【作者】 李灿飞；

【导师】 王耀南；

【作者基本信息】 湖南大学 ， 模式识别与智能系统， 2012， 博士

【摘要】 医学图像分析是临床影像诊断和手术计划必不可少的重要工具。现代成像技术的快速发展,在提高目标分辨率的同时导致数据量和复杂度显著增加,进而对图像处理算法的性能和自动化程度提出更高的要求。图像增强与图像分割是医学图像分析的基本步骤,也是病灶定位和量化评估的必要环节,因而在整个计算机辅助诊疗系统中发挥着不可或缺的作用。偏微分方程(PDE)方法以其坚实的数学基础和灵活的开放框架,有利于融合其它理论,开发新模型以满足不同成像模态、不同应用背景图像分析需求,已成为医学图像处理领域最流行的方法之一。作为偏微分方程图像分析理论的基石,非线性扩散、主动轮廓线模型以及水平集方法,在医学图像增强滤波以及分割中得到广泛应用。本文主要针对当前医学图像增强滤波和分割中的若干难题,开展偏微分方程医学图像处理算法研究,为计算机辅助诊疗系统的开发奠定核心技术基础。具体工作如下：1)在超声图像相关斑点噪声抑制方面,通过引入S型流导函数改进传统的噪声各项异性扩散模型SRAD,提出了新的斑点噪声各项异性扩散模型NSRAD。基本思想是结合不同区域图像特点,采用分段式扩散系数设计：即扩散系数在同质区域取值趋近常数1,在过渡区域为急剧下降函数,在强边界区域则几乎为O。受益于S型流导函数,新的NSRAD模型与原SRAD相比,具有更好的噪声抑制平滑能力,更好的细节与弱边界保留能力、以及更强的锐化强边界的能力。此外,扩散系数的同质区域尺度控制比率与速度控制系数可以调节,能够解决超声图像中存在的不同尺度同质区域的问题,使模型能够满足不同的应用要求。2)针对传统多相Chan-Vese模型由于单纯依靠区域灰度均值的速度函数构造方法,容易引起波阵面错乱,可能导致各演化曲线被同一目标吸引,而产生错误结果的问题。本文在Chan-Vese模型的基础上提出了一种层级分裂的Chan-Vese主动轮廓线模型。基本思想是在基本模型基础上,加入层级分裂的思想,即在上层分割结果的基础上得到并标注子图像,根据需要,提取进一步需要分割的子图像进行更深层次的分割,直到分割结果满足不同层次的应用要求时终止。该模型除了保持了原Chan-Vese模型的所有优点之外,还具有自己独特的优点：第一,下级的子分割,仅仅在上一级分割后得到的子区域而不是在整个图像区域进行,演化曲线有了区域约束,解决了多相Chan-Vese模型中各相曲线同时演化时、由于没有相互约束、可能被同一目标所吸引,导致不能得到正确分割结果的缺点；第二,由于该模型在每次分割中只需考虑一个水平集函数,采用层级计算,相比于多相水平集方法更容易实现；第三,通过层级处理技术,逐步深入分割以满足不同层次的应用要求。3)模糊聚类分割属于低层次图像处理技术,通常需要后续的边界连接等人工处理,不利于图像处理的自动化分析。而主动轮廓线是能够融合上层先验知识的封闭光滑的演化曲线。因此本文提出一种结合模糊聚类与主动轮廓线的模型,应用于图像,特别是医学图像分割。其基本思想是：耦合由模糊聚类提供的先验统计信息基础上计算得到的区域信息和边界信息,并增加一个人工约束项作为互斥项,保证提高曲线收敛能力的同时,避免区域重迭或者象素被漏掉的情况,从而建立起耦合边界与区域信息的最小化目标函数。通过极速下降法,求得最小化目标函数所对应的偏微分方程,并利用水平集技术求解。新模型具有如下优点：第一,解决了传统的模糊聚类分割存在边界不连续,而需要后续连接边界处理的问题；第二,水平集技术的利用,使新模型具有自由处理拓扑变形的能力；第三,新模型是在最小能量驱动下的光滑曲线演化,减少了模糊聚类分割中存在的孤立噪声点引起的伪区域；第四,该模型除了可以用于图像分割之外还可以应用于图像跟踪。4)在分析血管图像微分检测原理的基础上,提出一种改进的GVF扩散3D血管图像增强滤波新方法,并且把最大通量法融入水平集框架,进行血管图像分割。新方法推导定义出新的血管增强滤波似然函数,具有如下优点：第一,摒弃了血管径向方向的特征值,从而对轴向密度变化不敏感,有利于保持轴向密度；第二,通过加入抑制因子,抑制边界重叠与模糊,锐化了边缘；第三,不需要使用参数,简化了计算并有利于实现。此外,新方法采用梯度向量场未归一化进行计算,与已存在的梯度向量场归一化方法相比,不仅比较完整的保留了血管的网络拓扑结构,而且克服了原梯度向量场归一化方法,在血管半径估计方面的不足,取得了更满意的增强滤波与分割结果。本文的研究,旨在为偏微分方程在医学图像处理中的研究和应用添砖加瓦,主要在非线性扩散图像增强滤波,曲线演化图像分割,以及比较棘手的3D血管图像增强滤波与分割等内容上,做了更深一步的研究和扩充。文中提出的各种新模型和新方法,在为研究者提供广阔的视野以及良好的应用前景上具有重要的意义。更多还原

