基于变分水平集方法的图像分割和目标轮廓跟踪研究
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摘要
基于变分水平集方法的图像分割模型在医学图像分割、视频跟踪等众多领域有着广泛应用。然而，现有的主动轮廓模型主要是针对目标和背景区域的灰度值比较均匀的图像而提出的，因而很难对灰度异质或低对比度图像的区域信息进行正确建模，这直接限制了该模型在图像分割领域的应用。而且，主动轮廓模型本身也存在一些需要改进的地方，如计算效率较低、对初始演化曲线的位置和形状较敏感、容易陷入局部极小值解等。
针对图像分割方法目前所存在的问题，本文以提高图像分割的精确度、降低图像分割的耗时量和增强分割算法的适用性为目标，对基于变分水平集方法的图像分割算法展开了系统全面的研究，提出了三类适用于灰度异质图像分割和序列图像分割的主动轮廓模型，以及与之相关的图像分割算法，并且均得到了理想的实验结果，具体的一些具有理论意义和实用价值的成果包括：
（一）在变分水平集分割算法中，C-V模型无法分割目标与背景灰度不均匀的图像，而LBF分割模型只考虑图像的局部灰度信息，有时会出现过度分割现象。针对此问题，提出一种基于局部和全局信息的活动轮廓模型（LGBF），将C-V模型与LBF模型的优势相结合，确定符合实际需要的能量泛函，详细讨论了所改进模型的局部能量项、全局能量项和惩罚能量项。由于引入了水平集函数的能量惩罚项，不仅消除了耗时的演化曲线重新初始化的步骤，而且还降低了模型对于初始演化曲线位置与形状设置的敏感性。同时，对曲线演化方程进行了理论求解，给出半隐差分格式的数值近似方案以及相应的灰度异质图像分割算法。通过对灰度异质图像和医学CT图像等实测数据进行实验，将改进算法的实验结果与现有的C-V活动轮廓模型以及LBF活动轮廓模型的实验结果进行比较，验证了所提模型是可靠和有效的。
（二）针对医学图像处理中的多相图像分割问题，利用多相水平集函数将两区域的LGBF模型推广到多区域的LGBF模型，从而刻画出所给定的医学CT图像的多个目标区域的结构特征。根据变分水平集方法，建立出适用于多相图像分割的能量泛函表达式。医学CT图像和MR图像的目标区域具有很明显的结构特征，一般由白色物质、浅灰色物质、深灰色物质以及黑色背景这四种区域构成，而且这些目标区域的强度是不均匀的。为了更加清晰地划分图像目标中各个不同的子区域，以四相图像分割为例，推导出新模型演化方程的理论求解过程，并设计出无条件稳定的半隐式差分格式的数值实现方案。经过对灰度不均匀的医学图像等实测数据进行分割实验，获得了比较令人满意的多相分割效果。
（三）对于医学视频中的目标轮廓检测与跟踪问题，需要满足实时性和精确性的要求。针对心脏冠状动脉的跟踪问题，其序列图像具有目标和背景的灰度比较接近、图像的灰度不均匀以及目标的形状变化明显等特点。本研究提出一种快速的单参数无边缘活动轮廓模型，可以根据测地线活动区域特征对目标位置进行快速定位。所给出新模型的能量泛函表达式包括测地线活动区域项、局部二值拟合项、长度约束项和符号距离惩罚项；利用变分水平集方法，通过Euler-Lagrange方程得到最小化能量泛函的梯度下降流方程；接着确定运动目标的边界特征，提取运动目标的背景并估计运动矢量场；同时还利用边界特征来提供更精确的目标形状信息，通过对运动矢量的估计与修正达到了适应运动目标的拓扑结构变化。最后，对心脏冠状动脉造影的序列图像进行了运动目标检测与跟踪，实验结果理想。
The variational level set method are widely used in many areas, such as the medicalimage segmentation and video tracking. However, the existing active contour models aresuitable for the intensity uniform gray images, and not suitable for the intensityinhomogeneity images and low-contrast grayscale images, which have directly limited theapplication of the active contour models. Moreover, there are some fields need to be improved,such as the calculation complexity, the sensitiveness of initial conditions, and which are easyto fall into the local minima solution.
