基于偏微分方程的图像分割
|
摘要
图像分割和边界提取对于图像理解、模式识别、计算机视觉等具有非常重要的意义,是进一步图像分析的基础。目前,在图像分割领域,并没有对各类图像都适用的通用方法。如何快速且准确地检测到图像中目标物体或者感兴趣部分的边界,一直是人们研究的热点问题。近年来,基于偏微分方程的图像分割的研究十分活跃,成为图像分割研究领域一项受到广泛关注的技术。
本学位论文首先介绍了现有的图像分割方法,以及图像分割中的偏微分方程方法,然后针对几何活动轮廓模型(GAC)进行了研究,得到如下的结果:
在基于偏微分方程的图像分割中,基于边界的GAC模型几乎都依赖于停止速度函数(HSF),该函数通常是基于图像梯度定义的,其作用是使活动轮廓(演化曲线)停止在所希望的目标边界上。然而,在GAC模型中,由于传统的HSF在同质区域不够大,导致活动轮廓线不能均匀快速的演化到希望的目标边界,故基于GAC模型的图像分割有演化时间长的缺点。为了加快活动轮廓的演化速度,本文提出对HSF进行尺度变换的方法,实验结果显示,本学位论文提出的方案能够大大减少分割时间,同时,对于凹陷边界和弱边界的分割取得了更好的效果。
针对无须重新初始化水平集方法(LX模型)对二值图像分割时间长的问题,本学位论文提出一种新的模型,意在分割二值图像时,可以自适应地确定曲线的演化方向,大大缩短二值图像的分割时间。实验结果表明,该算法可以大大缩短图像分割时间。
Image segmentation and boundary extraction are very important in the fields of image understanding, pattern recognition, computer vision and so on. They are also the basis of the later image analysis. Up to now, there is still not a common method for any type of images in image segmentation. There are great deal of researches on how to detect the objects in an image quickly and accurately. Recently, image segmentations based on partial differential equation (PDE) has been studied broadly and become a key technique in the field of image processing.
After reviewing the literatures involved image segmentation techniques and PDE–based segmentation methods, this dissertation discusses geometric active contour(GAC) models (implemented via level set methods) and obtains the following results:
In PDE-based image segmentations, edge-based GAC models rely on the halting speed function (HSF), which is typically the function of image gradient, to stop the active contour (evolving curve) on the edges of the desired objects. However, the GAC models with original HSF are not able to make the active contour quickly move towards the desired object edges because the HSF is not large enough in homogenous region. Therefore, they have the drawbacks of long evolving time. In order to speed up the evolution of the active contour, this dissertation proposes a scheme that the scale transform is applied to the HSF. Experimental results show that the proposed scheme can significantly reduce segmentation time and perform better in the presence of concave and weak edges.
Then, level set method without reinitialization proposed by Li etc [Level set evolution without re-initialization: a new variational formulation. IEEE International Conference on Computer Vision and Pattern Recognition, 2005] is discussed. It has also the drawback of long evolving time. In order to make the curve precisely converge to the object boundary and shorten the segmentation time, this dissertation proposes a new model for binary image segmentations. Experimental results on binary images show the proposed model perform well and greatly reduce the segmentation time.
本学位论文首先介绍了现有的图像分割方法,以及图像分割中的偏微分方程方法,然后针对几何活动轮廓模型(GAC)进行了研究,得到如下的结果:
在基于偏微分方程的图像分割中,基于边界的GAC模型几乎都依赖于停止速度函数(HSF),该函数通常是基于图像梯度定义的,其作用是使活动轮廓(演化曲线)停止在所希望的目标边界上。然而,在GAC模型中,由于传统的HSF在同质区域不够大,导致活动轮廓线不能均匀快速的演化到希望的目标边界,故基于GAC模型的图像分割有演化时间长的缺点。为了加快活动轮廓的演化速度,本文提出对HSF进行尺度变换的方法,实验结果显示,本学位论文提出的方案能够大大减少分割时间,同时,对于凹陷边界和弱边界的分割取得了更好的效果。
针对无须重新初始化水平集方法(LX模型)对二值图像分割时间长的问题,本学位论文提出一种新的模型,意在分割二值图像时,可以自适应地确定曲线的演化方向,大大缩短二值图像的分割时间。实验结果表明,该算法可以大大缩短图像分割时间。
Image segmentation and boundary extraction are very important in the fields of image understanding, pattern recognition, computer vision and so on. They are also the basis of the later image analysis. Up to now, there is still not a common method for any type of images in image segmentation. There are great deal of researches on how to detect the objects in an image quickly and accurately. Recently, image segmentations based on partial differential equation (PDE) has been studied broadly and become a key technique in the field of image processing.
