CDRISHTI-GS1数据集对本文方法进行实验验证。该数据集主要用来验证视杯及视盘分割方法的鲁棒性和有效性。本文方法在数据集上对视杯和视盘区域进行分割,取得了67.52%的视杯平均重叠率,81.04%的视盘平均重叠率,0.719的视杯F1分数和0.845的视盘F1分数,结果优于基于COSFIRE（combination of shifted filter responses）滤波模型的视杯视盘分割方法、基于先验形状约束的多相Chan-Vese（C-V）模型和基于聚类融合的水平集方法。结论 实验结果表明,本文方法能够有效克服眼底图像灰度不均匀、血管及病变区域的干扰等影响,更为准确地提取视杯与视盘区域。