基于活动轮廓模型和闭合形式的图像分割方法研究
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摘要
图像分割是图像处理、分析与理解、图像识别和计算机视觉研究领域的一个重要组成部分,也是一个经典难题,特别是对于普遍存在的复杂图像(如医学、自然)分割问题,目前并没有统一且有效的解决办法。
近年来,基于活动轮廓模型的图像分割方法凭借其严谨的数学理论框架、灵活的数值方案以及优越的性能得到图像处理领域相关专家的广泛关注。它用数学模型来表示图像分割问题,根据给定的初始轮廓,通过最小化有关图像信息的能量泛函,驱使轮廓线不断演化并在目标边界达到最小值。除此之外,基于透明度的图像抠图技术也是现如今的研究热点,该类方法将透明度作为图像的一种内在属性,通过寻求其最优解达到目标分割的目的,其中闭合形式(Closed-form)方法在分割目标边缘模糊图像上能够取得理想的效果。该方法将图像看成是由前景和背景组成,通过图像由前景和背景合成的模型建立能量函数,最后通过数学的方法求解能量函数最小时的透明度α值作为分割的最后结果。闭合形式方法和活动轮廓模型的相似之处：通过模型建立能量函数,求解最小能量函数来进行图像分割。
本文首先综述了图像分割的研究意义和现状,对当前分割方法进行分类并作简要介绍,较全面地分析了基于活动轮廓模型的图像分割和图像抠图技术,然后介绍了几何活动轮廓模型的理论基础-曲线演化理论和水平集方法,简要介绍了几种代表性的活动轮廓模型的基本原理和闭合形式方法的理论基础。通过分析国内外文献,本文提出了对两种方法的改进和应用：
(1)基于全局和局部信息的GAC模型。本文分析和研究了基于GAC模型提出的SBGFRLS水平集方法的核心：二值水平集方法和SPF模型。然后针对SPF模型不能处理非同质图像的缺陷提出了一个结合全局灰度信息和局部灰度信息的新活动轮廓模型。最后通过对比实验证明了新模型可以有效地克服了SPF模型的缺点,具有较好的抗噪性,而且由于计算上采用了二值水平集方法使其效率远远高于LBF模型。
(2)基于闭合形式的脑肿瘤分割。脑肿瘤组织边缘模糊不清和凹凸多变,传统的分割方法提取脑肿瘤效果不是很好。本文讨论了闭合形式方法在医学图像脑肿瘤组织的提取中的应用,并取得较理想的实验结果。由于原方法的手动标记容易带来繁琐和造成误分割,提出了通过KNN方法预分割自动标记出脑肿瘤和背景,实验证明改进后的闭合形式方法降低了对用户的要求,而且提高了分割的效率和精确度。
Image segmentation is not only an important part but also a prevalent puzzle in image processing, image recognition and computer-vision research field; especially in the segmentation problems for complex images (such as medical, natural types), there is not an uniform and effective solution.
In recent years, image segmentation based on the active contour models has received widespread concern since it has rigorous mathematical theory framework, flexible numerical programs as well as superior performance. It uses mathematical models to represent the problem in image segmentation. According to the given initial contours, by minimizing the energy functional with image information, the contours are evolved to achieve the minimum in the target boundary. In addition, transparency-related image matting technique is now a research hotspot. This method treats transparency as an intrinsic nature. By seeking the optimal solution, it manages to obtain the target partition purpose. Closed-form solution performs well in segmenting the targets from blurred images. This solution treats images foreground and background through establishing the mathematical function to get the transparency when the energy function is at its lowest level.
This thesis first gives a brief introduction to the significance and literature of image segmentation, which includes a brief classification of methods and a comprehensive overview over image segmentation and image matting technology. Then it introduces the geometric active contour model-curve evolution theory and level set method, presents briefly the basic principle of several kinds of representative active contour model and the theoretical basis of the Closed-form solution method. Motivated by others'recent work, this thesis presents two improvements and applications lying in the two methods:
Firstly, GAC model:based on the global and local information. This thesis investigates SBGFRLS which is based on the GAC model:binary level set method and the SPF model. Then aiming at defects that SPF Model cannot handle non homogeneous image, a new active contour model is proposed to combine with global and local gray information. Finally, by comparing experiments, it proves that the new model overcomes the shortcomings of the SPF model and has better noise immunity, and makes it far more efficient than the LBF model using binary level set method.