After reviewing the literatures involved image segmentation techniques and PDE–based segmentation methods, this dissertation discusses geometric active contour(GAC) models (implemented via level set methods) and obtains the following results:
In PDE-based image segmentations, edge-based GAC models rely on the halting speed function (HSF), which is typically the function of image gradient, to stop the active contour (evolving curve) on the edges of the desired objects. However, the GAC models with original HSF are not able to make the active contour quickly move towards the desired object edges because the HSF is not large enough in homogenous region. Therefore, they have the drawbacks of long evolving time. In order to speed up the evolution of the active contour, this dissertation proposes a scheme that the scale transform is applied to the HSF. Experimental results show that the proposed scheme can significantly reduce segmentation time and perform better in the presence of concave and weak edges.
Then, level set method without reinitialization proposed by Li etc [Level set evolution without re-initialization: a new variational formulation. IEEE International Conference on Computer Vision and Pattern Recognition, 2005] is discussed. It has also the drawback of long evolving time. In order to make the curve precisely converge to the object boundary and shorten the segmentation time, this dissertation proposes a new model for binary image segmentations. Experimental results on binary images show the proposed model perform well and greatly reduce the segmentation time.
引文
[1]章毓晋,图像分割[M].北京科学出版社,2001.
[2] Lee J, Haralick R, Shapiro L. Morphologic edge detection[J]. IEEE Trans on Robotics and Automation[J]. 1987,3(2): 142-156.
[3]杨新.图像偏微分方程的原理与应用[M].上海交通大学出版社. 2003.
[4] Paragios N D. Geodesic active contours and Level Sets for the detection and tracking of moving objects[J]. IEEE Transactions On Patten Analysis and Machine Itelligence, 2000, 22(3): 266-280.
[5]李俊,杨新等.基于Mumford-Shan准则的快速Level Set图像分割方法及其应用[J].北京:计算机学报,2002,11.
[6] Paragios N, Mellina-Gottardo O, Ramesh V. Gradient vector flow fast geometric active contours[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(3): 402-407.
[7]何传江,唐利明.几何活动轮廓模型中停止速度场的异性扩散[J].北京:软件学报,2007, 03.
[8] Lee, MyungEun, Park, SoonYoung; Cho, WanHyun; Kim, SooHyung. Medical Image Segmentation Using a Geometric Active Contour Model Based on Level Set Method[J]. IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, 2007,22-24 : 577-580.
[9] Koenderink J J. The structure of images[J]. Biological. Cybern. 1984, 50: 363-370.
[10] Alvaerz L, Guichard F, Lions P L. Axioms and fundamental equations of image processing[J]. Archive for Rational Mechanics and Analysis. 1993, 16(9):200-257.
[11] Hummel R A. Kimia B, Zucker S. De-blurring Gaussian blur[J]. Comput. Vision, Graphics, Image Processing, 1987, (38):184～195.
[12] Perona P, Malik J. Scale-space and edge detection using anisotropic difusion[J]. IEEE Transactionson Patern Analysis and MachineIn telligence 1990,12(7):629-639.
[13] Osher S J, Rudin L I. Feature - oriented Image Enhancement Using Shock Filters[J]. SIAM Journal Numerical Analysis, 1990, 27(4):919 - 940.
[14] L. Rudin, S. Osher, E. Fatemi. Nonlinear total variation based noise removal algorithms[J]. Physical, 1992, 60:259-260.
