基于广义Gamma分布的水平集SAR图像分割
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摘要
合成孔径雷达(Synthetic Aperture Radar, SAR)能够在任何天气、任何时刻进行工作,并且SAR的分辨率与距离无关,能够穿透云雾、烟尘等障碍物,从而获得大面积地表信息,因此SAR的地位举足轻重。但是由于SAR的成像机理是相干成像系统,不可避免的存在相干斑噪声,因此,适用于光学图像的一般分割方法对SAR图像不适用,本文需要研究针对SAR的分割方法。
在SAR图像分割领域,水平集方法是一类比较重要的方法。水平集方法由于能够处理曲线拓扑结构变化、分割速度快等优点,得到了广泛的应用。针对SAR图像的特点,水平集方法研究主要集中在两点上：一种是先对SAR图像进行滤波,然后利用针对一般光学图像的水平集方法进行分割；一种是直接对SAR图像进行分割。因为第一种方法在滤波的同时也消损了图像本身的边缘信息,因此我们采用直接对SAR图像进行分割的方法。本文提出了两点基于广义Gamma统计模型的SAR图像水平集分割方法：
1)针对各种分布均匀、不均匀以及极度不均匀的强度和幅度SAR图像,本文提出了一种基于广义Gamma分布似然函数的水平集SAR图像分割方法。该方法把图像分为背景区域和目标区域,背景和目标分别服从广义Gamma分布,能量函数由区域能量和基于曲线长度的能量组成,其中区域能量函数是根据最大似然准则建立的。鉴于一般水平集方法稳定性低,对步长要求高,水平集函数需要重新初始化的缺点,我们采用变分水平集方法描述能量函数,然后通过变分法最小化能量泛函,求出水平集演化方程,从而实现分割。实验结果验证了本算法对合成图像和真实SAR图像的有效性。
2)针对第一种方法运算速度慢的缺点,我们以另一种思路提出了一种新的基于广义Gamma累积分布函数的水平集SAR图像分割方法,该方法利用广义Gamma分布的参数设计能量函数,即基于每一点的累积分布函数设计能量函数,通过参数估计,求得整幅图像的能量函数。然后通过最小化关于能量函数的代价函数,得到水平集演化方程,从而实现SAR图像的分割。分割结果证明了本算法对合成SAR图像和真实SAR图像都有效。
Synthetic aperture radar (SAR) can be operated day and night under all-weather conditions, with its resolution being independent of distance and having the capability of penetrating the obstacles such as cloud and smoke, thereby it can obtain the surface information over large areas, also plays a decisive role. In virtue of the nature of coherent imaging, the SAR images are inherently susceptible to speckle. This thesis focuses on the segmentation of SAR images, since the generic segmentation methods of optical images are not appropriate to SAR case.
As an important method, level set has been widely used in the field of SAR image segmentation due to the ability of handling the change of curve topology structure and fast segmentation speed. In terms of the characteristics of SAR images, the research of level set method mainly lies in two perspectives:one is to first despeckle the SAR images, and then segment the resulting images by using the level sets for optical images; the other is directly to implement the segmentation of SAR images. Because the despeckling step in the former scheme will lose the edge information, here we adopt the latter one, and propose two level-set methods of SAR image segmentation based on Generalized Gamma Distribution.
Firstly, a variational level set method is introduced based on the Generalized Gamma Distribution to segment the intensity and amplitude SAR images with homogeneous, heterogeneous, and extremely heterogeneous regions. Specifically, it divides the given SAR image into background and object areas, respectively following the Generalized Gamma Distribution, whose energy function is composed of the regional energy and the energy based on the length of the curve. Among them, the regional energy is designed according to the maximum likelihood criterion. Considering the disadvantages of general level set method, such as unstability, high requirement of step size, and reinitialization, we make use of a variational level set method to describe the energy function, and then minimize the energy functional with variational approach to solve the evolution equation for the purpose of segmentation. The experimental results verify the validity of the proposed method on synthetic and actual SAR images.
Secondly, to address the issue of slow segmentation speed in the above method, we present a new level set method for SAR image segmentation from another perspective, for which the parameters of Generalized Gamma Distribution are used to design the energy function. With the parameter estimates for each pixel in image region, the cumulative distribution function is derived as the related energy function in the level set evolution by the criterion of maximizing the regional mean energy. The final level set stage achieves S AR image segmentation according to the energy bands. The experimental results demonstrate the effectiveness of this proposed method on synthetic and actual SAR images.
