数字图像分割与算法研究
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摘要
图像分割是将图像划分成一系列相似特征区域,并能提取出关键特征区域进而对图像进行识别与理解。在图像分割之前先对图像进行预处理,分别从图像复原和图像增强两方面着手,以改善图像质量和效果,然后从两个大的方面来对图像进行分割:阈值化技术与基于偏微分方程的方法。对图像目标和背景性质差异较显著,图像能量较集中的情况下采用阈值化技术,并分别从单阈值法、双阈值法、多阈值法进行分析:单阈值法,采用了基于最小误差的阈值分割、OTSU分割法等进行了分析;双阈值法,例如改进的OTSU分隔法、基于二维灰度的分割法等;多阈值分割法,例如基于多阈值的OTSU分割法、分水岭算法等。而后使用智能算法来对目标函数求解,提高了计算效率。
在智能算法研究的过程中,首先列举了传统的遗传算法的特点,并根据算法流程分析了遗传算法的优越性,但却也存在明显不足。对于收敛于局部最优的情况时,文章采用了与模拟退火相结合的算法对其进行改进,即设置一个退火温度,从而改进其陷入局部最优的情况;另一方面,当演化进行到后期,对于交叉概率与变异概率应逐渐进行控制以达到正常收敛,文章采用了模糊逻辑控制器,根据当前的收敛情况适当控制交叉和变异过程中的概率系数,使得算法的效率得以提高。
针对目标与背景较复杂的图像文章采用了基于偏微分方程的活动轮廓线法进行分割,进而分析了一些主动轮廓线模型:snake模型、Mulnford-Shall模型,以及改进后的C-V模型。对于C-V模型,文章使用水平集方法,将曲线对应为一个更高维的曲面的演化函数,用偏微分方程进行表示,这样可以自然地改变轮廓曲线的拓扑结构,解决了因轮廓线不封闭或分离造成的不当分割。并用极小能量泛函来描述,而后采用窄带方法进行差分求解,简化了计算。根据实验结果可以发现,对渐变灰度的背景,并且与目标的灰度接近的图像,以及对边缘不封闭的目标可以得到较好的结果。
Image segmentation divides the image into some parts which is different from each other, in order to recognize and understand the image by extracting the key features in the parts. Before the segmentation we firstly do some image pre-processing job, separately in the aspects of image restoration and enhancement. Then we do the image segmentation job by the methods of threshold technique and PDE respectively. When the difference between the object and the background in the image is significant and the image energy is concentrated, we can take the threshold method, separately analyzing in the single-threshold method, double-threshold method and multi-threshold method. For the single-threshold method, we take the measure based on the minimum error, OTSU method etc; for the double-threshold method, we use the improved OTSU method, segmentation based on two-dimension gray etc; for the multi-threshold method, we take the way of watershed algorithm, the multi-threshold OTSU segmentation, and so on. Then, we take the intelligent algorithm to solve the object function, which improves the computational efficiency.
Researching on the intelligent algorithm, we firstly list the advantages of the traditional genetic algorithm, and analysis the GA's superiority through the algorithmic process, although some clearly insufficient. On the one hand, while convergence to the local optimum, the paper combines with the simulated annealing algorithm to improve the algorithm, that is, to set an annealing temperature in order to avoid the local optimum; on the other hand, while in the late stage of the evolution, the probability of crossover and mutation should be controlled gradually in order to convergence, so we uses the Fuzzy Logic Controller to set the probabilities according to the current situation so as to improve the efficiency of the algorithm.
For the images whose objects and backgrounds are confused to recognize, we take the active contour method based on Partial Differential Equation (PDE) to do the image segmentation, and separately analysis some active contour models: snake model, Mulnford-Shall model, and the improved model—C-V model. For the C-V model, we take the level set method that it convert the curve into a higher-dimensional function that the surface evolution function, described by PDE, so as to change the contour topology naturally , and solve the problem that the segmentation contour lines are not closed. Then we describe the problem by using the minimal energy functional, and take the Narrow-Band method to solve the problem. According to the experiment we find that it can get good results from the image whose background is gray gradient and close to the target, as well as the non-closure of the edge.