[15] Kass M, Witkin A, Terzopoulous D. Snakes: active contour models. In: Brady IM, Rosenfield A eds. Proceedings of the 1st International conference on computer Vision. London[J]. IEEE Computer Society Press, 1987,259-268.
[16] Mumford D, Shah J. Boundary detection by minimizing functionals[J]. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, 1985, 22-26.
[17] Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems[J].Communications on Pure and Applied Mathematics.1989, 42:577-685.
[18] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models[J]. International Journal of Computer Vision. 1988, 321-331.
[19] Sethian J. Curvature and evolution of fronts[J]. Communications in Mathematical Physics. 1985, 101: 487-499.
[20] Osher S; Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics.1988,79 :12 -49.
[21] Xu Y, Pham D, Prince J. Medical image segmentation using deformable models[M]. SPIE Handbook on Medical Imaging, Medical Image Processing and Analysis. 2000, (2):129-174.
[22] Zhu S, Yuille A. Region competition: umifying snakes, region growing, and Bayes/MDL for mufti-band image segmentation[J]. IEEE T ransactions on Pattern Analysis and Machine Intelligence.1996,18(9):884-900.
[23] Chan T, Vese L, Active contours without edges[J]. IEEE Trans. On Image Processing. 2001, 10(2):266-277.
[24]李俊,杨新,施鹏飞.基于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.
[25]肖亮,吴慧中,韦志辉.图像分割中段光滑模型的水平集算法[J].计算机研究与发展. 2004, 41(1):129-135.
[26] Luminita A. Vese, Tony F. Chan. A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model[J]. International Journal of Computer Vision. 2002, 50(3):271-293.
[27] V.Caselles, F.Catte, T.Coll, F.Dibos. A geometric model for active contours[J]. Numerische Mathematik. 1993, 66:1-31.
[28] Caselles V, Kimmel R, Sapiro G. Geodesic active contours[J]. Int J Comput Vis, 1997,22:61-79.
[29] Siddiqi K, Lauziere Y, Tannenbaum A. Area and length minimizing flows for shape segmentation[J]. IEEE Ttansactions on Image Processing. 1998,7(3):433-443.
[30] Chunming Li, Chenyang Xu,Changfeng Gui, Martin D.Fox. Level Set Evolution Without Re-initialization: A New Variational Formulation[J]. IEEE International Conference on Computer Vision and Pattern Recognition, 2005,430-436.
[31] Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: a Level Set approach[J]. IEEE Trans. On PAMI, 1995,17(2):158-175.
[32] Alvarez L, Lions P L, Morel J M. Image selective amoothing and edge detection by nonlinear diffusionⅡ[J]. SIAM Journal on Numerical Analysis,1992,29(3): 845-866.
[33] Paragios N, Deriche R. Geodesic active contours for aupervised textures Segmentation[J]. IEEE Conference on Computer Vision and Pattrn Recognition, Coloradl, USA, 1999.
[34] Bertalmio M, Sapiro G, Randall G. Region tracking on level-set methods[J]. IEEE Transactions on Medical Imaging. 1999,18(5):448-451.
[35] Masouri A-R, Sirivong B, Konrad J. Multiple motion segmentation with level sets[J]. Proceedings of the SPIE, 2000,3974:584-595.
[36] Paragios N, Deriche R. Geodesic active regions and level set methods for motion estimation and tracking[J]. Computer Vision and Image Understanding. 2005,3:259-282.
[37] Sethian J A. Level Set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vesion, and materials science[M]. Cambridge University Press,1999.
[38] Chop D. Computing minimal surfaces via Level Set curvature flow[J]. Journal of Computational Physics, 1993, 106:77-91.
[39] Sethian J A. A fast marching level set method for monotonically advancing fronts[J]. In Proc. Nat. Ac. Science, 1996, 93:1591-1694.
[40] B.A.Dubrovin, A.T.Fomenko, S.P.Novikov. Modern Geometry-Methods and Applications I [M]. Springer-Verlag, New York, 1984.
[41] Caselles V, Catte F, Coll T, Dibos F. A geometric model for active contours in image processing [J]. Numer, Math, 1993, 66. 1-31.
[42] V.I.Arnold. Geometrical Methods in the Theory of Ordinary Differential Equations[M]. New York: Springer-Verlag, 1983.
