基于活动轮廓模型的SAR图像分割算法研究
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摘要
图像分割是SAR图像处理的一个基础问题,也是影响SAR图像自动解译性能的关键技术之一。传统分割算法所存在的分割精度不高、分割边界不完整以及难以融合高层理解机制提供的先验知识等缺点,使其无法满足实际的SAR图像分割需求,因而迫切需要一种能将图像本身的低层次视觉属性与待分割区域的先验知识有机结合起来的灵活分割框架,以获得分割区域的完整表达。顺应这种需求,基于活动轮廓模型的分割算法应运而生,并获得了较大的成功。然而,现有的活动轮廓模型一般基于非相干图像提出,因而不能对相干SAR图像的边缘和区域信息正确建模,直接限制了该模型在SAR图像分割领域的应用。而且,活动轮廓模型本身尚存在一些亟待改进之处,如计算效率低下、对初始条件敏感、易陷入局部极小值解等。
针对上述问题,本文以提高分割精度、加快分割速度和提高算法的鲁棒性为目标,对基于活动轮廓模型的SAR图像分割算法开展了系统全面的研究,提出了三类适用于SAR图像分割的活动轮廓模型及与之关联的图像分割算法,且都取得了令人满意的实验结果,具体的创新性研究成果主要包括:
(1)基于SAR图像边缘检测算子,提出了两种改进的短程活动轮廓模型——ROEWA-GAC模型和高效ROEWA-GAC模型,并给出相应的SAR图像分割算法。两种模型的新颖之处主要在于:(a)采用基于ROEWA算子的边缘指示函数,提高了模型对于SAR图像的边缘检测能力和边缘定位精度,更加适合于SAR图像分割;(b)在两种模型的能量泛函中增加“气球力”项,不但加快了曲线演化的速度,而且也在一定程度上降低了模型对初始轮廓的敏感性;(c)两种模型采用不同的方案提高了分割算法的收敛速度。其中,ROEWA-GAC模型的做法是,采用无条件稳定的AOS差分格式并辅以快速的水平集函数重新初始化算法;高效ROEWA-GAC模型的做法是,在能量泛函中加入水平集函数惩罚项,彻底消除水平集函数重新初始化的需求,同时采用简单的显式差分格式并辅以窄带快速算法。
(2)基于最大后验概率准则和变分水平集方法,提出了一种基于区域统计信息的统计活动轮廓模型——MAP-SAC模型,并给出了与之对应的SAR图像分割算法。MAP-SAC模型模型的创新之处在于:(a)直接定义关于水平集函数的能量泛函,并以此为基础推导水平集函数的演化方程。该模型的推导不用假设统计分布的具体形式,具有较强的通用性;对于不同类型的分割问题,只需采用合适的统计分布进行求解。具体到SAR图像分割,采用G~0分布拟合图像数据,增强了模型的分割能力;(b)使用区域统计信息定位分割边界,具有良好的弱边缘检测能力,更适合于SAR图像的分割;(c)引入水平集函数惩罚项,不仅消除了耗时的重新初始化步骤,而且还降低了模型对于初始轮廓设置的敏感性;(d)采用一种半隐式差分格式进行数值近似,保证了模型的无条件稳定性。
(3)基于短程活动轮廓模型和统计活动轮廓模型,提出了一种适用于SAR图像分割的混合活动轮廓模型——HAC模型及其全局优化模型——GHAC模型,并给出了GHAC模型的快速求解算法以及对应的SAR图像分割算法。该模型的新颖之处在于:(a) HAC模型同时结合边缘信息和区域信息定位目标边界,更有利于实现图像的精确分割;(b)在HAC模型中添加基于SAR图像边缘检测算子的边缘信息项,有利于将活动轮廓线吸引到真实的SAR图像边缘;(c)在HAC模型的区域统计信息项中,采用G 0分布拟合SAR图像数据,提高了模型的对图像数据的拟合能力;(d)采用GHAC模型实现HAC模型,克服了HAC模型易陷入局部极小值点的缺点,从而提高了模型的鲁棒性;(e)给出了GHAC模型的快速求解算法,显著地提高了模型的求解效率,进而增强了模型的实用性。
Image segmentation is a fundamental problem for SAR image processing and also one of crucial steps that heavily influences the performance of SAR image automatic interpretation. Because of the limitation of extracting only local information with disconnected boundary of the segmented region, and lack of ability to integrate prior knowledge about the segmented objects, classical image segmentation techniques cannot satisfy the requirement of complex SAR image segmentation applications. In this case, a flexible framework is required that can integrate both low vision information from images and prior knowledge about target objects seamlessly for a consistent representation of the segmentation of the segmented regions. The active contour model based image segmentation techniques just meet this requirement. However, current active contour models are usually proposed for noncoherent images, thus they cannot correctly model the edge-based and region-based information for coherent SAR images, which limits their applications to SAR images. Moreover, there exit some reasons for improving and extending current models further. First, they are inefficient for most images. Second, they are sensitive to initial conditions. Finally, they are prone to trapping into local minima.
