基于边界约束的水平集方法应用
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摘要
水平集(Level Set)方法最早由Osher和Sethian提出的,该方法的基本原理是将演化的曲线或者曲面作为零水平集嵌入到高一维的水平集函数中,通过演化高维中的函数,达到演化零水平集的目的。在高维中不仅易于拓扑变换,而且无需重新参数化,计算更加精确,并且水平集方法可以非常容易的向更高维推广。水平集方法自提出以来,其良好的特性在图像处理和计算机视觉领域都得到了广泛的应用。
针对水平集在演化过程中要不断重复计算修正符号距离函数的问题,Li提出的无须重新初始化水平集轮廓分割模型(Li模型)。该模型很好地保持水平集函数为符号距离函数,无需重新初始化,极大的提高了计算的速度和准确度,但几乎对于所有的水平集方法,在处理那些对象与背景颜色相近的图像时,任意零水平集进行演化都无法准确的分割出目标。水平集在处理图像时,对象与背景有明显的区别,即在对象边缘表现为灰度值的突变,否则就会出现过分割。本文在Li模型的基础上,提出了基于边界约束的水平集分割方法。该方法利用对象边界临近像素值近似相等的特性,在水平集进行演化过程中添加约束项,使其更加快速精确的分割出目标对象。
针对自动白平衡算法计算色温存在较大误差的问题,本文提出基于水平集的色温估计方法。先将RGB彩色图像转换为YCbCr颜色空间的图像,通过亮度和颜色的差值与阈值的比较,计算出符号距离函数,再利用水平集方法进行演化,得到处理区域,那些孤立的像素点以及正常的近似白像素点将随着水平集的演化而被排除在外,使色温估计更加准确。
The Level Set method is proposed by American mathematicians Stanley Osher and James Sethian, the basic principle of this method is the curve evolution, it is embedded in a higher dimensional space as zero horizontal level set function. The advantage of the Level Set method is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. Also, the Level Set method makes it very easy to follow shapes that change topology. And the calculation method can be used in higher dimension. Because of its good properties, it has become popular in many disciplines, such as image processing, computer graphics, computational geometry, optimization, and computational fluid dynamics.
Li proposed a model: level set evolution without re-initialization a new variational formulation. The level set function can be initiatized with general functions that are more efficient to construct and easier to use in practice than the widely used signed distance function. The level set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. However almost all of the level set method can deal with those objects color which is obvious difference with the background , otherwise it will produce over-segmentation. In this paper, a new model based on boundary constraint level set is proposed. This method utilizes the property that the object boundary has approximately equal value. This restrictions will make the segment step more quickly and accurately.
Estimating color-temperature about automatic white balance algorithm is not accurate. This paper proposed a method estimating color temperature based on the level set. First of all, change RGB color images to YCbCr color space, then calculate the sign distance function, through the difference about brightness, chromatism and the threshold, the evolution of the level set will remove those isolated pixels and the normal approximation white pixels, make more accurately to estimate color temperature.
针对水平集在演化过程中要不断重复计算修正符号距离函数的问题,Li提出的无须重新初始化水平集轮廓分割模型(Li模型)。该模型很好地保持水平集函数为符号距离函数,无需重新初始化,极大的提高了计算的速度和准确度,但几乎对于所有的水平集方法,在处理那些对象与背景颜色相近的图像时,任意零水平集进行演化都无法准确的分割出目标。水平集在处理图像时,对象与背景有明显的区别,即在对象边缘表现为灰度值的突变,否则就会出现过分割。本文在Li模型的基础上,提出了基于边界约束的水平集分割方法。该方法利用对象边界临近像素值近似相等的特性,在水平集进行演化过程中添加约束项,使其更加快速精确的分割出目标对象。
针对自动白平衡算法计算色温存在较大误差的问题,本文提出基于水平集的色温估计方法。先将RGB彩色图像转换为YCbCr颜色空间的图像,通过亮度和颜色的差值与阈值的比较,计算出符号距离函数,再利用水平集方法进行演化,得到处理区域,那些孤立的像素点以及正常的近似白像素点将随着水平集的演化而被排除在外,使色温估计更加准确。
The Level Set method is proposed by American mathematicians Stanley Osher and James Sethian, the basic principle of this method is the curve evolution, it is embedded in a higher dimensional space as zero horizontal level set function. The advantage of the Level Set method is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. Also, the Level Set method makes it very easy to follow shapes that change topology. And the calculation method can be used in higher dimension. Because of its good properties, it has become popular in many disciplines, such as image processing, computer graphics, computational geometry, optimization, and computational fluid dynamics.
