基于变分水平集的图像分割方法研究
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摘要
图像分割是图像理解和识别的前提，并作为图像处理的基础环节，一直是图像处理和计算机视觉领域的热点和难点问题。基于水平集图像分割方法，由于其具有自由拓扑变换以及多信息共融性的优点，近年来受到众多学者的关注。但水平集方法仍处于发展阶段，用它来分割灰度不均匀或目标类型多且拓扑关系复杂场景的图像并不理想，其理论和应用有待进一步完善。
在此背景下，本论文开展了基于变分水平集图像分割方法的研究，并取得了如下研究成果：提出了基于局部驱动核活动轮廓模型、基于多分辨率多水平集分割方法、基于统计方法区域合并优先多水平集分割方法、多区域图像分割的多层水平集方法等。本文主要研究内容及创新点包括：
（1）为解决灰度不均匀现象对医学图像的干扰问题，本文提出了基于局部驱动核活动轮廓（LKAC）模型。通过引入局部图像信息，该模型能有效地分割灰度不均匀图像。在规则化项中增加的能量惩罚项，使得水平集函数在演化过程中保持为近似的符号距离函数。与LIF模型和LBF模型相比，LKAC模型在迭代过程中无需进行卷积操作，极大地提高了计算效率。实验结果进一步证实LKAC模型比LIF模型和LBF模型有更好的分割效果和更快的计算效率，并对轮廓曲线初始条件不敏感。
（2）针对多水平集方法中的混分现象，本文提出基于多分辨率多水平集图像分割方法。该方法用N1个水平集函数将图像分割成N (N﹥1)个区域，每个水平集函数表达一个区域，通过建立独立多水平集函数可以消除多余的轮廓，避免分割区域的重叠和漏分。多分辨率技术能防止水平集能量函数陷入局部最小值，缓解遥感图像中噪声等引起的类别错分问题，并能减小计算量。为了避免水平集函数在每次迭代后需重新初始化符号距离函数，增加的能量惩罚项能使水平集函数在演化过程中保持为逼近的符号距离函数。
（3）针对多相图像中未知分割区域数问题，本文提出了基于统计方法的区域合并优先的多水平集（MRLSM-RMP-SA）方法。通过在能量项中增加了区域合并优先项，该项能使部分水平集函数在曲线演化过程中消失，从而得到理想的分割区域数。用贝叶斯理论估计整个图像域强度和高斯分布核函数估算图像的先验概率，使得计算简单而有效。通过与多种多水平集方法实验对比，实验结果显示只有MRLSM-RMP-SA方法能使分割区域数达到理想数目，得到较好的分割效果。
（4）通过在水平集方法中引入图像层概念，本文提出了一种多区域图像分割的多层水平集方法。与通常所用的多水平集方法不同，通过在单图像层上用双水平集分割方法进行分割图像，当演化曲线满足终止条件时提取目标，然后用前景填充技术将提取的目标用背景区域的灰度均值进行填充，直至水平集演化过程再没有任何目标区域可以分割为止。在整个曲线演化过程中不需要人工干涉，并且具有较低的计算复杂度和更快的收敛速度。
Image segmentation, which is a basic part of image processing, isthe premise of image understanding and target recognition, and has beena hot and difficult problem in the field of image processing and computervision. Level set method for image segmentation has advantages overtopological changes in a natural way and can be implemented by fusingmore information. Thus, in recent years, many researchers have also donea great deal of effort to improve the performance of the imagesegmentation algorithms. But level set method is still staying in thedeveloping stage, and can’t obtain the satisfactory results when theimages with intensity inhomogeneity or complex homogeneous objectswith multiple regions and topological changes are segmented. Thus, theinvestigation of its theory and application should be improved.
