摘要
量子力学是二十世纪物理学最重要的科学成就之一,具有划时代意义。量子力学中的规律不仅支配着微观世界,而且也支配着宏观世界。信号作为自然界中客观存在的物理实体,它在物理上也受量子力学原理约束。本文借鉴并利用量子力学的基本概念与基本原理,充分发挥量子特性优势,在经典计算机上,提出了解决基于量子力学原理的图像处理新方法或改进方法。这些方法不依赖于量子级物理设备,实现了量子力学理论与图像处理技术的相互渗透与有机结合,不仅取得了较好的图像处理效果,而且为图像处理技术引入了一种新的理论工具。
本论文从实际图像处理应用背景出发,结合量子力学的基本概念、原理,围绕图像去斑、图像增强、图像分割三个关键图像处理技术,展开了如下研究工作:
首先,在系统分析各种图像去斑方法的基础上,从医学超声图像去斑方法研究出发,借鉴量子力学的基本理论,利用双树复小波变换,提出了两种量子衍生图像去斑方法。在这两种方法中,首先提出了两种带可调参数的改进信号模型。改进信号模型较传统的信号模型自适应更强,能适合各种不同概率分布的信号,可调参数的拟合过程简单有效。然后,考虑到小波系数的尺度间相关性,根据父-子代小波系数的归一化乘积,在高频子带中引入量子衍生信号与噪声出现概率。随后,利用贝叶斯估计理论,提出了一种基于量子衍生收缩因子的图像去斑方法和一种基于量子衍生阈值的图像去斑方法。这两种方法通过采用局部自适应的量子衍生参数,较好地解决了抑斑平滑与保持细节之间的矛盾。本论文提出的两种图像去斑方法计算复杂度低,自适应性强和鲁棒性好,不仅能有效地抑制斑点噪声,而且能更好地保持图像细节。此外,这两种方法具有一定普遍适用性,不仅对医学超声图像的去斑非常有效,而且对SAR图像相干斑抑制同样有效,具有很好的推广应用前景。
其次,结合医学图像的特点,本论文提出了一种基于量子概率统计的图像增强方法。该方法首先利用量子力学基本原理,定义了两种不同的像素量子比特表达形式;然后,结合3×3邻域像素灰度关联性,提出了一种基于量子概率统计的图像增强算子。为了优化图像增强的效果,本算子的灰度阂值参数可根据子采样图像信息熵自适应确定。本论文提出的图像增强方法,综合考虑了图像全局与局部信息,较传统方法能更有效地提高图像成像质量,不仅增强图像细节信息与图像对比度,而且较好地保持了图像的基本信息。此外,本论文提出的方法计算复杂度低,具有一定的普适性,不仅能有效增强医学图像,而且能有效改善其它非医学图像的视觉效果。
最后,定义了一种自适应隶属度函数,提出了一种基于自适应最大模糊熵的多阈值图像分割方法。为了提高多阈值的求解效率,本论文将量子遗传算法应用于图像分割方法中,并对已有的量子遗传算法进行了一些有益的改进,提高了多阈值图像分割结果准确性、稳定性以及算法的实时处理能力。结合本论文提出的自适应最大模糊熵评价函数,本论文提出了一种基于改进量子遗传算法的多阈值图像分割方法。实验结果表明本论文提出的方法具有稳定的求解性能和更好的图像分割效果。
Quantum mechanics is one of the most important scientific achievements of physics in the twentieth century. Microscopic world is not only dominated by the laws of quantum mechanics, but also the macroscopic world is also done. As an objective physical entity in nature, the Image signal is also affected by the physical constraints of quantum mechanics. With the principle, the basic concepts of quantum mechanics and the advantages of quantum properties, the novel methods of image processing are proposed for the solution of some specific problems in the classical computer, which don't depend on the quantum level of physical equipment. It promotes the realization of the combination and mutual penetration between quantum mechanics and image processing technology. Not only the better image processing results are achieved, but also a new theoretical tool is introduced into the image processing theory.
From practical applications of image processing, three key image processing techniques are studied with the basic concept and principle of quantum mechanics in this thesis which focus on the image despeckling, image enhancement and image segmentation. The main work of this thesis is summarized as follows.