[43]唐利明,何传江,申小娜.基于几何活动轮廓模型的多尺度扩散分割算法[J],计算机辅助设计与图形学学报, 2007, 19(5):661-666.
[44] Cohen L D.On active contour models and balloons[J]. CV GIP: Image Understanding, 1991, 53(2):211-218.
[45] Xu C, Prince J L. Snake, shapes and gradient vector flow[J]. IEEE Transactions on Image Processing, 1998, 7(3):359-369.
[46] Yezzi A, Kichenassamy S, Kumar A, Olver P, Tannenbaum A. A geometric snake for segmentation of medical imagery[J]. IEEE Transactions on Medical Imageing, 1997,16(2):199-209.
[47] J.Gomes, O.Faugeras. Reconciling distance functions and Level Sets[J]. J.Visiual Communic. And Image.Representation, 2000,(11): 209-223.
[2] Lee J, Haralick R, Shapiro L. Morphologic edge detection[J]. IEEE Trans on Robotics and Automation[J]. 1987,3(2): 142-156.
[3]杨新.图像偏微分方程的原理与应用[M].上海交通大学出版社. 2003.
[4] Paragios N D. Geodesic active contours and Level Sets for the detection and tracking of moving objects[J]. IEEE Transactions On Patten Analysis and Machine Itelligence, 2000, 22(3): 266-280.
[5]李俊,杨新等.基于Mumford-Shan准则的快速Level Set图像分割方法及其应用[J].北京:计算机学报,2002,11.
[6] Paragios N, Mellina-Gottardo O, Ramesh V. Gradient vector flow fast geometric active contours[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(3): 402-407.
[7]何传江,唐利明.几何活动轮廓模型中停止速度场的异性扩散[J].北京:软件学报,2007, 03.
[8] Lee, MyungEun, Park, SoonYoung; Cho, WanHyun; Kim, SooHyung. Medical Image Segmentation Using a Geometric Active Contour Model Based on Level Set Method[J]. IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, 2007,22-24 : 577-580.
[9] Koenderink J J. The structure of images[J]. Biological. Cybern. 1984, 50: 363-370.
[10] Alvaerz L, Guichard F, Lions P L. Axioms and fundamental equations of image processing[J]. Archive for Rational Mechanics and Analysis. 1993, 16(9):200-257.
[11] Hummel R A. Kimia B, Zucker S. De-blurring Gaussian blur[J]. Comput. Vision, Graphics, Image Processing, 1987, (38):184～195.
[12] Perona P, Malik J. Scale-space and edge detection using anisotropic difusion[J]. IEEE Transactionson Patern Analysis and MachineIn telligence 1990,12(7):629-639.
[13] Osher S J, Rudin L I. Feature - oriented Image Enhancement Using Shock Filters[J]. SIAM Journal Numerical Analysis, 1990, 27(4):919 - 940.
[14] L. Rudin, S. Osher, E. Fatemi. Nonlinear total variation based noise removal algorithms[J]. Physical, 1992, 60:259-260.
[15] Kass M, Witkin A, Terzopoulous D. Snakes: active contour models. In: Brady IM, Rosenfield A eds. Proceedings of the 1st International conference on computer Vision. London[J]. IEEE Computer Society Press, 1987,259-268.
[16] Mumford D, Shah J. Boundary detection by minimizing functionals[J]. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, 1985, 22-26.
[17] Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems[J].Communications on Pure and Applied Mathematics.1989, 42:577-685.
[18] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models[J]. International Journal of Computer Vision. 1988, 321-331.
[19] Sethian J. Curvature and evolution of fronts[J]. Communications in Mathematical Physics. 1985, 101: 487-499.
[20] Osher S; Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics.1988,79 :12 -49.
[21] Xu Y, Pham D, Prince J. Medical image segmentation using deformable models[M]. SPIE Handbook on Medical Imaging, Medical Image Processing and Analysis. 2000, (2):129-174.
[22] Zhu S, Yuille A. Region competition: umifying snakes, region growing, and Bayes/MDL for mufti-band image segmentation[J]. IEEE T ransactions on Pattern Analysis and Machine Intelligence.1996,18(9):884-900.
