New Possibilities with Sobolev Active Contours

Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric outperforms the traditional metric for the same energy in many cases such as for tracking where the coarse scale changes of the contour are important. Some interesting properties of Sobolev gradient flows include that they stabilize certain unstable traditional flows, and the order of the evolution PDEs are reduced when compared with traditional gradient flows of the same energies. In this paper, we explore new possibilities for active contours made possible by Sobolev metrics. The Sobolev method allows one to implement new energy-based active contour models that were not otherwise considered because the traditional minimizing method render them ill-posed or numerically infeasible. In particular, we exploit the stabilizing and the order reducing properties of Sobolev gradients to implement the gradient descent of these new energies. We give examples of this class of energies, which include some simple geometric priors and new edge-based energies. We also show that these energies can be quite useful for segmentation and tracking. We also show that the gradient flows using the traditional metric are either ill-posed or numerically difficult to implement, and then show that the flows can be implemented in a stable and numerically feasible manner using the Sobolev gradient. Sundaramoorthi and Yezzi were supported by NSF CCR-0133736, NIH/NINDS R01-NS-037747, and Airforce MURI; Sapiro was partially supported by NSF, ONR, NGA, ARO, DARPA, and the McKnight Foundation.     

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.     

一种基于AOS格式的多相水平集快速分割方法

采用迎风格式的水平集算法实现需要在曲线演化过程中重新初始化水平集函数的要求,为保证算法的稳定,时间步长选取较小值,算法运行速度较慢。文中基于无须重新初始化的水平集方法,在算法数值实现中引入AOS半隐格式,对基于不同统计模型的水平集分割算法给出统一的数值实现。以二相水平集分割算法为基础提出一种新的多相水平集分割方法。该方法采用一个水平集函数进行多次演化实现多区域分割,其优点包括：1)采用AOS半隐格式,该格式无条件稳定,可采用较大的时间步长;2)对多个统计模型进行统一处理;3)采用单一的水平集函数进行演化,减少水平集演化方程的数量,算法更加灵活。实验结果表明,该方法具有较快的分割速度,对具有多个区域的图像能够进行较准确的分割。     

Using the Shape Gradient for Active Contour Segmentation: from the Continuous to the Discrete Formulation

A variational approach to image or video segmentation consists in defining an energy depending on local or global image characteristics, the minimum of which being reached for objects of interest. This study focuses on energies written as an integral on a domain of a function which can depend on this domain. The derivative of the energy with respect to the domain, the so-called shape derivative, is a function of a velocity field applied to the domain boundary. For a given, non-optimal domain, the velocity should be chosen such that the shape derivative is negative, thus indicating a way to deform the domain in order to decrease its energy. Minimizing the energy through an iterative deformation process is known as the active contour method. In the continuous framework, setting the velocity to the opposite of the gradient associated with the L ² inner product is a common practice. In this paper, it is noted that the negativity of the shape derivative is not preserved, in general, by the discretization of this velocity required by implementation. In order to guarantee that the negativity condition holds in the discrete framework, it is proposed to choose the velocity as a linear combination of pre-defined velocities. This approach also gives more flexibility to the active contour process by allowing to introduce some a priori knowledge about the optimal domain. Some experimental results illustrate the differences between the classical and the proposed approach.

基于变宽邻域图割和活动轮廓的目标分割方法

基于图割的活动轮廓算法是一个结合图割优化工具和活动轮廓模型迭代变形思想的目标分割算法。针对算法在迭代过程中对已达目标边界的活动轮廓线所在邻域重复切割的不足,将活动轮廓线分为已达目标曲线段和未达目标曲线段,仅对未达目标曲线段进行膨胀得到可变宽度轮廓线邻域,从而减少了对邻域的切割时间。实验表明,改进算法效率提高为原来的2~3倍。     

基于水平集的多运动目标时空分割与跟踪

针对背景运动时的运动目标分割问题,提出了一种对视频序列中的多个运动目标进行分割和跟踪的新方法。该方法着眼于运动的且较为复杂的背景,首先利用光流约束方程和背景运动模型建立一个基于时空域的能量函数,然后用该函数进行背景运动速度的估算和运动目标的分割和跟踪。而时空域中的运动目标的最佳分割,乃是通过使该能量函数最小化来驱动时空曲面演化实现。时空曲面的演化采用了水平集PDEs(Partial Differential Equations)方法。实验中,用实际的图像序列验证了该算法及其数值实现。实验表明,该方法能够同时进行背景运动速度的估算、运动目标的分割和跟踪。     

Computer Vision and Pattern Recognition Techniques for 2-D and 3-D MR Cerebral Cortical Segmentation (Part I): A State-of-the-Art Review