In this paper, the variational level set methods have been deeplyinvestigated. Some efficient algorithms have been proposed, such as localkernel-driven active contour model, multiple level set method withmultiresolution, statistical approaches to automatic level set imagesegmentation with multiple regions, and multilayer level set method withmultiple regions. The main works can be summarized as follows:
(1) To solve the problem caused by intensity inhomogeneity inmedical images, we proposed local kernel-driven active contour (LKAC)model. By incorporating local image information, the proposed modelcan efficiently segment the image with intensity inhomogeneity. The levelset function can maintain an approximate signed distance function byintroducing a penalizing energy into the regularization term. Compared with the LIF model and LBF model, the LKAC model can greatlyimprove the computational cost due to no need for the convolutionoperation during iterations. The experimental results show the LKACmodel has better performance and higher computational efficiency thanthe LIF model and LBF model. In addition, the proposed model is notsensitive to initial conditions.
(2) To solve the problem of misclassification existing in multiplelevel set method, multi-resolution level set method with multiple regionsis proposed. The N regions in the image are segmented using N1curvesand each curve represents one region, which avoids generating theoverlapped segmentation regions. A multi-resolution level set schema isproposed to avoid the energy functional in a local minimum, alleviatemisclassification caused by noises in remote sensing images, and toreduce the computational cost. To ensure the smoothness of the level setfunction and eliminate the requirement of re-initialization, the distanceregularizing term is added to maintain an approximate signed distancefunction.
(3) To solve the unknown number of segmented regions in multiplelevel set methods, we propose a multi-region level set method with aregion merging prior based on statistical approach (MRLSM-RMP-SA).By incorporating a region merging prior term into the energy functional,the term makes some level-set functions disappear during curve evolutionand can obtain the ideal number of segmented regions. A Bayesian theory,which is used to compute the intensity probability in the whole imagedomain, and the Gaussian kernel function, which estimates the priorprobability, make the algorithm efficient and simple. Compared withmany multiphase level set methods, the experiments show only the MRLSM-RMP-SA method can obtain the ideal number of segmentedregions and get better segmentation results.
(4) By introducing a conception of image layer, a multilayer levelset method for multi-region image segmentation is proposed. Differentfrom usual multiple level set methods, the double level set method isemployed to segment the images in each image layer. The objects areextracted when a termination condition for each image layer is satisfied.Then, a foreground-filled technique is used to fill the object regions withan average of the intensities of outer regions. The process is over untilthere are no objects to segment. In the whole process of curve evolution,it does not need artificial interference, and has low complexity and fasterconvergence speed.
在此背景下，本论文开展了基于变分水平集图像分割方法的研究，并取得了如下研究成果：提出了基于局部驱动核活动轮廓模型、基于多分辨率多水平集分割方法、基于统计方法区域合并优先多水平集分割方法、多区域图像分割的多层水平集方法等。本文主要研究内容及创新点包括：
（1）为解决灰度不均匀现象对医学图像的干扰问题，本文提出了基于局部驱动核活动轮廓（LKAC）模型。通过引入局部图像信息，该模型能有效地分割灰度不均匀图像。在规则化项中增加的能量惩罚项，使得水平集函数在演化过程中保持为近似的符号距离函数。与LIF模型和LBF模型相比，LKAC模型在迭代过程中无需进行卷积操作，极大地提高了计算效率。实验结果进一步证实LKAC模型比LIF模型和LBF模型有更好的分割效果和更快的计算效率，并对轮廓曲线初始条件不敏感。
（2）针对多水平集方法中的混分现象，本文提出基于多分辨率多水平集图像分割方法。该方法用N1个水平集函数将图像分割成N (N﹥1)个区域，每个水平集函数表达一个区域，通过建立独立多水平集函数可以消除多余的轮廓，避免分割区域的重叠和漏分。多分辨率技术能防止水平集能量函数陷入局部最小值，缓解遥感图像中噪声等引起的类别错分问题，并能减小计算量。为了避免水平集函数在每次迭代后需重新初始化符号距离函数，增加的能量惩罚项能使水平集函数在演化过程中保持为逼近的符号距离函数。
（3）针对多相图像中未知分割区域数问题，本文提出了基于统计方法的区域合并优先的多水平集（MRLSM-RMP-SA）方法。通过在能量项中增加了区域合并优先项，该项能使部分水平集函数在曲线演化过程中消失，从而得到理想的分割区域数。用贝叶斯理论估计整个图像域强度和高斯分布核函数估算图像的先验概率，使得计算简单而有效。通过与多种多水平集方法实验对比，实验结果显示只有MRLSM-RMP-SA方法能使分割区域数达到理想数目，得到较好的分割效果。
（4）通过在水平集方法中引入图像层概念，本文提出了一种多区域图像分割的多层水平集方法。与通常所用的多水平集方法不同，通过在单图像层上用双水平集分割方法进行分割图像，当演化曲线满足终止条件时提取目标，然后用前景填充技术将提取的目标用背景区域的灰度均值进行填充，直至水平集演化过程再没有任何目标区域可以分割为止。在整个曲线演化过程中不需要人工干涉，并且具有较低的计算复杂度和更快的收敛速度。