Firstly, through analyzing and comparing various image despeckling methods, two quantum-inspired despeckling methods for medical ultrasound images are proposed by combining the dual-tree complex wavelet transform (DTCWT) with the basic theory of quantum mechanics. In the two proposed methods, two improved signal models with an adjustable parameter are built up for the log-transformed images wavelet coefficients firstly. Both the improved signal models have much better adaptability than the traditional signal models which can suit different probability distribution signals and the fitting procedure of adjustable parameter is simple and effective. And then, considering the inter-scale dependency of coefficients, the quantum-inspired probability of signal and noise is firstly introduced based on the normalized products of the coefficients and their parents. Finally, using the Bayesian estimation theory, two image despeckling methods are proposed, where one is based on a quantum-inspired shrinkage factor and the other is based on quantum-inspired threshold. By adopting different local adaptive quantum-inspired parameters, both methods can notably reduce speckle noise and preserve image details effectively, which have low computational complexity, strong adaptability and robustness. In addtion, both methods have universal applicability to some degree, which can effectively suppress speckle noise not only for medical ultrasound images but also Synthetic Aperture Radar (SAR) images, which have good generalization and application.
Secondly, two different mathematics expressions of pixel quantum bit are given first according to the basic principle of quantum mechanics. Then, aiming at the characteristics of medical images and combining with gray correlative characteristics of pixels in 3x3 neighborhoods, an image enhancement operator is proposed based on quantum probability statistics. In order to optimize the effect of image enhancement, the gray threshold parameter of the operator is adaptively chosen based on the sub-sampling image entropy. The proposed image enhancement method considers both global and local image information and can improve images quality effectively. In addtion, it has low computational complexity and universal applicability to some degree, which can not only enhance medical images effectively, but also improve vision effect of nonmedical images.
Finally, an adaptive membership function is defined and a method of multi-threshold image segmentation is proposed based on the adaptive maximum fuzzy entropy. In order to improve searching efficiency of multi-threshold, quantum genetic algorithm is applied to image segmentation and some improvements of existed quantum genetic algorithm are made which can not only increase accuracy and stablility for the results of multi-threshold image segmentation but also improve the real-time dealing ability. In this thesis, a method of multi-threshold image segmentation is proposed based on an improved quantum genetic algorithm, which combines with the evaluation function of adaptive maximum fuzzy entropy. Experimental results demonstrated that the proposed method had a more stable performance of solution and can achieve much better image segmentation effect.
引文
[1]曾谨言.量子力学(第三版).北京:科学出版杜,1984.
[2]周世勋.量子力学教程.北京:高等教育出版社,1979.
[3]王鹏,李建平.量子信号处理.计算机应用研究,2008,25(4):1033-1035.
[4]佐川弘幸,吉田宣章.突破经典信息科学的极限-量子信息论.宋鹤山,宋天译.大连:大连理工大学出版社,2007.
[5]郝宁湘.量子信息论及其哲学思考.科技导报(北京),2003:18-21.
[6]谢可夫.量子衍生图像处理方法的研究.[博士学位论文]:中南大学图书馆,2007.
[7]Klappenecker A, Rotteler M. Discrete cosine transforms on quantum computers. in:the 2nd International Symposium on Image and Signal Processing and Analysis. Pula, Croatia,2001.464-468.
[8]Piischel M, R tteler M, Beth T. Fast quantum Fourier transforms for a class of non-abelian groups. Lecture Notes In Computer Science,1999,1719:148-159.
[9]Fijany A, Williams C. Quantum wavelet transforms:fast algorithms and complete circuits. Lecture Notes in Computer Science,1999,1509:10-33.
[10]Kak S. Quantum neural computing. Advances in Imaging and Electron Physics, 1995,94:260-314.
[11]Menneer T. Quantum artificial neural networks. [Ph.D Dissertation]:University of Exeter,1999.
[12]Purushothaman G, Karayiannis N. Quantum neural networks (QNN's):Inherently fuzzy feedforward neural networks. IEEE Transactions on neural networks,1997, 8(3):679-693.
[13]Eldar Y, Oppenheim A. Quantum signal processing. IEEE Signal Processing Magazine,2002,19(6):12-32.
[14]Gonzalez R C, Woods R E.数字图像处理(第二版).阮秋琦等译.北京:电子工业出版社,2003.
[15]Benioff P. Quantum mechanical Hamiltonian models of Turing machines. Journal of Statistical Physics,1982,29(3):515-546.
[16]Benioff P. Quantum mechanical Hamiltonian models of discrete processes that erase their own histories:application to Turing machines. International Journal of Theoretical Physics,1982,21(3):177-201.
[17]Feynman R. Simulating physics with computers. International Journal of Theoretical Physics,1982,21(6):467-488.