Extensive growth in functional brain imaging, perfusion-weighted imaging, diffusion-weighted imaging, brain mapping and brain scanning techniques has led tremendously to the importance of the cerebral cortical segmentation, both in 2-D and 3-D, from volumetric brain magnetic resonance imaging data sets. Besides that, recent growth in deformable brain segmentation techniques in 2-D and 3-D has brought the engineering community, such as the areas of computer vision, image processing, pattern recognition and graphics, closer to the medical community, such as to neuro-surgeons, psychiatrists, oncologists, neuro-radiologists and internists. This paper is an attempt to review the state-of-the-art 2-D and 3-D cerebral cortical segmentation techniques from brain magnetic resonance imaging based on three main classes: region-based, boundary/surface-based and fusion of boundary/surface-based with region-based techniques. In the first class, region-based techniques, we demonstrated more than 18 different techniques for segmenting the cerebral cortex from brain slices acquired in orthogonal directions. In the second class, boundary/surface-based, we showed more than ten different techniques to segment the cerebral cortex from magnetic resonance brain volumes. Particular emphasis will be placed by presenting four state-of-the-art systems in the third class, based on the fusion of boundary/surface-based with region-based techniques outlined in Part II of the paper, also called regional-geometric deformation models, which take the paradigm of partial differential equations in the level set framework. We also discuss the pros and cons of various techniques, besides giving the mathematical foundations for each sub-class in the cortical taxonomy. Received: 25 August 2000, Received in revised form: 28 March 2001, Accepted: 28 March 2001     

Active contours with selective local or global segmentation: A new formulation and level set method

A novel region-based active contour model (ACM) is proposed in this paper. It is implemented with a special processing named Selective Binary and Gaussian Filtering RegularizedLevel Set(SBGFRLS) method, which first selectively penalizes the level set function to be binary, and then uses a Gaussian smoothing kernel to regularize it. The advantages of our method are as follows. First, a new region-based signed pressure force (SPF) function is proposed, which can efficiently stop the contours at weak or blurred edges. Second, the exterior and interior boundaries can be automatically detected with the initial contour being anywhere in the image. Third, the proposed ACM with SBGFRLS has the property of selective local or global segmentation. It can segment not only the desired object but also the other objects. Fourth, the level set function can be easily initialized with a binary function, which is more efficient to construct than the widely used signed distance function (SDF). The computational cost for traditional re-initialization can also be reduced. Finally, the proposed algorithm can be efficiently implemented by the simple finite difference scheme. Experiments on synthetic and real images demonstrate the advantages of the proposed method over geodesic active contours (GAC) and Chan–Vese (C–V) active contours in terms of both efficiency and accuracy.     

Fusion of Region and Boundary/Surface-Based Computer Vision and Pattern Recognition Techniques for 2-D and 3-D MR Cerebral Cortical Segmentation (Part-II): A State-of-the-Art Review

Extensive growth in functional brain imaging, perfusion-weighted imaging, diffusion-weighted imaging, brain mapping and brain scanning techniques has led tremendously to the importance of cerebral cortical segmentation both in 2-D and 3-D from volumetric brain magnetic resonance imaging data sets. Besides that, recent growth in deformable brain segmentation techniques in 2-D and 3-D has brought the engineering community, such as the areas of computer vision, image processing, pattern recognition and graphics, closer to the medical community, such as to neuro-surgeons, psychiatrists, oncologists, neuro-radiologists and internists. In Part I of this research (see Suri et al [1]), an attempt was made to review the state-of-the-art in 2-D and 3-D cerebral cortical segmentation techniques from brain magnetic resonance imaging based on two main classes: region- and boundary/surface-based. More than 18 different techniques for segmenting the cerebral cortex from brain slices acquired in orthogonal directions were shown using region-based techniques. We also showed more than ten different techniques to segment the cerebral cortex from magnetic resonance brain volumes using boundary/surface-based techniques. This paper (Part II) focuses on presenting state-of-the-art systems based on the fusion of boundary/surface-based with region-based techniques, also called regional-geometric deformation models, which takes the paradigm of partial differential equations in the level set framework. We also discuss the pros and cons of these various techniques, besides giving the mathematical foundations for each sub-class in the cortical taxonomy. Special emphasis is placed on discussing the advantages, validation, challenges and neuro-science/clinical applications of cortical segmentation. Received: 25 August 2000, Received in revised form: 28 March 2001, Accepted: 28 March 2001     

Some Remarks on the Equivalence between 2D and 3D Classical Snakes and Geodesic Active Contours

Recently, Caselles et al. have shown the equivalence between a classical snake problem of Kass et al. and a geodesic active contour model. The PDE derived from the geodesic problem gives an evolution equation for active contours which is very powerfull for image segmentation since changes of topology are allowed using the level set implementation. However in Caselles' paper the equivalence with classical snake is only shown for 2D images and 1D curves, by using concepts of Hamiltonian theory which have no meanings for active surfaces. This paper propose to examine the notion of equivalence and to revisite Caselles et al. arguments. Then a notion equivalence is introduced and shown for classical snakes and geodesic active contours in the 2D (active contour) and 3D (active surface) case.     

