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.

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．     

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

International Journal of Computer Vision -     

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。     

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。     

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。     

计算机系统与计算机网络中的动态优化:模型、求解与应用

动态优化是计算机系统与计算机网络中进行资源分配与任务调度等方面研究所采用的主要理论工具之一.目前,国内外已开展大量研究,致力于深化动态优化的理论研究与工程应用.文中从模型、求解与应用3个角度,对马尔可夫决策过程动态优化理论模型进行了综述,并重点介绍了将动态优化理论与随机Petri网理论相结合的马尔可夫决策Petri网和随机博弈网模型,详细讨论了这些模型的建模方法、求解算法与一些应用实例.最后,对全文进行了总结,并对未来可能的研究方向进行了展望.     

Industrial geometry: recent advances and applications in CAD

Industrial Geometry aims at unifying existing and developing new methods and algorithms for a variety of application areas with a strong geometric component. These include CAD, CAM, Geometric Modelling, Robotics, Computer Vision and Image Processing, Computer Graphics and Scientific Visualization. In this paper, Industrial Geometry is illustrated via the fruitful interplay of the areas indicated above in the context of novel solutions of CAD related, geometric optimization problems involving distance functions: approximation with general B-spline curves and surfaces or with subdivision surfaces, approximation with special surfaces for applications in architecture or manufacturing, approximate conversion from implicit to parametric (NURBS) representation, and registration problems for industrial inspection and 3D model generation from measurement data. Moreover, we describe a ‘feature sensitive’ metric on surfaces, whose definition relies on the concept of an image manifold, introduced into Computer Vision and Image Processing by Kimmel, Malladi and Sochen. This metric is sensitive to features such as smoothed edges, which are characterized by a significant deviation of the two principal curvatures. We illustrate its applications at hand of feature sensitive curve design on surfaces and local neighborhood definition and region growing as an aid in the segmentation process for reverse engineering of geometric objects.     

Implementation and evaluation of the Level Set method: Towards efficient and accurate simulation of wet etching for microengineering applications

The use of atomistic methods, such as the Continuous Cellular Automaton (CCA), is currently regarded as a computationally efficient and experimentally accurate approach for the simulation of anisotropic etching of various substrates in the manufacture of Micro-electro-mechanical Systems (MEMS). However, when the features of the chemical process are modified, a time-consuming calibration process needs to be used to transform the new macroscopic etch rates into a corresponding set of atomistic rates. Furthermore, changing the substrate requires a labor-intensive effort to reclassify most atomistic neighborhoods. In this context, the Level Set (LS) method provides an alternative approach where the macroscopic forces affecting the front evolution are directly applied at the discrete level, thus avoiding the need for reclassification and/or calibration. Correspondingly, we present a fully-operational Sparse Field Method (SFM) implementation of the LS approach, discussing in detail the algorithm and providing a thorough characterization of the computational cost and simulation accuracy, including a comparison to the performance by the most recent CCA model. We conclude that the SFM implementation achieves similar accuracy as the CCA method with less fluctuations in the etch front and requiring roughly 4 times less memory. Although SFM can be up to 2 times slower than CCA for the simulation of anisotropic etchants, it can also be up to 10 times faster than CCA for isotropic etchants. In addition, we present a parallel, GPU-based implementation (gSFM) and compare it to an optimized, multicore CPU version (cSFM), demonstrating that the SFM algorithm can be successfully parallelized and the simulation times consequently reduced, while keeping the accuracy of the simulations. Although modern multicore CPUs provide an acceptable option, the massively parallel architecture of modern GPUs is more suitable, as reflected by computational times for gSFM up to 7.4 times faster than for cSFM.