Image segmentation, which is a basic part of image processing, isthe premise of image understanding and target recognition, and has beena hot and difficult problem in the field of image processing and computervision. Level set method for image segmentation has advantages overtopological changes in a natural way and can be implemented by fusingmore information. Thus, in recent years, many researchers have also donea great deal of effort to improve the performance of the imagesegmentation algorithms. But level set method is still staying in thedeveloping stage, and can’t obtain the satisfactory results when theimages with intensity inhomogeneity or complex homogeneous objectswith multiple regions and topological changes are segmented. Thus, theinvestigation of its theory and application should be improved.
In this paper, the variational level set methods have been deeplyinvestigated. Some efficient algorithms have been proposed, such as localkernel-driven active contour model, multiple level set method withmultiresolution, statistical approaches to automatic level set imagesegmentation with multiple regions, and multilayer level set method withmultiple regions. The main works can be summarized as follows:
(1) To solve the problem caused by intensity inhomogeneity inmedical images, we proposed local kernel-driven active contour (LKAC)model. By incorporating local image information, the proposed modelcan efficiently segment the image with intensity inhomogeneity. The levelset function can maintain an approximate signed distance function byintroducing a penalizing energy into the regularization term. Compared with the LIF model and LBF model, the LKAC model can greatlyimprove the computational cost due to no need for the convolutionoperation during iterations. The experimental results show the LKACmodel has better performance and higher computational efficiency thanthe LIF model and LBF model. In addition, the proposed model is notsensitive to initial conditions.
(2) To solve the problem of misclassification existing in multiplelevel set method, multi-resolution level set method with multiple regionsis proposed. The N regions in the image are segmented using N1curvesand each curve represents one region, which avoids generating theoverlapped segmentation regions. A multi-resolution level set schema isproposed to avoid the energy functional in a local minimum, alleviatemisclassification caused by noises in remote sensing images, and toreduce the computational cost. To ensure the smoothness of the level setfunction and eliminate the requirement of re-initialization, the distanceregularizing term is added to maintain an approximate signed distancefunction.
(3) To solve the unknown number of segmented regions in multiplelevel set methods, we propose a multi-region level set method with aregion merging prior based on statistical approach (MRLSM-RMP-SA).By incorporating a region merging prior term into the energy functional,the term makes some level-set functions disappear during curve evolutionand can obtain the ideal number of segmented regions. A Bayesian theory,which is used to compute the intensity probability in the whole imagedomain, and the Gaussian kernel function, which estimates the priorprobability, make the algorithm efficient and simple. Compared withmany multiphase level set methods, the experiments show only the MRLSM-RMP-SA method can obtain the ideal number of segmentedregions and get better segmentation results.
(4) By introducing a conception of image layer, a multilayer levelset method for multi-region image segmentation is proposed. Differentfrom usual multiple level set methods, the double level set method isemployed to segment the images in each image layer. The objects areextracted when a termination condition for each image layer is satisfied.Then, a foreground-filled technique is used to fill the object regions withan average of the intensities of outer regions. The process is over untilthere are no objects to segment. In the whole process of curve evolution,it does not need artificial interference, and has low complexity and fasterconvergence speed.
引文
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