Secondly, brain tumor segmentation:closed-form solution. Brain tumor tissues have blurred edges and are uneven. The traditional segmentation method is hard to extract the brain tumor. This thesis proposes an application of closed-form solution for the extraction of brain tumors, which achieves desirable results. The traditional manual marking is cumbersome and may cause mal-segmentation. KNN method is used to pre-split and automatically mark brain tumor and background. Experiments show improved closed-form solution method reduces requirements for the users, but also improves the efficiency and accuracy of the segmentation.
近年来,基于活动轮廓模型的图像分割方法凭借其严谨的数学理论框架、灵活的数值方案以及优越的性能得到图像处理领域相关专家的广泛关注。它用数学模型来表示图像分割问题,根据给定的初始轮廓,通过最小化有关图像信息的能量泛函,驱使轮廓线不断演化并在目标边界达到最小值。除此之外,基于透明度的图像抠图技术也是现如今的研究热点,该类方法将透明度作为图像的一种内在属性,通过寻求其最优解达到目标分割的目的,其中闭合形式(Closed-form)方法在分割目标边缘模糊图像上能够取得理想的效果。该方法将图像看成是由前景和背景组成,通过图像由前景和背景合成的模型建立能量函数,最后通过数学的方法求解能量函数最小时的透明度α值作为分割的最后结果。闭合形式方法和活动轮廓模型的相似之处：通过模型建立能量函数,求解最小能量函数来进行图像分割。
本文首先综述了图像分割的研究意义和现状,对当前分割方法进行分类并作简要介绍,较全面地分析了基于活动轮廓模型的图像分割和图像抠图技术,然后介绍了几何活动轮廓模型的理论基础-曲线演化理论和水平集方法,简要介绍了几种代表性的活动轮廓模型的基本原理和闭合形式方法的理论基础。通过分析国内外文献,本文提出了对两种方法的改进和应用：
(1)基于全局和局部信息的GAC模型。本文分析和研究了基于GAC模型提出的SBGFRLS水平集方法的核心：二值水平集方法和SPF模型。然后针对SPF模型不能处理非同质图像的缺陷提出了一个结合全局灰度信息和局部灰度信息的新活动轮廓模型。最后通过对比实验证明了新模型可以有效地克服了SPF模型的缺点,具有较好的抗噪性,而且由于计算上采用了二值水平集方法使其效率远远高于LBF模型。
(2)基于闭合形式的脑肿瘤分割。脑肿瘤组织边缘模糊不清和凹凸多变,传统的分割方法提取脑肿瘤效果不是很好。本文讨论了闭合形式方法在医学图像脑肿瘤组织的提取中的应用,并取得较理想的实验结果。由于原方法的手动标记容易带来繁琐和造成误分割,提出了通过KNN方法预分割自动标记出脑肿瘤和背景,实验证明改进后的闭合形式方法降低了对用户的要求,而且提高了分割的效率和精确度。
Image segmentation is not only an important part but also a prevalent puzzle in image processing, image recognition and computer-vision research field; especially in the segmentation problems for complex images (such as medical, natural types), there is not an uniform and effective solution.
In recent years, image segmentation based on the active contour models has received widespread concern since it has rigorous mathematical theory framework, flexible numerical programs as well as superior performance. It uses mathematical models to represent the problem in image segmentation. According to the given initial contours, by minimizing the energy functional with image information, the contours are evolved to achieve the minimum in the target boundary. In addition, transparency-related image matting technique is now a research hotspot. This method treats transparency as an intrinsic nature. By seeking the optimal solution, it manages to obtain the target partition purpose. Closed-form solution performs well in segmenting the targets from blurred images. This solution treats images foreground and background through establishing the mathematical function to get the transparency when the energy function is at its lowest level.
This thesis first gives a brief introduction to the significance and literature of image segmentation, which includes a brief classification of methods and a comprehensive overview over image segmentation and image matting technology. Then it introduces the geometric active contour model-curve evolution theory and level set method, presents briefly the basic principle of several kinds of representative active contour model and the theoretical basis of the Closed-form solution method. Motivated by others'recent work, this thesis presents two improvements and applications lying in the two methods:
Firstly, GAC model:based on the global and local information. This thesis investigates SBGFRLS which is based on the GAC model:binary level set method and the SPF model. Then aiming at defects that SPF Model cannot handle non homogeneous image, a new active contour model is proposed to combine with global and local gray information. Finally, by comparing experiments, it proves that the new model overcomes the shortcomings of the SPF model and has better noise immunity, and makes it far more efficient than the LBF model using binary level set method.