To address these problems, this thesis presented some studies concentrated in three topics:
(1) Based on SAR image edge detectors, two novel geodesic active contour models, the ROEWA-GAC model and efficient ROEWA-GAC model, are proposed. The basic idea is that we use an edge indicator function based on the ROEWA operator to replace the original edge indicator function based on gradients. Thus, the ability of detecting edges and the accuracy of locating edges are increased, which make the models more appropriate for SAR image segmentation. In addition, a“balloon force”term is added to the original model’s energy functional in order to enhance the power for curve evolution. As a result, the speed of curve evolution increases and the sensitivity to the initial contour is reduced. Besides, we use two different ways to improve the speed of the models. For the ROEWA-GAC model, an unconditionally stable AOS difference scheme and a fast algorithm for re-initialization of the level set function are adopted, which not only enhance the model’s stability, but also speed up the model’s convergence. For the efficient ROEWA-GAC model, a term penalizing the level set function is added to the energy functional in order to force the level set function to be close to a signed distance function and therefore completely eliminates the need of the costly re-initialization procedure. Thanks to the contribution of this term, the numerical calculation of the model can be implemented by a simple explicit difference scheme; at the same time the evolution speed keeps very fast.
(2) Based on the MAP criterion and variational level set methods, the author proposes a general statistical active contour model and gives a thorough discussion on the theoretical solutions, numerical calculation schemes and segmentation algorithms based on it. The model has several advantages. First, the concrete formulation of the statistical distribution is not assumed in advance. An appropriate distribution is assigned to handle a concrete segmentation problem. Thus it makes our model suitable for various kinds of segmentation problem. This paper adopts the G 0 distribution to fit the SAR image, which overcomes the shortcomings that the distribution used in the current model does not have the good fitting ability for SAR images. As a result, the segmentation accuracy increases. Second, the model uses the regional statistical information to locate the boundaries, which makes it very suitable for SAR edge detection. Third, a level set function penalizing term is added, which makes sure the level set function as a signed distance function. Consequently, the exhaustive reinitialization steps are eliminated and the sensitivity to the initial contours is reduced. Finally, a semi-implicit difference scheme is used to make the numerical calculation unconditionally stable.
(3) Based on the geodesic active contour model and statistical active contour model, the author proposes a novel active contour model with global minimizers and gives a thorough discussion on its theoretical solution, numerical calculation scheme and the corresponding segmentation algorithm. The novelties of the model are as follows. First, the model uses both the edge and region terms to locate object boundaries, which further favors the accurate image segmentation. Second, the edge term based on SAR image edge detectors attracts the contour to the actual image edges. Third, the region term based on the G 0 distribution enhances the fitting ability for SAR images. Finally, a fast global algorithm based on the dual formulation of the total variation is introduced to strengthen the practicability of the model. The experimental results on the simulated images and real MSTAR, ERS, Radasat and NASA/JPL AIRSAR data show that the segmentation algorithm based on the proposed model has several advantages. First, it produces accurate segmented region boundaries. Second, the segmented regions are homogeneous. Third, the computational efficiency is very high and no post-processing steps are needed. Finally, the algorithm is not sensitive to the setup of parameters and robust to initial conditions.