在智能算法研究的过程中,首先列举了传统的遗传算法的特点,并根据算法流程分析了遗传算法的优越性,但却也存在明显不足。对于收敛于局部最优的情况时,文章采用了与模拟退火相结合的算法对其进行改进,即设置一个退火温度,从而改进其陷入局部最优的情况;另一方面,当演化进行到后期,对于交叉概率与变异概率应逐渐进行控制以达到正常收敛,文章采用了模糊逻辑控制器,根据当前的收敛情况适当控制交叉和变异过程中的概率系数,使得算法的效率得以提高。
针对目标与背景较复杂的图像文章采用了基于偏微分方程的活动轮廓线法进行分割,进而分析了一些主动轮廓线模型:snake模型、Mulnford-Shall模型,以及改进后的C-V模型。对于C-V模型,文章使用水平集方法,将曲线对应为一个更高维的曲面的演化函数,用偏微分方程进行表示,这样可以自然地改变轮廓曲线的拓扑结构,解决了因轮廓线不封闭或分离造成的不当分割。并用极小能量泛函来描述,而后采用窄带方法进行差分求解,简化了计算。根据实验结果可以发现,对渐变灰度的背景,并且与目标的灰度接近的图像,以及对边缘不封闭的目标可以得到较好的结果。
Image segmentation divides the image into some parts which is different from each other, in order to recognize and understand the image by extracting the key features in the parts. Before the segmentation we firstly do some image pre-processing job, separately in the aspects of image restoration and enhancement. Then we do the image segmentation job by the methods of threshold technique and PDE respectively. When the difference between the object and the background in the image is significant and the image energy is concentrated, we can take the threshold method, separately analyzing in the single-threshold method, double-threshold method and multi-threshold method. For the single-threshold method, we take the measure based on the minimum error, OTSU method etc; for the double-threshold method, we use the improved OTSU method, segmentation based on two-dimension gray etc; for the multi-threshold method, we take the way of watershed algorithm, the multi-threshold OTSU segmentation, and so on. Then, we take the intelligent algorithm to solve the object function, which improves the computational efficiency.
Researching on the intelligent algorithm, we firstly list the advantages of the traditional genetic algorithm, and analysis the GA's superiority through the algorithmic process, although some clearly insufficient. On the one hand, while convergence to the local optimum, the paper combines with the simulated annealing algorithm to improve the algorithm, that is, to set an annealing temperature in order to avoid the local optimum; on the other hand, while in the late stage of the evolution, the probability of crossover and mutation should be controlled gradually in order to convergence, so we uses the Fuzzy Logic Controller to set the probabilities according to the current situation so as to improve the efficiency of the algorithm.
For the images whose objects and backgrounds are confused to recognize, we take the active contour method based on Partial Differential Equation (PDE) to do the image segmentation, and separately analysis some active contour models: snake model, Mulnford-Shall model, and the improved model—C-V model. For the C-V model, we take the level set method that it convert the curve into a higher-dimensional function that the surface evolution function, described by PDE, so as to change the contour topology naturally , and solve the problem that the segmentation contour lines are not closed. Then we describe the problem by using the minimal energy functional, and take the Narrow-Band method to solve the problem. According to the experiment we find that it can get good results from the image whose background is gray gradient and close to the target, as well as the non-closure of the edge.
引文
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[7]Chambolle A.An algorithm for total variation minimization and application.Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
[8]Ramesh Neelamani.Inverse Problems in Image Processing.Thesis for the degree of Doctor in Rice University.HOUSTON,TEXAS,June 2003.
[9]Mehran Ebrahimi Kahrizsangi.Inverse Problems and Self-similarity in Imaging.Thesis for the degree of Doctor in Waterloo University.Canada,2008.
[10]Peter Valter Blomagren.Total Variation Methods for Restoration of Vector Valued Images.Dissertation for the degree of Doctor in California University,1998.
[11]Otsu N.A threshold selection method from gray 2-level histogram.IEEE Trans.,1979,SMC9(1):62-66.
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[14]孙即祥.图像分析.北京:科学出版社,2005.
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[16]边肇琪,张学工等.模式识别.北京:清华大学出版社,2000.
[17]姚敏等.数字图像处理.北京:机械工业出版社,2006.
[18][美]冈萨雷斯.数字图像处理(第二版).北京:电子工业出版社,2007.
[19]闫敬文.数字图像处理技术与图形图像学基本教程.北京:科学出版社,2002.
[20]吴一全,潘带.基于最小类内绝对差和最大差的图像阈值分割,信号处理,2008;6(24),943-946.
[21]张伟,蒋宏,任章.自适应多阈值图像分割算法,自动化技术与应用,2007;26(8),71-74.
[22]罗三定,张中良.自动分布阈值图像多目标分割算法,计算技术与自动化,2008;27(2),77-80.
[23]徐立中,杨锦堂,遗传操作的一般性算子及图像恢复处理,电路与系统学报,1999;4(3),80-85.
[24]张玲,郭磊民,何伟,陈丽敏.一种基于最大类间方差和区域生长的图像分割法,信息与电子工程,2005;3(2),91-96.
[25]王茜,彭中,刘莉.一种基于自适应阈值的图像分割算法,北京理工大学学报,2003;23(4),521-524.