In order to improving the segmentation accuracy and reducing the segmentation time,three active contour models are proposed after the research of image segmentation algorithm,which can segment the inhomogeneity intensity images and serial images. Three kinds of theimage segmentation algorithm have achieved the good experiment results. The maintheoretical and practical results are as following:
(1) In the variational level set segmention algorithms, the C-V model can not segmentthe images with inhomogeneity target and background, and the local intensity information areonly considered into the LBF model which has appeared the over segmentation phenomenon.For these problems, we have proposed the local and global binary fitting active contoursmodel, which has combined the advantage of C-V model and LBF model. Three energyfunctionals are determined, which are local energy functional, global energy functional andpunishment energy functional. Due to introduce the punishment items of level set function,we have not only eliminated the reinitialized steps, but also reduced the sensitivity of theLGBF model for initial contours. At the same time, this research has given the theory solutionof curve evolution, the numerical approximate solutions of the half implicit difference scheme,and inhomogeneity image segmentation algorithm. We have taken experiments for theinhomogeneity gray images and medical CT images, and compared with the C-V model andLBF model. It can be concluded that the LGBF model is reliable and effective.
(2) In view of multiphase segmentation problem in medical image processing, the two regional LGBF model has been extended into the multiphase level set method for activecontours model, which can characterize the target areas of the given medical CT images.According to the variational level set method, the energy functional expressions for themultiphase image segmentation have been proposed in this research. The target areas of themedical CT images and MR images have obvious structure characteristic, which arecomposed of four parts, white substance area, pale gray matter area, dark grey area and blackbackground. The intensity of the four areas are not uniform. In order to classified the differenttarget areas more clearly, four-phase image segmentation has been taken as an example, andthe evolution equations of the improved model have been derived from the theory of solvingprocess. It has been designed that the half implicit difference scheme of numericalimplementation scheme with unconditional stability. We have obtained the satisfactorymultiphase segmentation results through the segmentation experiments of inhomogeneitymedical images.
(3) The object detection and tracking have need to meet the requirements of real-timeand accuracy in medical video stream. The serial images of coronary artery have thecharacteristic with inhomogeneity intensity, and the target areas are closed to the backgroundareas, also the shape of target areas have changed obviously. This research work has proposeda fast single-parameter active contour model without edges, which can quickly locate thetarget position based on the geodesic active contours model. The given energy functionalexpressions of the new model have included the geodesic active region items, local binaryfitting items, the length constraint items and the symbol distance penalty items; according tothe variational level set method, the energy functionals are minimized by Euler-Lagrangeequation, and we have got the gradient descent flow equations; then determined the boundaryof moving object, extracted the background of moving object and estimated the motion vectorfield, which have adapted the topology changes of moving targets. Finally, we have done theexperiment of the serial images of coronary angiography, and the experimental results aresatisfactory.
针对图像分割方法目前所存在的问题，本文以提高图像分割的精确度、降低图像分割的耗时量和增强分割算法的适用性为目标，对基于变分水平集方法的图像分割算法展开了系统全面的研究，提出了三类适用于灰度异质图像分割和序列图像分割的主动轮廓模型，以及与之相关的图像分割算法，并且均得到了理想的实验结果，具体的一些具有理论意义和实用价值的成果包括：
（一）在变分水平集分割算法中，C-V模型无法分割目标与背景灰度不均匀的图像，而LBF分割模型只考虑图像的局部灰度信息，有时会出现过度分割现象。针对此问题，提出一种基于局部和全局信息的活动轮廓模型（LGBF），将C-V模型与LBF模型的优势相结合，确定符合实际需要的能量泛函，详细讨论了所改进模型的局部能量项、全局能量项和惩罚能量项。由于引入了水平集函数的能量惩罚项，不仅消除了耗时的演化曲线重新初始化的步骤，而且还降低了模型对于初始演化曲线位置与形状设置的敏感性。同时，对曲线演化方程进行了理论求解，给出半隐差分格式的数值近似方案以及相应的灰度异质图像分割算法。通过对灰度异质图像和医学CT图像等实测数据进行实验，将改进算法的实验结果与现有的C-V活动轮廓模型以及LBF活动轮廓模型的实验结果进行比较，验证了所提模型是可靠和有效的。
（二）针对医学图像处理中的多相图像分割问题，利用多相水平集函数将两区域的LGBF模型推广到多区域的LGBF模型，从而刻画出所给定的医学CT图像的多个目标区域的结构特征。根据变分水平集方法，建立出适用于多相图像分割的能量泛函表达式。医学CT图像和MR图像的目标区域具有很明显的结构特征，一般由白色物质、浅灰色物质、深灰色物质以及黑色背景这四种区域构成，而且这些目标区域的强度是不均匀的。为了更加清晰地划分图像目标中各个不同的子区域，以四相图像分割为例，推导出新模型演化方程的理论求解过程，并设计出无条件稳定的半隐式差分格式的数值实现方案。经过对灰度不均匀的医学图像等实测数据进行分割实验，获得了比较令人满意的多相分割效果。