【Abstract】 The rapid development of modern imaging techniques improves the resolution of the target, but leads to a significant increase in the amount of data and complexity simultaneously, which puts forward higher requirements on the performance and automaticity of image processing algorithms. As the basic steps to medical image analysis, image enhancement and segmentation are the necessary parts of lesion localization and quantitative assessment thus play an indispensable role in the computer-aided diagnosis and treatment system.For the solid mathematical foundation and the flexible open framework, Partial Differential Equations (PDE) is conducive to integrating other theories and developing new models to meet the needs of different imaging modes and image analysis in different application background, which has become one of the most popular methods in the field of medical image processing. As a footstone of PDE image analysis theory, nonlinear diffusion, the active contour model and level set method have been widely used in image filtering and segmentation in medical image enhancement.This dissertation concentrates on some difficulties in medical image enhancement and segmentation to carry out PDE research on medical image processing and lay the basis of the core technology for the development of computer-aided diagnosis system. The main work and innovations of this dissertation are listed as follows:1) In the area of speckle noise suppression for ultrasound image, a new speckle reducing anisotropic diffuse (NSRAD) is proposed by introducing a sigmoid function to the diffusion coefficient in the traditional SRAD. The basic route of NSRAD is to combine the image characteristics of different regions using segmented diffusion coefficient, in which the diffusion coefficient approaches to a constant number one in the homogeneous regions, and declines rapidly in the transition regions, then approaches to zero in the strong boundary regions. Benefited by the sigmoid function in the new diffusion function, the NSRAD has better noise-suppressing ability, as well as the abilities of retaining details and weak edges, even sharp the strong boundary, compared to the traditional SRAD. Moreover, the control ratio of the homogeneous regions and the speed control coefficient are adjustable, which well meet different application requirements by solving the problem of different homogeneous regions scales in the ultrasound image.2) The traditional multi-phase Chan-Vese model may generate error results as it solely relies on the speed function constructed by the regional mean gray, which may easily cause wave front disorder and lead several evolution curves attracting to the same goal. To solve this problem, a new hierarchical splitting Chan-Vese active contour method for image segmentation is presented. Its basic route is to add the hierarchical splitting segmentation to the basic Chan-Vese model. In detail, the segmentation results are obtained and the sub-images are marked by the upper level segmentation, and then further segmented by extracting the sub-images that need further segmentation. The whole process is terminated when the segmentation results meet different levels of application requirements. The model has all the advantages of the original Chan-Vese model, as well as the following advantages:Firstly, the lower level segmentation is only performed on the sub-image obtained by the upper level segmentation rather than the entire image area. This solves the problem that the segmentation results are incorrect due to the lack of mutual constraints in the multi-phase Chan-Vese model when several curves evolution attract to the same goal. Secondly, only one level set function is considered at each split computing. Accordingly, the mode is easier to achieve compared to the multiphase level set method. Thirdly, segmentation can been deepen gradually to meet different levels of application requirements by the hierarchical method.3) Fuzzy classification of segmentation is a low-level image processing techniques and performs weakly in the automated image processing due to its requirement of subsequent manual boundary connections. However, the active contour is a closed smooth evolution curve, which can fuse the upper prior knowledge. Thus, in this dissertation, a new model is presented to integrate the fuzzy clustering and active contour for image segmentation, especially for medical image segmentation. The basic idea is as follows:by coupling the region information and the boundary one which are calculated by the priori statistical information gotten from the fuzzy clustering, and adding an artificial force not only to increase the robustness and the convergence rate by imposing the idea of mutually exclusive propagating curves but also to constrain regions not overlap and no pixels not assigned to any region, the minimum objective function coupling region and boundary one is established. The PDE corresponding to the defined objective function minimization is established by a gradient descent method. And a level set approach is used to solve the PDE system. The new model has the following advantages:firstly, the new model solves the problem that the boundary requires subsequent connections in the traditional fuzzy classification segmentation for its discontinuity boundary. Secondly, the new model has the ability to freely deal with the topological deformation due to the level set method. Thirdly, the new model is the curves evolution driven by the minimum energy, which can reduce the pseudo-region caused by the isolated noise points. Fourthly, the model can be used not only for image segmentation but also for image tracking.4) Based on the analysis of vascular image differential detection principle, an improved GVF diffusion3D blood vessel image enhancement filter is presented, which fuses maximum flux method into the level set framework for vascular image segmentation. The new blood vessels likelihood function is derived and defined in the new method. It has the following advantages:Firstly, the new blood vessels likelihood function is insensitive to the changes in the axial density by abandoning the eigenvalues for the blood vessels radial direction, which well preserves the axial density. Secondly, the new blood vessels likelihood function can inhibit the overlapped and vague border, and sharpen the edge by adding the inhibitory factor. Thirdly, the new blood vessels likelihood function does not require any parameter, which is conducive to simplify implementation. Moreover, the new method calculated by non-normalized gradient vector field is better than the existing method calculated by the corresponding normalized vector field. The new method can achieve better effect in the image enhance filter, which can well keep the whole topology of the3D blood vessel network, and overcome the deficiency in estimating the blood vessel radius than the existing one.This dissertation contributes to the application domains of PDE method in image processing and provides new techniques for nonlinear diffusion, curve evolution method and the intractable3D blood vessel enhancement filtering and segmentation. The new models and methods proposed in this dissertation widen the research horizon of contemporary and have a promising future.更多还原