[23] Chan T, Vese L, Active contours without edges[J]. IEEE Trans. On Image Processing. 2001, 10(2):266-277.
[24]李俊,杨新,施鹏飞.基于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.
[25]肖亮,吴慧中,韦志辉.图像分割中段光滑模型的水平集算法[J].计算机研究与发展. 2004, 41(1):129-135.
[26] Luminita A. Vese, Tony F. Chan. A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model[J]. International Journal of Computer Vision. 2002, 50(3):271-293.
[27] V.Caselles, F.Catte, T.Coll, F.Dibos. A geometric model for active contours[J]. Numerische Mathematik. 1993, 66:1-31.
[28] Caselles V, Kimmel R, Sapiro G. Geodesic active contours[J]. Int J Comput Vis, 1997,22:61-79.
[29] Siddiqi K, Lauziere Y, Tannenbaum A. Area and length minimizing flows for shape segmentation[J]. IEEE Ttansactions on Image Processing. 1998,7(3):433-443.
[30] Chunming Li, Chenyang Xu,Changfeng Gui, Martin D.Fox. Level Set Evolution Without Re-initialization: A New Variational Formulation[J]. IEEE International Conference on Computer Vision and Pattern Recognition, 2005,430-436.
[31] Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: a Level Set approach[J]. IEEE Trans. On PAMI, 1995,17(2):158-175.
[32] Alvarez L, Lions P L, Morel J M. Image selective amoothing and edge detection by nonlinear diffusionⅡ[J]. SIAM Journal on Numerical Analysis,1992,29(3): 845-866.
[33] Paragios N, Deriche R. Geodesic active contours for aupervised textures Segmentation[J]. IEEE Conference on Computer Vision and Pattrn Recognition, Coloradl, USA, 1999.
[34] Bertalmio M, Sapiro G, Randall G. Region tracking on level-set methods[J]. IEEE Transactions on Medical Imaging. 1999,18(5):448-451.
[35] Masouri A-R, Sirivong B, Konrad J. Multiple motion segmentation with level sets[J]. Proceedings of the SPIE, 2000,3974:584-595.
[36] Paragios N, Deriche R. Geodesic active regions and level set methods for motion estimation and tracking[J]. Computer Vision and Image Understanding. 2005,3:259-282.
[37] Sethian J A. Level Set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vesion, and materials science[M]. Cambridge University Press,1999.
[38] Chop D. Computing minimal surfaces via Level Set curvature flow[J]. Journal of Computational Physics, 1993, 106:77-91.
[39] Sethian J A. A fast marching level set method for monotonically advancing fronts[J]. In Proc. Nat. Ac. Science, 1996, 93:1591-1694.
[40] B.A.Dubrovin, A.T.Fomenko, S.P.Novikov. Modern Geometry-Methods and Applications I [M]. Springer-Verlag, New York, 1984.
[41] Caselles V, Catte F, Coll T, Dibos F. A geometric model for active contours in image processing [J]. Numer, Math, 1993, 66. 1-31.
[42] V.I.Arnold. Geometrical Methods in the Theory of Ordinary Differential Equations[M]. New York: Springer-Verlag, 1983.
[43]唐利明,何传江,申小娜.基于几何活动轮廓模型的多尺度扩散分割算法[J],计算机辅助设计与图形学学报, 2007, 19(5):661-666.
[44] Cohen L D.On active contour models and balloons[J]. CV GIP: Image Understanding, 1991, 53(2):211-218.
[45] Xu C, Prince J L. Snake, shapes and gradient vector flow[J]. IEEE Transactions on Image Processing, 1998, 7(3):359-369.
[46] Yezzi A, Kichenassamy S, Kumar A, Olver P, Tannenbaum A. A geometric snake for segmentation of medical imagery[J]. IEEE Transactions on Medical Imageing, 1997,16(2):199-209.
[47] J.Gomes, O.Faugeras. Reconciling distance functions and Level Sets[J]. J.Visiual Communic. And Image.Representation, 2000,(11): 209-223.