[26]孔明,孙希平,王永骥.一种改进的基于类间方差的阈值分割法,华中科技大学学报(自然科学版),2004;32(7),46-47.
[27]李敏,卢成武,冯象初.一类针对图像放大中反问题的变分模,电子与信息学报,2008;30(6),1201-1204.
[28]马文,周绍光,丁慧珍.基于遗传算法的OTSU法在图像分割中的应用,沿海企业与科技,2005;66(8),160-162.
[29]游国忠,赵晓丹,苏清祖.基于改进遗传算法的反卷积信号识别,振动与冲击,2006:25(2),101-106.
[30]黄小为,吴传生,朱华平.求解不适定问题的TSVD正则化方法.武汉理工大学学报,2005,27(2).
[31]何忠蛟.基于遗传算法的图像恢复研究,《机床与液压》.2005,No.2.
[32]张德刚,戴冠中,刘航,郝兴茂,李美峰.改进的指纹自适应阈值分割算法,计算机应用研究,2008;25(6),1739-1741.
[33]杨卫平,李忠科,王勇,吕培军.基于区域的图像分割算法综述,电子测量与仪器学报,2007(增刊),278-281.
[34]向日华,王润生.一种基于高斯混合模型的距离图像分割算法,软件学报,2003;14(7),1250-1257.
[35]张志佳,黄莎白,史泽林.一种改进的势函数聚类多阈值图像分割算法,光电工程,2005; 32[8),64-68.
[36]马剑英,张晓娜.基于免疫算法的图像多阈值分割.微计算机信息,2007,23(1-3):309-311.
[37]雷辉.基于多扫描阈值的图像分割编码算法.计算机与数字工程,2008,36(5):137-138.
[38]金聪,彭嘉雄.利用遗传算法实现数字图像分割.小型微型计算机系统,2002,23(7):875-877.
[39]张怀柱,向长波等.改进的遗传算法在实时图像分割中的应用.光学精密工程,2008,16(2):333-337.
[40]程国胜.遗传算法的收敛估计.高等学校计算数学学报,2004,26(4):306-313.
[41]王雪梅,王义和.模拟退火算法与遗传算法的结合.计算机学报,1997,20(4):381-384.
[42]任文杰.图像边缘检测方法的研究,山东大学硕士学位论文.2008,5.
[43]王凤娥.改进的分水岭算法在图像分割中的应用与研究,山东大学硕士学位论文.2008,4.
[44]孔凡壮.遥感图像分割算法的研究与应用,国防科学技术大学硕士学位论文.2005,11.
[45]姚远.车脸图像的特征提取,中南大学硕士学位论文.2008,6.
[46]谢昭.图像理解的关键问题和方法研究,合肥工业大学硕士学位论文.2007,5.
[47]潘建江.数字图像分割及变形技术的研究,浙江大学博士学位论文,2004,4.
[48]陈强.图像分割若干理论方法及应用研究,南京理工大学博士学位论文,2007,6.
[49]李兰兰.基于偏微分方程的图像复原和增强算法研究,东南大学博士学位论文,2005,5.
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[2]Igor Dydenko,Fadi Jamal,Olivier Bernard,Jan D_hooge,Isabelle E.Magnin,Denis Friboulet.A level set framework with a shape and motion prior for segmentation and region tracking in echocardiography,Medical Image Analysis 2006,10:162-177.
[3]Kaput J N,Sahoo P K,Wong A K C.A new method for gray 2-level picture thresholding using the entropy of the histogram.Computer Vision,Graphics and Image Processing,1985,29(2):273-285.
[4]Chambolle A,DeVore R A,Lee N Y,and Bradley J L.Nonlinear wavelet image processing:Variational problems,compression and noiseremoval through wavelet shrinkage.IEEE Transactions on Image Processing,1998,7(3):319-335.
[5]Chambolle A,Bradley J L.Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space.IEEE Transactions on Image Processing,2001,10(7):993-1000.
[6]Lorenz D A.Variational denoising in Besov spaces and interpolation of hard and soft wavelet shrinkage.University of Bremen,DFG-Schwerpunkt program 1114,2003:1-12.
[7]Chambolle A.An algorithm for total variation minimization and application.Journal of Mathematical Imaging and Vision,2004,20(1-2):89-97.
[8]Ramesh Neelamani.Inverse Problems in Image Processing.Thesis for the degree of Doctor in Rice University.HOUSTON,TEXAS,June 2003.
[9]Mehran Ebrahimi Kahrizsangi.Inverse Problems and Self-similarity in Imaging.Thesis for the degree of Doctor in Waterloo University.Canada,2008.
[10]Peter Valter Blomagren.Total Variation Methods for Restoration of Vector Valued Images.Dissertation for the degree of Doctor in California University,1998.