心脏序列图像运动估计新方法:基于广义模糊梯度矢量流场的形变曲线运动估计与跟踪

应用动态轮廓线模型(ACM)解决心脏运动估计问题是该领域的主要研究方法之一．采用经典外力和传统ACM模型对感兴趣边缘进行搜索及跟踪时，普遍存在模型的局部适应性程度不高的缺陷．为解决这一挑战性难题，该文提出了广义模糊梯度矢量流(GFGVF)的概念，并构造出一组新的Snake平衡方程，该方程可对心脏内部边缘逐帧进行鲁棒跟踪．为进一步跟踪每一特征点的运动，该文将前一步的轮廓跟踪结果作为似然条件，结合一致性和连续性先验条件，通过最大后验概率(MAP)的方法对整个过程进行了优化计算．通过对MR及CT两类心脏序列图像进行运动跟踪实验并对计算结果进行多种比较，此方法显示了较好的鲁棒性．     

基于先验形状的混杂活动轮廓模型及其在图像分割中的应用

提出了一种新颖的基于先验形状学习的混杂活动轮廓(SHAC)模型,该模型采用变分水平集方法,融合自适应区域信息与边界信息,运用主成分分析的方法从给定的含有目标物体轮廓的训练集学习得到最佳形状信息,并将其作为先验形状。将自适应区域特征和轮廓特征作为局部信息,先验形状作为全局信息,在迭代过程中结合全局和局部信息实现对演化曲线的形变进行指导和约束,达到分割目标物体的目的。通过定量和定性地分析低对比度的乳腺核磁共振图像中的乳腺轮廓的分割,以及具有复杂背景的自然图像中感兴趣区域的分割结果,验证了SHAC模型比传统活动轮廓模型具有更高的准确率,表明了该模型不仅提高了图像分割中对弱边界的识别度,减弱了非目标轮廓的干扰,而且具有良好的抗噪能力。     

Guest Editorial: Special Issue on Variational and Level Set Methods in Computer Vision

International Journal of Computer Vision -     

Level Set方法在轮廓界面追踪问题中的应用

运用LevelSet方法研究图像轮廓追踪问题。首先,运用差分法检测出图像的初始轮廓线,然后采用基于LevelSet方法的偏微分方程数值解理论来进行图像轮廓界面的提取。Matlab实验结果表明,该方法可以测出模糊或离散的边界,得到精确的图像轮廓界面。     

一种新的水平截集函数初始化和重新初始化方法——距离函数光滑法

水平截集(LevelSet)方法是求解曲线进化方程的一种重要方法,该方法主要缺陷是每隔一定时间需要重新初始化水平截集函数,使水平截集函数具有距离函数和充足光滑性的特征。现有各种重新初始化方法均不能使水平截集函数同时具有这两种特性。论文提出了一种新的水平截集初始化和重新初始化方法-距离函数光滑法,该方法可使初始化和重新初始化后的水平截集函数同时具有上述两种特性。该方法适用于数值求解精度为网格的界面运动问题的初始化和重新初始化,也可作为任意数值求解精度界面运动问题的初始化方法。数值试验表明了所建议方法的有效性,也表明了该方法可降低重新初始化的次数以及数值计算达到稳态的时间。     

改进的Mumford-Shah模型及其基于逐段常数水平集方法在图像处理中的应用

为了快速的分割和去噪, 经典的 Mumford-Shah 模型需要增强惩罚项的作用, 即增大惩罚项系数, 但是将使目标逐渐的消失. 本文工作提出一个改进的 Mumford-Shah 模型避免了如此现象, 并结合逐段常数水平集方法和梯度下降法求解极小化问题. 并用仿真实验证明了新模型和运算的有效性.     

医学院校开设《ASP动态网页设计》课程的教学探索与实践

分析了医学院校计算机基础教学的现状和存在的弊端,提出通过开设《ASP动态网页设计》课程,在课程体系、教学内容和教学模式等方面进行改革的思路,并在教学实践过程中予以贯彻和实施,建立起了一套针对医学院校计算机基础教学改革行之有效的教学体系。