[18]Deutsch D. Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,1985,400(1818):97-117.
[19]Shor P W. Algorithms for quantum computation:Discrete logarithms and factoring. in:Proceedings of the 35th Annual Symposium on Foundations of Computer Science. New Mexico:1994.124-124.
[20]Grover L. A fast quantum mechanical algorithm for database search. in: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing. New York:1996.212-219.
[21]Grover L. A framework for fast quantum mechanical algorithms. in:Proceedings of the thirtieth annual ACM symposium on Theory of computing. New York:1998. 53-62.
[22]Shor P. Scheme for reducing decoherence in quantum computer memory. Physical review A,1995,52(4):2493-2496.
[23]Shor P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review,1999,41(2):303-332.
[24]Shor P W. Algorithms for quantum computation:discrete logarithms and factoring. in:Proceedings of the 35th Annual Symposium on Foundations of Computer Science. New Mexico:IEEE Computer Society Press,1994.124-134.
[25]Ventura D, Martinez T. An artificial neuron with quantum mechanical properties. In:Proceedings of the International Conference on Artificial Neural Networks and Genetic Algorithms.1997.482-485.
[26]Ventura D, Martinez T. Quantum associative memory with exponential capacity. in:Proceedings of the International Joint Conference on Neural Networks:1998. 509-513.
[27]解光军,庄镇泉.量子神经网络.计算机科学,2001,28(7):1-6.
[28]Zhou J, Gan Q, Krzy ak A, et al. Recognition of handwritten numerals by quantum neural network with fuzzy features. International Journal on Document Analysis and Recognition,1999,2(1):30-36.
[29]Kouda N, Matsui N, Nishimura H. Image compression by layered quantum neural networks. Neural Processing Letters,2002,16(1):67-80.
[30]Liu Z, Bai Z, Shi J, et al. Image segmentation by using discrete tchebichef moments and quantum neural network. in:Proceedings of the 3rd International Conference on Natural Computation:2007.137-140.
[31]Yu S, Ma N. Quantum neural network and its application in vehicle classification. in:Proceedings of the Fourth International Conference on Natural Computation: 2008.499-503.
[32]吴茹石.基于量子神经网络的手写体数字识别研究.[硕士学位论文]:江南大学图书馆,2007.
[33]周日贵,姜楠,丁秋林.量子Hopfield神经网络及图像识别.中国图象图形学报,2008,13(1):119-123.
[34]周日贵.量子神经网络模型研究.[博士学位论文]:南京航空航天大学图书馆,2008.
[35]Narayanan A, Moore M. Quantum-inspired genetic algorithms. in:Proceedings of IEEE International Conference on Evolutionary Computation. Nagoya,Japan: 1996.61-66.
[36]Han K, Kim J. Genetic quantum algorithm and its application to combinatorial optimization problem. in:Proceedings of IEEE International Conference on Evolutionary Computation:2000.1354-1360.
[37]Han K, Kim J. Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Transactions on Evolutionary Computation, 2002,6(6):580-593.
[38]李映,张艳宁,赵荣椿等.免疫量子进化算法.西北工业大学学报,2005,23(4):543-547.
[39]Han K, Kim J. On setting the parameters of quantum-inspired evolutionary algorithm for practical applications. in:Congress on Evolutionary Computation. Canberra, Australia:Citeseer,2003.178-184.
[40]Han K, Kim J. Quantum-inspired evolutionary algorithms with a new termination criterion, He Gate, and two-phase scheme. IEEE Transactions on Evolutionary Computation,2004,8(2):156-169.
[41]张葛祥,李娜,金炜东等.一种新量子遗传算法及其应用.电子学报,2004,32(3):476-479.
[42]李士勇,李盼池等.量子计算与量子优化算法.哈尔滨:哈尔滨工业大学出版社,2009.
[43]王凌,吴昊,唐芳等.混合量子遗传算法及其性能分析.控制与决策,2005,20(2):156-160.
[44]熊焰,陈欢欢,苗付友等.一种解决组合优化问题的量子遗传算法QGA.电子学报,2004,32(11):1855-1858.
[45]Jang J-S, Han K-H, Kim J-H. Quantum-inspired evolutionary algorithm-based face verification. in:Genetic and Evolutionary Computation Conference. Chicago, IL, USA:2003.214-214.
[46]Talbi H, Batouche M, Draa A. A quantum-inspired genetic algorithm for multi-source affine image registration. in:International Conference on Image Analysis and Recognition Porto, Portugal:2004.147-154.