[11]Otsu N.A threshold selection method from gray 2-level histogram.IEEE Trans.,1979,SMC9(1):62-66.
[12]M.R.Banham and A.K.Katsaggelos,Digital image restoration,IEEE Signal Proc.Magazine,14(1997),pp.24-41.
[13]孙即祥,王晓华等.模式识别中的特征提取与计算机视觉不变量.北京:国防工业出版社,2001.
[14]孙即祥.图像分析.北京:科学出版社,2005.
[15]章毓晋.图像处理和分析.北京:清华大学出版社,1999.
[16]边肇琪,张学工等.模式识别.北京:清华大学出版社,2000.
[17]姚敏等.数字图像处理.北京:机械工业出版社,2006.
[18][美]冈萨雷斯.数字图像处理(第二版).北京:电子工业出版社,2007.
[19]闫敬文.数字图像处理技术与图形图像学基本教程.北京:科学出版社,2002.
[20]吴一全,潘带.基于最小类内绝对差和最大差的图像阈值分割,信号处理,2008;6(24),943-946.
[21]张伟,蒋宏,任章.自适应多阈值图像分割算法,自动化技术与应用,2007;26(8),71-74.
[22]罗三定,张中良.自动分布阈值图像多目标分割算法,计算技术与自动化,2008;27(2),77-80.
[23]徐立中,杨锦堂,遗传操作的一般性算子及图像恢复处理,电路与系统学报,1999;4(3),80-85.
[24]张玲,郭磊民,何伟,陈丽敏.一种基于最大类间方差和区域生长的图像分割法,信息与电子工程,2005;3(2),91-96.
[25]王茜,彭中,刘莉.一种基于自适应阈值的图像分割算法,北京理工大学学报,2003;23(4),521-524.
[26]孔明,孙希平,王永骥.一种改进的基于类间方差的阈值分割法,华中科技大学学报(自然科学版),2004;32(7),46-47.
[27]李敏,卢成武,冯象初.一类针对图像放大中反问题的变分模,电子与信息学报,2008;30(6),1201-1204.
[28]马文,周绍光,丁慧珍.基于遗传算法的OTSU法在图像分割中的应用,沿海企业与科技,2005;66(8),160-162.
[29]游国忠,赵晓丹,苏清祖.基于改进遗传算法的反卷积信号识别,振动与冲击,2006:25(2),101-106.
[30]黄小为,吴传生,朱华平.求解不适定问题的TSVD正则化方法.武汉理工大学学报,2005,27(2).
[31]何忠蛟.基于遗传算法的图像恢复研究,《机床与液压》.2005,No.2.
[32]张德刚,戴冠中,刘航,郝兴茂,李美峰.改进的指纹自适应阈值分割算法,计算机应用研究,2008;25(6),1739-1741.
[33]杨卫平,李忠科,王勇,吕培军.基于区域的图像分割算法综述,电子测量与仪器学报,2007(增刊),278-281.
[34]向日华,王润生.一种基于高斯混合模型的距离图像分割算法,软件学报,2003;14(7),1250-1257.
[35]张志佳,黄莎白,史泽林.一种改进的势函数聚类多阈值图像分割算法,光电工程,2005; 32[8),64-68.
[36]马剑英,张晓娜.基于免疫算法的图像多阈值分割.微计算机信息,2007,23(1-3):309-311.
[37]雷辉.基于多扫描阈值的图像分割编码算法.计算机与数字工程,2008,36(5):137-138.
[38]金聪,彭嘉雄.利用遗传算法实现数字图像分割.小型微型计算机系统,2002,23(7):875-877.
[39]张怀柱,向长波等.改进的遗传算法在实时图像分割中的应用.光学精密工程,2008,16(2):333-337.
[40]程国胜.遗传算法的收敛估计.高等学校计算数学学报,2004,26(4):306-313.
[41]王雪梅,王义和.模拟退火算法与遗传算法的结合.计算机学报,1997,20(4):381-384.
[42]任文杰.图像边缘检测方法的研究,山东大学硕士学位论文.2008,5.
[43]王凤娥.改进的分水岭算法在图像分割中的应用与研究,山东大学硕士学位论文.2008,4.
[44]孔凡壮.遥感图像分割算法的研究与应用,国防科学技术大学硕士学位论文.2005,11.
[45]姚远.车脸图像的特征提取,中南大学硕士学位论文.2008,6.
[46]谢昭.图像理解的关键问题和方法研究,合肥工业大学硕士学位论文.2007,5.
[47]潘建江.数字图像分割及变形技术的研究,浙江大学博士学位论文,2004,4.
[48]陈强.图像分割若干理论方法及应用研究,南京理工大学博士学位论文,2007,6.
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