Li proposed a model: level set evolution without re-initialization a new variational formulation. The level set function can be initiatized with general functions that are more efficient to construct and easier to use in practice than the widely used signed distance function. The level set evolution in our formulation can be easily implemented by simple finite difference scheme and is computationally more efficient. However almost all of the level set method can deal with those objects color which is obvious difference with the background , otherwise it will produce over-segmentation. In this paper, a new model based on boundary constraint level set is proposed. This method utilizes the property that the object boundary has approximately equal value. This restrictions will make the segment step more quickly and accurately.
Estimating color-temperature about automatic white balance algorithm is not accurate. This paper proposed a method estimating color temperature based on the level set. First of all, change RGB color images to YCbCr color space, then calculate the sign distance function, through the difference about brightness, chromatism and the threshold, the evolution of the level set will remove those isolated pixels and the normal approximation white pixels, make more accurately to estimate color temperature.
引文
[1]章毓晋.图像工程(中册)[M].(第2版).北京:清华大学出版社,2007.
[2]王大凯,候榆青,彭进业.图像处理的偏微分方法[M],北京:科学出版社,2008:1~7.
[3] Sven Loncaric, Marko Subasic and Erich Sorantin, 3-D Deformable Model for Aortic Aneurysm Segmentation from CT Images[C], In Proceedings of the 22nd Annual EMBS International Conference, Chicago, 2002, 398~401.
[4]张丽飞,王东峰,时永刚等.基于形变模型的图像分割技术综述电子与信息学报,2003, 25(3): 395~403.
[5]李俊,杨新,施鹏飞.基于Mumford-Shah模型的快速水平集图像分割方法[J],计算机学报.2002, 25(11): 1175~1183.
[6]孔平,严广乐,杨晖.遗传算法在指纹图像阈值分割中的应用[J],计算机工程与应用.2007, 43(27): 181~183.
[7]王振杰,盛焕烨.一种基于边缘梯度的图像分割方法[J].计算机应用研究.2004,2: 254~257.
[8]张爱华.一种基于熵优化的区域生长图像分割方法[J].华中科技大学学报.2004, 32(7): 40~42.
[9]夏勇.基于特征的纹理图像分割技术研究[D].西北工业大学硕士学位论文.2008.
[10]彭启民,贾云得.一种形态学色彩图像多尺度分割算法[J].中国图象图形学报,2006, 11(5): 635~639.
[11]杨在原.有噪声图像的小波变换多分辨率分割[D].吉林大学硕士学位论文.2005.
[12]吕庆文,周少为,陈武凡.基于TS-MRF与模糊MLL模型的图像分割[J].计算机工程与应用,2007, 30
[13]付树军,阮秋琦,王文洽.偏微分方程(PDEs)模型在图像处理中的若干应用[J].计算机工程与应用,2005,2
[14] Kass M, Witkin A, Terzopoulos D. Snakes: Active Contour Models[J]. International Journal of computer Vision. 1987, 1(4):321~ 331.
[15] Caselles V, Morel J M, Sapiro G. Geodesic active contours[J]. International Journal of Computer Vision. 1997, 22(1): 61~79.
[16] Laurent D Cohen, Isaac Cohen. Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Image[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1993, 15(11):1131~1147.
[17] G Xu, E Segawa, S Tsuji. Robust Active Contours with Insensitive Parameters[J]. Pattern Recognition. 1994, 27(7): 879~884.
[18] T McInerney, D Terzopoulos. Topology Adaptive Deformable Surfaces for Medical ImageVolume Segmentation[J]. IEEE Trans. On Medical Image. 1999,18(10): 840~850.
[19] R Malladi, J Sethian, B C Vemuri. Shape Modeling with Front Propagation: A Level Set Approach[J]. IEEE Trans. Patt. Anal. Mach. Intell. 1995, 17(2): 158~175.
[20] V Caselles, F Catte, T Coll, et al. A Geometric Model for Active Contours in Image Processing[J]. Numerische Mathematik. 1993, 66(1):1~31.
[21] Stanley Osher, James A Sethian. Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations[J]. Journal of Computational Physics, 1988, 79: 12~49.
[22] Zhao H K, Chan T, Merriman B, et al. A Variational Level Set Approach to Multiphase Motion[J]. Journal of Computational Physics, 1996, 127(1): 179~195.