Secondly, brain tumor segmentation:closed-form solution. Brain tumor tissues have blurred edges and are uneven. The traditional segmentation method is hard to extract the brain tumor. This thesis proposes an application of closed-form solution for the extraction of brain tumors, which achieves desirable results. The traditional manual marking is cumbersome and may cause mal-segmentation. KNN method is used to pre-split and automatically mark brain tumor and background. Experiments show improved closed-form solution method reduces requirements for the users, but also improves the efficiency and accuracy of the segmentation.
引文
[1]李朝辉.数字图像处理及应用[M].北京：北京机械工业出版社,2004：153-155.
[2]李荣艳,熊文生,曹佃国.一种改进的分水岭人脑MR图像分割方法[J].北京师范大学学报：自然科学版,2006,42(6)：582-584.
[3]刘爱平,付琨,尤红建,等.基于MAR-MRF的SAR图像分割方法[J].电子与信息学报,2009,31(11)：2556-2562.
[4]白利波,郝晓莉,李杰.基于模糊集的车牌提取方法[J].北京交通大学学报,2006,30(2)：48-52.
[5]Gonzalez R C,Woods R E,Eddins S L阮秋琦,等译[J].数字图像处理.第2版.北京：电子工业出版社,2007,217.
[6]Adams R, Bischof L.Seeded region growing[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1994,16(6):641-647.
[7]Sahoo P K, Soltani S, Wong A K C.A survey of thresholding techniques[J]. Computer vision, graphics, and image processing,1988,41(2):233-260.
[8]Tremeau A, Borel N. A region growing and merging algorithm to color segmentation[J].Pattern recognition,1997,30(7):1191-1203.
[9]Xia Y, Wang T, Zhao R, et al. Image segmentation by clustering of spatial patterns[J]. Pattern Recognition Letters,2007,28(12):1548-1555.
[10]陈勇滨,王水丽.基于阈值分割与边缘检测的对象轮廓提取方法研究[J].成都信息工程学院学报,2010,25(3)：246-251.
[11]常莹,何东健,李宗儒.基于聚类与边缘检测的自然场景文本提取方法[J].计算机工程与设计.2010,31(18)：4040-4043.
[12]Kass M, Witkin A, Terzopoulos D. Snakes:Active contour models[J]. International journal of computer vision,1988,1(4):321-331.
[13]Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of computational physics,1988,79(1):12-49.
[14]Cohen L D. On active contour models and balloons[J]. CVGIP:Image understanding,1991,53(2):211-218.
[15]Xu C, Prince J L. Snakes, shapes, and gradient vector flow[J]. Image Processing, IEEE Transactions on,1998,7(3):359-369.
[16]Li C, Liu J, Fox M D. Segmentation of edge preserving gradient vector flow: an approach toward automatically initializing and splitting of snakes[C]//Computer Vision and Pattern Recognition,2005. CVPR 2005. IEEE Computer Society Conference on. IEEE,2005,1:162-167.
[17]Xie X, Mirmehdi M. RAGS:Region-aided geometric snake[J]. Image Processing, IEEE Transactions on,2004,13(5):640-652.
[18]Caselles V, Catte F, Coll T, et al. A geometric model for active contours in image processing[J]. Numerische mathematik,1993,66(1):1-31.
[19]Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: A level set approach[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1995,17(2):158-175.
[20]Caselles V, Kimmel R, Sapiro G. Geodesic active contours[J]. International journal of computer vision,1997,22(1):61-79.
[21]Xu C, Yezzi Jr A, Prince J L. On the relationship between parametric and geometric active contours[C]//Signals, Systems and Computers,2000. Conference Record of the Thirty-Fourth Asilomar Conference on. IEEE,2000,1:483-489.
[22]Leventon M E, Grimson W E L, Faugeras O. Statistical shape influence in geodesic active contours[C]//Computer Vision and Pattern Recognition,2000. Proceedings. IEEE Conference on. IEEE,2000,1:316-323.
[23]Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation:A new formulation and level set method[J]. Image and Vision Computing,2010,28(4):668-676.
124] Chan T F, Vese L A. Active contours without edges[J]. Image Processing, IEEE Transactions on,2001,10(2):266-277.
[25]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems[J]. Communications on pure and applied mathematics,1989,42(5):577-685.
[26]Li C, Kao C Y, Gore J C, et al. Implicit active contours driven by local binary fitting energy[C]//Computer Vision and Pattern Recognition,2007. CVPR'07. IEEE Conference on. IEEE,2007:1-7.
[27]Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy[J]. Pattern recognition,2010,43(4):1199-1206.
[28]张文哲.基于区域生长的poisson抠图技术[D].山东科技大学,2006.