在SAR图像分割领域,水平集方法是一类比较重要的方法。水平集方法由于能够处理曲线拓扑结构变化、分割速度快等优点,得到了广泛的应用。针对SAR图像的特点,水平集方法研究主要集中在两点上：一种是先对SAR图像进行滤波,然后利用针对一般光学图像的水平集方法进行分割；一种是直接对SAR图像进行分割。因为第一种方法在滤波的同时也消损了图像本身的边缘信息,因此我们采用直接对SAR图像进行分割的方法。本文提出了两点基于广义Gamma统计模型的SAR图像水平集分割方法：
1)针对各种分布均匀、不均匀以及极度不均匀的强度和幅度SAR图像,本文提出了一种基于广义Gamma分布似然函数的水平集SAR图像分割方法。该方法把图像分为背景区域和目标区域,背景和目标分别服从广义Gamma分布,能量函数由区域能量和基于曲线长度的能量组成,其中区域能量函数是根据最大似然准则建立的。鉴于一般水平集方法稳定性低,对步长要求高,水平集函数需要重新初始化的缺点,我们采用变分水平集方法描述能量函数,然后通过变分法最小化能量泛函,求出水平集演化方程,从而实现分割。实验结果验证了本算法对合成图像和真实SAR图像的有效性。
2)针对第一种方法运算速度慢的缺点,我们以另一种思路提出了一种新的基于广义Gamma累积分布函数的水平集SAR图像分割方法,该方法利用广义Gamma分布的参数设计能量函数,即基于每一点的累积分布函数设计能量函数,通过参数估计,求得整幅图像的能量函数。然后通过最小化关于能量函数的代价函数,得到水平集演化方程,从而实现SAR图像的分割。分割结果证明了本算法对合成SAR图像和真实SAR图像都有效。
Synthetic aperture radar (SAR) can be operated day and night under all-weather conditions, with its resolution being independent of distance and having the capability of penetrating the obstacles such as cloud and smoke, thereby it can obtain the surface information over large areas, also plays a decisive role. In virtue of the nature of coherent imaging, the SAR images are inherently susceptible to speckle. This thesis focuses on the segmentation of SAR images, since the generic segmentation methods of optical images are not appropriate to SAR case.
As an important method, level set has been widely used in the field of SAR image segmentation due to the ability of handling the change of curve topology structure and fast segmentation speed. In terms of the characteristics of SAR images, the research of level set method mainly lies in two perspectives:one is to first despeckle the SAR images, and then segment the resulting images by using the level sets for optical images; the other is directly to implement the segmentation of SAR images. Because the despeckling step in the former scheme will lose the edge information, here we adopt the latter one, and propose two level-set methods of SAR image segmentation based on Generalized Gamma Distribution.
Firstly, a variational level set method is introduced based on the Generalized Gamma Distribution to segment the intensity and amplitude SAR images with homogeneous, heterogeneous, and extremely heterogeneous regions. Specifically, it divides the given SAR image into background and object areas, respectively following the Generalized Gamma Distribution, whose energy function is composed of the regional energy and the energy based on the length of the curve. Among them, the regional energy is designed according to the maximum likelihood criterion. Considering the disadvantages of general level set method, such as unstability, high requirement of step size, and reinitialization, we make use of a variational level set method to describe the energy function, and then minimize the energy functional with variational approach to solve the evolution equation for the purpose of segmentation. The experimental results verify the validity of the proposed method on synthetic and actual SAR images.
Secondly, to address the issue of slow segmentation speed in the above method, we present a new level set method for SAR image segmentation from another perspective, for which the parameters of Generalized Gamma Distribution are used to design the energy function. With the parameter estimates for each pixel in image region, the cumulative distribution function is derived as the related energy function in the level set evolution by the criterion of maximizing the regional mean energy. The final level set stage achieves S AR image segmentation according to the energy bands. The experimental results demonstrate the effectiveness of this proposed method on synthetic and actual SAR images.
引文
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[2]章毓晋.“图像分割,”北京：科学出版社,pp.20-25,2001.
[3]Crimmins T. "Geometric filter for speckle reduction," Applied Optics, pp.1438-1443,1985.
[4]Lee J. S. "Refined filtering of image noise using local statistics," Computer Graph Image Process, pp.380-389,1981.
[5]Safe F, Flouzat G "Speckle removal on radar imagery based on mathematical morphology," Signal processing, pp.319-333,1989.
[6]P. A. Kelly, H. Derin, et al. "Adaptive segmentation of speckled images using a hierarchical random field model," IEEE Trans. Acoustics, Speech, Signal Process, vol.36, no.10, pp. 1628-1641,1988.
[7]P. C. Smits, S. G. Dellepiane. "Synthetic aperture radar image segmentation by a detail preserving markov random field," IEEE Trans. Geosci. Remote Sens, vol.3.5, no.4, pp. 844-857,1997.
[8]Kass M, Witkin A, Terzopoulos D. "Snakes:active contour models," International Journal of Computer Vision, pp.321-331,1987.
[9]C. Xu, J. L. Prince. "Snakes, shapes, and gradient vector flow," IEEE Trans. Image Process, pp. 359-369,1998.
[10]Xu Chen-yang, Prince J L. "Gradient vector flow:a new external force for snake," IEEE Proceedings Conference on Computer Vision and Pattern Recognition, San Juan, Puerto Rico, USA, pp.66-71,1997.
[11]Xu Chen yang, Yezzi A and Prince J L. "On the relationship between parametric and geometric active contours," Proceedings of 34th Asilomar Conferences on Signals, Systems, and Computers, Pacific Grove, pp.483-489,2000.