[23] Li Chunming, Xu Chenyang, Gui Changfeng, etal. Level Set Eolution Without Re-initialization: A New Variational Formulation[C]. Proceedings 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 1: 430~436.
[24]汪海滨.Level Set算法及其应用[D].西北工业大学硕士学位论文.2006.
[25]宗士伟.基于水平集的图像去噪与分割算法研究[D].中南大学硕士学位论文.2009.
[26]李晓伟.基于水平集方法的分割[D].西安理工大学硕士学位论文.2007.
[27]石洁.基于水平集的多相图像分割方法研究[D].青岛大学硕士学位论文.2009.
[28]刘军伟.基于水平集的图像分割方法研究及其在医学图像中的应用[D].中国科学技术大学博士学位论文.2009.
[29] Wikipedia. Hamilton-Jacobi equation. http://en.wikipedia.org/wiki/Hamilton%E2%80%93 Jacobi _equation.
[30] Adalsteinsson D, Sethian J A. A Fast Level Set Method for Propagating Interfaces[J]. Journal of Computational Physics, 1995, 118(2): 269.
[31] Malladi R, Sethian J A. Level Set and Fast Marching Methods in Image Processing and Computer Vision[C]. IEEE International Conference on Image Processing, 1996, 1: 489~492.
[32] Zhao H K, Chan T, Merriman, Osher S. A Variational Level Set Approach to Multiphase Motion[J]. Journal of Computational Physics, 1996, 127(1): 179.
[33] L Evans. Partial Differential Equations, Providence: American Mathematical Society, 1998.
[34]周军,徐奕,周源华,等.基于局部能量特征的视频字幕分割[J].中国图象图形学报,2002, 7 (11): 1134～1138.
[35] Byung T C, Younglae B, Tai-Yun K, et a1.A Method for Origianl Image Recovery for Caption Areas in Video [J].Proceedings of the IEEE international Conference on Systems , Man and Cybe Man and Cybernetics,1999,2: 930-935.
[36] Satoh, Nakamura, et a1. Naming and detecting faces in news videos[J]. IEEE Multimedia,1999, 6(1): 22~35.
[37]蔡波,周洞汝,胡宏斌,等.数字视频中字幕检测及提取的研究和实现[J].计算机辅助设计与图形学学报,2003, 15(7): 898-903.
[38]李文,张大鹏,刘志勇,等.跳跃与环路最优匹配的快速图像恢复算法[J].计算机辅助设计与图形学报,2002, 14 (4): 351-355.
[39] Criminisi A, Perez P, Toyama K. Object Removal by Exemplar-Based Painting [J]. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003, 2: 721~728.
[40]周荣政,何捷,洪志良.自适应的数码相机自动白平衡算法[J],计算机辅助设计与图形学学报,2005 ,17(3):529-533.
[2]王大凯,候榆青,彭进业.图像处理的偏微分方法[M],北京:科学出版社,2008:1~7.
[3] Sven Loncaric, Marko Subasic and Erich Sorantin, 3-D Deformable Model for Aortic Aneurysm Segmentation from CT Images[C], In Proceedings of the 22nd Annual EMBS International Conference, Chicago, 2002, 398~401.
[4]张丽飞,王东峰,时永刚等.基于形变模型的图像分割技术综述电子与信息学报,2003, 25(3): 395~403.
[5]李俊,杨新,施鹏飞.基于Mumford-Shah模型的快速水平集图像分割方法[J],计算机学报.2002, 25(11): 1175~1183.
[6]孔平,严广乐,杨晖.遗传算法在指纹图像阈值分割中的应用[J],计算机工程与应用.2007, 43(27): 181~183.
[7]王振杰,盛焕烨.一种基于边缘梯度的图像分割方法[J].计算机应用研究.2004,2: 254~257.
[8]张爱华.一种基于熵优化的区域生长图像分割方法[J].华中科技大学学报.2004, 32(7): 40~42.
[9]夏勇.基于特征的纹理图像分割技术研究[D].西北工业大学硕士学位论文.2008.
[10]彭启民,贾云得.一种形态学色彩图像多尺度分割算法[J].中国图象图形学报,2006, 11(5): 635~639.
[11]杨在原.有噪声图像的小波变换多分辨率分割[D].吉林大学硕士学位论文.2005.