[29]Berman A, Dadourian A, Vlahos P. Method for removing from an image the background surrounding a selected object:U.S. Patent 6,134,346[P].2000-10-17.
[30]Chuang Y Y, Curless B, Salesin D H, et al. A bayesian approach to digital matting[C]//Computer Vision and Pattern Recognition,2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on. IEEE,2001,2: Ⅱ-264-Ⅱ-271 vol.2.
[31]Sun J, Jia J, Tang C K, et al. Poisson matting[C]//ACM Transactions on Graphics (ToG). ACM,2004,23(3):315-321.
[32]Levin A, Lischinski D, Weiss Y. A closed-form solution to natural image matting[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2008, 30(2):228-242.
[33]张春,黄勤超.改进的Closed-Form Solution景物提取算法[J].微计算机信息,2010,26(12)：218-220.
[34]刘玉洁.2D转3D中Grab Cut抠图技术的研究[D].安徽工业大学,2012.
[35]Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of computational physics,1988,79(1):12-49.
[36]Sethian J A. Level set methods and fast marching methods:evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science[M]. Cambridge university press,1999.
[37]Adalsteinsson D. A fast level set method for propagating interfaces[D]. University of California,1994.
[38]Sethian J A. A fast marching level set method for monotonically advancing fronts[J]. Proceedings of the National Academy of Sciences,1996,93(4): 1591-1595.
[39]Weickert J, Romeny B M T H, Viergever M A. Efficient and reliable schemes for nonlinear diffusion filtering[J]. Image Processing, IEEE Transactions on,1998, 7(3):398-410.
[40]Kichenassamy S, Kumar A, Olver P, et al. Conformal curvature flows:from phase transitions to active vision[J]. Archive for Rational Mechanics and Analysis, 1996,134(3):275-301.
[41]Caselles V, Kimmel R, Sapiro G. Geodesic active contours[J]. International journal-of computer vision,1997,22(1):61-79.
[42]朱国普.基于活动轮廓模型的图像分割[D].哈尔滨工业大学,2007.
[43]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems[J]. Communications on pure and applied mathematics,1989,42(5):577-685.
[44]Li C, Kao C Y, Gore J C, et al. Minimization of region-scalable fitting energy for image segmentation[J]. Image Processing, IEEE Transactions on,2008,17(10): 1940-1949.
[45]Li C, Kao C Y, Gore J C, et al. Implicit active contours driven by local binary fitting energy[C]//Computer Vision and Pattern Recognition,2007. CVPR'07. IEEE Conference on. IEEE,2007:1-7.
[46]Lankton S, Nain D, Yezzi A, et al. Hybrid geodesic region-based curve evolutions for image segmentation[C]//Medical Imaging. International Society for Optics and Photonics,2007:65104U-65104U-10.
[47]林瑶,田捷.医学图像分割方法法综述[J].模式识与人工智能,2002,15(2)：192-204.
[48]王臣,叶春涛.基于K-Means及KNN的磁共振颅脑图像分割初探[J].上海医学影像,2011,20(1)：9-14.
[49]傅伟,万洪晓,熊平.基于透明度的肝脏肿瘤提取的的研究[J].生物医学工程学,2009,26(4)：735-738.
[2]李荣艳,熊文生,曹佃国.一种改进的分水岭人脑MR图像分割方法[J].北京师范大学学报：自然科学版,2006,42(6)：582-584.
[3]刘爱平,付琨,尤红建,等.基于MAR-MRF的SAR图像分割方法[J].电子与信息学报,2009,31(11)：2556-2562.
[4]白利波,郝晓莉,李杰.基于模糊集的车牌提取方法[J].北京交通大学学报,2006,30(2)：48-52.
[5]Gonzalez R C,Woods R E,Eddins S L阮秋琦,等译[J].数字图像处理.第2版.北京：电子工业出版社,2007,217.
[6]Adams R, Bischof L.Seeded region growing[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1994,16(6):641-647.
[7]Sahoo P K, Soltani S, Wong A K C.A survey of thresholding techniques[J]. Computer vision, graphics, and image processing,1988,41(2):233-260.
[8]Tremeau A, Borel N. A region growing and merging algorithm to color segmentation[J].Pattern recognition,1997,30(7):1191-1203.
[9]Xia Y, Wang T, Zhao R, et al. Image segmentation by clustering of spatial patterns[J]. Pattern Recognition Letters,2007,28(12):1548-1555.
[10]陈勇滨,王水丽.基于阈值分割与边缘检测的对象轮廓提取方法研究[J].成都信息工程学院学报,2010,25(3)：246-251.