针对上述问题,本文以提高分割精度、加快分割速度和提高算法的鲁棒性为目标,对基于活动轮廓模型的SAR图像分割算法开展了系统全面的研究,提出了三类适用于SAR图像分割的活动轮廓模型及与之关联的图像分割算法,且都取得了令人满意的实验结果,具体的创新性研究成果主要包括:
(1)基于SAR图像边缘检测算子,提出了两种改进的短程活动轮廓模型——ROEWA-GAC模型和高效ROEWA-GAC模型,并给出相应的SAR图像分割算法。两种模型的新颖之处主要在于:(a)采用基于ROEWA算子的边缘指示函数,提高了模型对于SAR图像的边缘检测能力和边缘定位精度,更加适合于SAR图像分割;(b)在两种模型的能量泛函中增加“气球力”项,不但加快了曲线演化的速度,而且也在一定程度上降低了模型对初始轮廓的敏感性;(c)两种模型采用不同的方案提高了分割算法的收敛速度。其中,ROEWA-GAC模型的做法是,采用无条件稳定的AOS差分格式并辅以快速的水平集函数重新初始化算法;高效ROEWA-GAC模型的做法是,在能量泛函中加入水平集函数惩罚项,彻底消除水平集函数重新初始化的需求,同时采用简单的显式差分格式并辅以窄带快速算法。
(2)基于最大后验概率准则和变分水平集方法,提出了一种基于区域统计信息的统计活动轮廓模型——MAP-SAC模型,并给出了与之对应的SAR图像分割算法。MAP-SAC模型模型的创新之处在于:(a)直接定义关于水平集函数的能量泛函,并以此为基础推导水平集函数的演化方程。该模型的推导不用假设统计分布的具体形式,具有较强的通用性;对于不同类型的分割问题,只需采用合适的统计分布进行求解。具体到SAR图像分割,采用G~0分布拟合图像数据,增强了模型的分割能力;(b)使用区域统计信息定位分割边界,具有良好的弱边缘检测能力,更适合于SAR图像的分割;(c)引入水平集函数惩罚项,不仅消除了耗时的重新初始化步骤,而且还降低了模型对于初始轮廓设置的敏感性;(d)采用一种半隐式差分格式进行数值近似,保证了模型的无条件稳定性。
(3)基于短程活动轮廓模型和统计活动轮廓模型,提出了一种适用于SAR图像分割的混合活动轮廓模型——HAC模型及其全局优化模型——GHAC模型,并给出了GHAC模型的快速求解算法以及对应的SAR图像分割算法。该模型的新颖之处在于:(a) HAC模型同时结合边缘信息和区域信息定位目标边界,更有利于实现图像的精确分割;(b)在HAC模型中添加基于SAR图像边缘检测算子的边缘信息项,有利于将活动轮廓线吸引到真实的SAR图像边缘;(c)在HAC模型的区域统计信息项中,采用G 0分布拟合SAR图像数据,提高了模型的对图像数据的拟合能力;(d)采用GHAC模型实现HAC模型,克服了HAC模型易陷入局部极小值点的缺点,从而提高了模型的鲁棒性;(e)给出了GHAC模型的快速求解算法,显著地提高了模型的求解效率,进而增强了模型的实用性。
Image segmentation is a fundamental problem for SAR image processing and also one of crucial steps that heavily influences the performance of SAR image automatic interpretation. Because of the limitation of extracting only local information with disconnected boundary of the segmented region, and lack of ability to integrate prior knowledge about the segmented objects, classical image segmentation techniques cannot satisfy the requirement of complex SAR image segmentation applications. In this case, a flexible framework is required that can integrate both low vision information from images and prior knowledge about target objects seamlessly for a consistent representation of the segmentation of the segmented regions. The active contour model based image segmentation techniques just meet this requirement. However, current active contour models are usually proposed for noncoherent images, thus they cannot correctly model the edge-based and region-based information for coherent SAR images, which limits their applications to SAR images. Moreover, there exit some reasons for improving and extending current models further. First, they are inefficient for most images. Second, they are sensitive to initial conditions. Finally, they are prone to trapping into local minima.