（三）对于医学视频中的目标轮廓检测与跟踪问题，需要满足实时性和精确性的要求。针对心脏冠状动脉的跟踪问题，其序列图像具有目标和背景的灰度比较接近、图像的灰度不均匀以及目标的形状变化明显等特点。本研究提出一种快速的单参数无边缘活动轮廓模型，可以根据测地线活动区域特征对目标位置进行快速定位。所给出新模型的能量泛函表达式包括测地线活动区域项、局部二值拟合项、长度约束项和符号距离惩罚项；利用变分水平集方法，通过Euler-Lagrange方程得到最小化能量泛函的梯度下降流方程；接着确定运动目标的边界特征，提取运动目标的背景并估计运动矢量场；同时还利用边界特征来提供更精确的目标形状信息，通过对运动矢量的估计与修正达到了适应运动目标的拓扑结构变化。最后，对心脏冠状动脉造影的序列图像进行了运动目标检测与跟踪，实验结果理想。
The variational level set method are widely used in many areas, such as the medicalimage segmentation and video tracking. However, the existing active contour models aresuitable for the intensity uniform gray images, and not suitable for the intensityinhomogeneity images and low-contrast grayscale images, which have directly limited theapplication of the active contour models. Moreover, there are some fields need to be improved,such as the calculation complexity, the sensitiveness of initial conditions, and which are easyto fall into the local minima solution.
In order to improving the segmentation accuracy and reducing the segmentation time,three active contour models are proposed after the research of image segmentation algorithm,which can segment the inhomogeneity intensity images and serial images. Three kinds of theimage segmentation algorithm have achieved the good experiment results. The maintheoretical and practical results are as following:
(1) In the variational level set segmention algorithms, the C-V model can not segmentthe images with inhomogeneity target and background, and the local intensity information areonly considered into the LBF model which has appeared the over segmentation phenomenon.For these problems, we have proposed the local and global binary fitting active contoursmodel, which has combined the advantage of C-V model and LBF model. Three energyfunctionals are determined, which are local energy functional, global energy functional andpunishment energy functional. Due to introduce the punishment items of level set function,we have not only eliminated the reinitialized steps, but also reduced the sensitivity of theLGBF model for initial contours. At the same time, this research has given the theory solutionof curve evolution, the numerical approximate solutions of the half implicit difference scheme,and inhomogeneity image segmentation algorithm. We have taken experiments for theinhomogeneity gray images and medical CT images, and compared with the C-V model andLBF model. It can be concluded that the LGBF model is reliable and effective.
(2) In view of multiphase segmentation problem in medical image processing, the two regional LGBF model has been extended into the multiphase level set method for activecontours model, which can characterize the target areas of the given medical CT images.According to the variational level set method, the energy functional expressions for themultiphase image segmentation have been proposed in this research. The target areas of themedical CT images and MR images have obvious structure characteristic, which arecomposed of four parts, white substance area, pale gray matter area, dark grey area and blackbackground. The intensity of the four areas are not uniform. In order to classified the differenttarget areas more clearly, four-phase image segmentation has been taken as an example, andthe evolution equations of the improved model have been derived from the theory of solvingprocess. It has been designed that the half implicit difference scheme of numericalimplementation scheme with unconditional stability. We have obtained the satisfactorymultiphase segmentation results through the segmentation experiments of inhomogeneitymedical images.
(3) The object detection and tracking have need to meet the requirements of real-timeand accuracy in medical video stream. The serial images of coronary artery have thecharacteristic with inhomogeneity intensity, and the target areas are closed to the backgroundareas, also the shape of target areas have changed obviously. This research work has proposeda fast single-parameter active contour model without edges, which can quickly locate thetarget position based on the geodesic active contours model. The given energy functionalexpressions of the new model have included the geodesic active region items, local binaryfitting items, the length constraint items and the symbol distance penalty items; according tothe variational level set method, the energy functionals are minimized by Euler-Lagrangeequation, and we have got the gradient descent flow equations; then determined the boundaryof moving object, extracted the background of moving object and estimated the motion vectorfield, which have adapted the topology changes of moving targets. Finally, we have done theexperiment of the serial images of coronary angiography, and the experimental results aresatisfactory.
引文
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