[11]常莹,何东健,李宗儒.基于聚类与边缘检测的自然场景文本提取方法[J].计算机工程与设计.2010,31(18)：4040-4043.
[12]Kass M, Witkin A, Terzopoulos D. Snakes:Active contour models[J]. International journal of computer vision,1988,1(4):321-331.
[13]Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of computational physics,1988,79(1):12-49.
[14]Cohen L D. On active contour models and balloons[J]. CVGIP:Image understanding,1991,53(2):211-218.
[15]Xu C, Prince J L. Snakes, shapes, and gradient vector flow[J]. Image Processing, IEEE Transactions on,1998,7(3):359-369.
[16]Li C, Liu J, Fox M D. Segmentation of edge preserving gradient vector flow: an approach toward automatically initializing and splitting of snakes[C]//Computer Vision and Pattern Recognition,2005. CVPR 2005. IEEE Computer Society Conference on. IEEE,2005,1:162-167.
[17]Xie X, Mirmehdi M. RAGS:Region-aided geometric snake[J]. Image Processing, IEEE Transactions on,2004,13(5):640-652.
[18]Caselles V, Catte F, Coll T, et al. A geometric model for active contours in image processing[J]. Numerische mathematik,1993,66(1):1-31.
[19]Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: A level set approach[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1995,17(2):158-175.
[20]Caselles V, Kimmel R, Sapiro G. Geodesic active contours[J]. International journal of computer vision,1997,22(1):61-79.
[21]Xu C, Yezzi Jr A, Prince J L. On the relationship between parametric and geometric active contours[C]//Signals, Systems and Computers,2000. Conference Record of the Thirty-Fourth Asilomar Conference on. IEEE,2000,1:483-489.
[22]Leventon M E, Grimson W E L, Faugeras O. Statistical shape influence in geodesic active contours[C]//Computer Vision and Pattern Recognition,2000. Proceedings. IEEE Conference on. IEEE,2000,1:316-323.
[23]Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation:A new formulation and level set method[J]. Image and Vision Computing,2010,28(4):668-676.
124] Chan T F, Vese L A. Active contours without edges[J]. Image Processing, IEEE Transactions on,2001,10(2):266-277.
[25]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems[J]. Communications on pure and applied mathematics,1989,42(5):577-685.
[26]Li C, Kao C Y, Gore J C, et al. Implicit active contours driven by local binary fitting energy[C]//Computer Vision and Pattern Recognition,2007. CVPR'07. IEEE Conference on. IEEE,2007:1-7.
[27]Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy[J]. Pattern recognition,2010,43(4):1199-1206.
[28]张文哲.基于区域生长的poisson抠图技术[D].山东科技大学,2006.
[29]Berman A, Dadourian A, Vlahos P. Method for removing from an image the background surrounding a selected object:U.S. Patent 6,134,346[P].2000-10-17.
[30]Chuang Y Y, Curless B, Salesin D H, et al. A bayesian approach to digital matting[C]//Computer Vision and Pattern Recognition,2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on. IEEE,2001,2: Ⅱ-264-Ⅱ-271 vol.2.
[31]Sun J, Jia J, Tang C K, et al. Poisson matting[C]//ACM Transactions on Graphics (ToG). ACM,2004,23(3):315-321.
[32]Levin A, Lischinski D, Weiss Y. A closed-form solution to natural image matting[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2008, 30(2):228-242.
[33]张春,黄勤超.改进的Closed-Form Solution景物提取算法[J].微计算机信息,2010,26(12)：218-220.
[34]刘玉洁.2D转3D中Grab Cut抠图技术的研究[D].安徽工业大学,2012.
[35]Osher S, Sethian J A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of computational physics,1988,79(1):12-49.
[36]Sethian J A. Level set methods and fast marching methods:evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science[M]. Cambridge university press,1999.
[37]Adalsteinsson D. A fast level set method for propagating interfaces[D]. University of California,1994.
[38]Sethian J A. A fast marching level set method for monotonically advancing fronts[J]. Proceedings of the National Academy of Sciences,1996,93(4): 1591-1595.
[39]Weickert J, Romeny B M T H, Viergever M A. Efficient and reliable schemes for nonlinear diffusion filtering[J]. Image Processing, IEEE Transactions on,1998, 7(3):398-410.
[40]Kichenassamy S, Kumar A, Olver P, et al. Conformal curvature flows:from phase transitions to active vision[J]. Archive for Rational Mechanics and Analysis, 1996,134(3):275-301.
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[42]朱国普.基于活动轮廓模型的图像分割[D].哈尔滨工业大学,2007.
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