To address these problems, this thesis presented some studies concentrated in three topics:
(1) Based on SAR image edge detectors, two novel geodesic active contour models, the ROEWA-GAC model and efficient ROEWA-GAC model, are proposed. The basic idea is that we use an edge indicator function based on the ROEWA operator to replace the original edge indicator function based on gradients. Thus, the ability of detecting edges and the accuracy of locating edges are increased, which make the models more appropriate for SAR image segmentation. In addition, a“balloon force”term is added to the original model’s energy functional in order to enhance the power for curve evolution. As a result, the speed of curve evolution increases and the sensitivity to the initial contour is reduced. Besides, we use two different ways to improve the speed of the models. For the ROEWA-GAC model, an unconditionally stable AOS difference scheme and a fast algorithm for re-initialization of the level set function are adopted, which not only enhance the model’s stability, but also speed up the model’s convergence. For the efficient ROEWA-GAC model, a term penalizing the level set function is added to the energy functional in order to force the level set function to be close to a signed distance function and therefore completely eliminates the need of the costly re-initialization procedure. Thanks to the contribution of this term, the numerical calculation of the model can be implemented by a simple explicit difference scheme; at the same time the evolution speed keeps very fast.
(2) Based on the MAP criterion and variational level set methods, the author proposes a general statistical active contour model and gives a thorough discussion on the theoretical solutions, numerical calculation schemes and segmentation algorithms based on it. The model has several advantages. First, the concrete formulation of the statistical distribution is not assumed in advance. An appropriate distribution is assigned to handle a concrete segmentation problem. Thus it makes our model suitable for various kinds of segmentation problem. This paper adopts the G 0 distribution to fit the SAR image, which overcomes the shortcomings that the distribution used in the current model does not have the good fitting ability for SAR images. As a result, the segmentation accuracy increases. Second, the model uses the regional statistical information to locate the boundaries, which makes it very suitable for SAR edge detection. Third, a level set function penalizing term is added, which makes sure the level set function as a signed distance function. Consequently, the exhaustive reinitialization steps are eliminated and the sensitivity to the initial contours is reduced. Finally, a semi-implicit difference scheme is used to make the numerical calculation unconditionally stable.
(3) Based on the geodesic active contour model and statistical active contour model, the author proposes a novel active contour model with global minimizers and gives a thorough discussion on its theoretical solution, numerical calculation scheme and the corresponding segmentation algorithm. The novelties of the model are as follows. First, the model uses both the edge and region terms to locate object boundaries, which further favors the accurate image segmentation. Second, the edge term based on SAR image edge detectors attracts the contour to the actual image edges. Third, the region term based on the G 0 distribution enhances the fitting ability for SAR images. Finally, a fast global algorithm based on the dual formulation of the total variation is introduced to strengthen the practicability of the model. The experimental results on the simulated images and real MSTAR, ERS, Radasat and NASA/JPL AIRSAR data show that the segmentation algorithm based on the proposed model has several advantages. First, it produces accurate segmented region boundaries. Second, the segmented regions are homogeneous. Third, the computational efficiency is very high and no post-processing steps are needed. Finally, the algorithm is not sensitive to the setup of parameters and robust to initial conditions.
引文
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