[12]L. D. Cohen. "On active contour models and balloons," Computer Vision, Graphics, and Image Processing:Image Understanding, pp.211-218,1991.
[13]T. J. Cham, R. Cipolla. "Stereo coupled active contours," Proceedings of the international conference on C-VPR. San Juan, Duero Rico. IEEE Computer Society Press, pp.1094-1099, 1997.
[14]S. Osher, J. A. Sethian, "Fronts propagating with curvature dependent speed:Algorithms based on Hamilton-Jacobi formulation," Journal of Computational Physics, vol.79, pp.12-49,1988.
[15]V. Caselles, F. Catte and T. Coll, et al. "A geometric model for active contours," Numeric Math, pp.1-31,1993.
[16]V. Caselles, J. Morel and G. Sapiro, "Geodesic active contours," International Journal of Computer Vision, vol.22, no.1, pp.61-79,1997.
[17]Chan T F, Vese L. "Active contours without edges," IEEE Trans. Image Process, pp.266-277, 2001.
[18]D. Mumford, J. Shah. "Optimal approximation by piecewise smooth functions and associated variational problems," Communications on Pure and Applied Mathematics, pp.577-685,1989.
[19]Zhao H K, Chan T, Merriman B, et al. "A variational level set approach to multiphase motion," Computer. Phys, pp.179-195,1996.
[20]L. A. Vese, T. F. Chan. "A multiphase level set framework for image segmentation using the Mumford and Shah Model," International Journal of Computer Vision, pp.271-293,2002.
[21]Chunming Li, Chenyang Xu, et al. "Level set evolution without re-initialization:a new variational formulation," IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.1063-6919,2005.
[22]Chunming Li, Chiu-Yen Kao, et al. "Implicit Active Contours Driven by Local Binary Fitting Energy," IEEE Conference on Computer Vision and Pattern Recognition, pp.1-7,2007.
[23]Chunming Li, Chiu-Yen Kao, et al. "Minimization of region-scalable fitting energy for image segmentation," IEEE trans, image process, vol.17, no.10,2008.
[24]Chunming Li, Rui Huang, et al. "A variational level set approach to segmentation and bias correction of images with intensity inhomogeneity," Springer-Verlag Berlin Heidelberg, pp. 1083-1091,2008.
[25]Chunming Li, Chenyang Xu, et al. "MRI tissue classification and bias field estimation based on coherent local intensity clustering:a unified energy minimization framework," Springer-Verlag Berlin Heidelberg, pp.288-299,2009.
[26]Chunming Li, Chenyang Xu, et al. "Distance regularized level set evolution and its application to image segmentation," IEEE Trans. Image process, vol.19, no.12,2010.
[27]Chunming Li, Rui Huang, et al. "A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI," IEEE Trans. Image process, vol.20, no.7, 2011.
[28]Kaihua Zhang, Lei Zhang, "Active contours with selective local or global segmentation:A new formulation and level set method," Image and Vision Computing, pp.0262-8856,2009.
[29]S. C. Zhu, A. YuiJle, "Region competition:Unifying snakes, region growing, and bayes/MDL for rnultiband image segmentation," IEEE Trans. Pattern Anal. Mach. Intell, vol.18, no.9, pp. 884-900,1996.
[30]A. Yezzi, A. Tsai, and A. Willsky. "A statistical approach to snakes for bimodal and trimodal imagery," International Conference of Computer Vision, pp.898-903,1999.
[31]N. Paragios, R. Deriche. "Geodesic active regions:A new paradigm to deal with frame partition problems in computer vision," Journal of Visual Communication and Image Representation, pp.249-268,2002.
[32]I. B. Ayed, A. Mitiche and Z. Belhadj, "Multiregion level-set partitioning of synthetic aperture radar images," IEEE Trans. Pattern Anal. Mach. Intell, vol.27, no.5, pp.793-800,2005.
[33]Ayed I B, Hennane N and Mitiche A. "Unsupervised variational image segmentation/classification using a Weibull observation model," IEEE Trans. Image Process, pp. 3431-3439,2006.
[34]P. Martin, P. Refregier and F. Goudail, et al. "Influence of the noise model on level set active contour segmentation," IEEE Trans. Pattern Anal. Mach. Intell, pp.799-803,2004.
[35]曹宗杰,闵锐等.“基于统计模型的变分水平集SAR图像分割方法,”电子与信息学报,pp.2862-2866,2008.Cao Zong-jie, Min Rui, and Pand Ling-li. et al. "A variational level set SAR image segmentation approach based on statistical model," Journal of Electronics & Information Technology, pp.2862-2866,2008.
[36]曹宗杰,庞伶俐等.“融合区域和边界信息的水平集SAR图像分割方法,”电子科技大学学报,pp.325-327,2008.
[37]Maria Eiena Buemi, Norberto Goussies,at el. "SAR Image Segmentation using level sets and region competition under the GH model." Springer-Verlag Berlin Heidelberg, pp.153-160, 2009.
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