[12]吕庆文,周少为,陈武凡.基于TS-MRF与模糊MLL模型的图像分割[J].计算机工程与应用,2007, 30
[13]付树军,阮秋琦,王文洽.偏微分方程(PDEs)模型在图像处理中的若干应用[J].计算机工程与应用,2005,2
[14] Kass M, Witkin A, Terzopoulos D. Snakes: Active Contour Models[J]. International Journal of computer Vision. 1987, 1(4):321~ 331.
[15] Caselles V, Morel J M, Sapiro G. Geodesic active contours[J]. International Journal of Computer Vision. 1997, 22(1): 61~79.
[16] Laurent D Cohen, Isaac Cohen. Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Image[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1993, 15(11):1131~1147.
[17] G Xu, E Segawa, S Tsuji. Robust Active Contours with Insensitive Parameters[J]. Pattern Recognition. 1994, 27(7): 879~884.
[18] T McInerney, D Terzopoulos. Topology Adaptive Deformable Surfaces for Medical ImageVolume Segmentation[J]. IEEE Trans. On Medical Image. 1999,18(10): 840~850.
[19] R Malladi, J Sethian, B C Vemuri. Shape Modeling with Front Propagation: A Level Set Approach[J]. IEEE Trans. Patt. Anal. Mach. Intell. 1995, 17(2): 158~175.
[20] V Caselles, F Catte, T Coll, et al. A Geometric Model for Active Contours in Image Processing[J]. Numerische Mathematik. 1993, 66(1):1~31.
[21] Stanley Osher, James A Sethian. Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations[J]. Journal of Computational Physics, 1988, 79: 12~49.
[22] Zhao H K, Chan T, Merriman B, et al. A Variational Level Set Approach to Multiphase Motion[J]. Journal of Computational Physics, 1996, 127(1): 179~195.
[23] Li Chunming, Xu Chenyang, Gui Changfeng, etal. Level Set Eolution Without Re-initialization: A New Variational Formulation[C]. Proceedings 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, 1: 430~436.
[24]汪海滨.Level Set算法及其应用[D].西北工业大学硕士学位论文.2006.
[25]宗士伟.基于水平集的图像去噪与分割算法研究[D].中南大学硕士学位论文.2009.
[26]李晓伟.基于水平集方法的分割[D].西安理工大学硕士学位论文.2007.
[27]石洁.基于水平集的多相图像分割方法研究[D].青岛大学硕士学位论文.2009.
[28]刘军伟.基于水平集的图像分割方法研究及其在医学图像中的应用[D].中国科学技术大学博士学位论文.2009.
[29] Wikipedia. Hamilton-Jacobi equation. http://en.wikipedia.org/wiki/Hamilton%E2%80%93 Jacobi _equation.
[30] Adalsteinsson D, Sethian J A. A Fast Level Set Method for Propagating Interfaces[J]. Journal of Computational Physics, 1995, 118(2): 269.
[31] Malladi R, Sethian J A. Level Set and Fast Marching Methods in Image Processing and Computer Vision[C]. IEEE International Conference on Image Processing, 1996, 1: 489~492.
[32] Zhao H K, Chan T, Merriman, Osher S. A Variational Level Set Approach to Multiphase Motion[J]. Journal of Computational Physics, 1996, 127(1): 179.
[33] L Evans. Partial Differential Equations, Providence: American Mathematical Society, 1998.
[34]周军,徐奕,周源华,等.基于局部能量特征的视频字幕分割[J].中国图象图形学报,2002, 7 (11): 1134～1138.
[35] Byung T C, Younglae B, Tai-Yun K, et a1.A Method for Origianl Image Recovery for Caption Areas in Video [J].Proceedings of the IEEE international Conference on Systems , Man and Cybe Man and Cybernetics,1999,2: 930-935.
[36] Satoh, Nakamura, et a1. Naming and detecting faces in news videos[J]. IEEE Multimedia,1999, 6(1): 22~35.
[37]蔡波,周洞汝,胡宏斌,等.数字视频中字幕检测及提取的研究和实现[J].计算机辅助设计与图形学学报,2003, 15(7): 898-903.
[38]李文,张大鹏,刘志勇,等.跳跃与环路最优匹配的快速图像恢复算法[J].计算机辅助设计与图形学报,2002, 14 (4): 351-355.
[39] Criminisi A, Perez P, Toyama K. Object Removal by Exemplar-Based Painting [J]. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003, 2: 721~728.
[40]周荣政,何捷,洪志良.自适应的数码相机自动白平衡算法[J],计算机辅助设计与图形学学报,2005 ,17(3):529-533.