[47]Talbi H, Draa A, Batouche M, et al. A new quantum-inspired genetic algorithm for solving the travelling salesman problem. in:IEEE International Conference on Industrial Technology,2004.1192-1197.
[48]Talbi H, Batouche M, Draa A. A quantum-inspired evolutionary algorithm for multiobjective image segmentation. International Journal of Mathematical, Physical and Engineering Sciences,2007,1(2):109-114.
[49]Yang J, Li B, Zhuang Z. Research of quantum genetic algorith and its application in blind source separation. Journal of Electronics (China),2003,20(1):62-68.
[50]杨俊安,解光军,庄镇泉等.量子遗传算法及其在图像盲分离中的应用研究.计算机辅助设计与图形学学报,2003,15(7):847-852.
[51]杨俊安,邹谊,庄镇泉.基于多宇宙并行量子遗传算法的非线性盲源分离算法研究.电子与信息学报,2004,26(8):1210-1217.
[52]李映,焦李成,王浩军.边缘检测的混合量子遗传算法.模式识别与人工智能,2003,16(2):219-224.
[53]黄蓓.量子遗传算法及其在图像自适应增强中的应用研究.[硕士学位论文]:江南大学图书馆,2005.
[54]周露芳,古乐野.基于量子遗传算法的二维最大熵图像分割.计算机应用,2005,25(8):1805-1807.
[55]Kennedy J, Eberhart R. Particle swarm optimization. in:Proceedings of IEEE International Conference on Neural Networks:1995.1942-1948.
[56]Dorigo M, Maniezzo V, Colorni A. Ant system:optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 1996,26(1):29-41.
[57]Clerc M, Kennedy J. The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation,2002,6(1):58-73.
[58]Sun J, Feng B, Xu W. Particle swarm optimization with particles having quantum behavior. in:Congress on Evolutionary Computation:2004.325-331.
[59]陈玉萍,须文波,孙俊.图像压缩中基于量子行为的粒子群优化算法研究.计算机应用,2006,26(10):2369-2371.
[60]高浩,须文波,孙俊.量子粒子群算法在图像分割中的应用.计算机工程与应用,2007,43(33):24-25.
[61]杨宁,张培林,任国全等.基于量子行为的微粒群优化算法与模糊C均值聚类算法的磨粒图像分割.润滑与密封,2009,34(5):79-81.
[62]徐文龙,须文波,孙俊.基于量子行为粒子群优化算法的图像插值方法.计算机应用,2007,27(9):2147-2149.
[63]谢景权,须文波,孙俊.基于量子粒子群算法的医学图像配准.计算机工程与设计,2008,29(2):430-432.
[64]孙勇强,须文波,孙俊.基于量子行为微粒群优化算法的图像增强方法.计算机应用,2008,28(1):202-204.
[65]孙勇强.基于群体智能优化算法的图像增强研究.[硕士学位论文]:江南大学图书馆,2008.
[66]Tseng C C, Tsung M. Quantum digital image processing algorithms. in:16th IPPR Conference on Computer Vision, Graphics and Image Processing (CVGIP 2003). Kinmen:2003.827-834.
[67]谢可夫,罗安.量子启发数学形态学的研究.电子学报,2005,33(2):284-287.
[68]谢可夫,罗安,周心一.量子衍生形态学图像边缘检测方法.计算机工程与应用,2007,43(11):87-89.
[69]谢可夫,周心一,许光平.量子衍生坍缩形态学滤波.中国图象图形学报,2009,14(5):967-972.
[70]谢可夫,罗安.量子衍生自适应中值滤波.计算机工程与应用,2006,42(36):11-13.
[71]娄联堂,丁明跃,周成平.基于量子力学目标轮廓提取方法.计算机工程与应用,2005,41(3):94-97.
[72]Lou L T, Ding M Y. Principle and approach of boundary extraction based on particle motion in quantum mechanics. Optical Engineering,2007,46(2): 0270051-02700516.
[73]Sun Y, Lan T, Fu X, et al. A statistical approach to contour extraction based on quantum mechanics. in:SPIE Medical Image. Orlando, Florida, USA:2009.7529: 75294N1-75294N9.
[74]陈汉武.量子信息与量子计算简明教程.南京:东南大学出版社,2006.
[75]韩亮.量子信号处理与量子信息在多用户检测中的应用研究.[硕士学位论文]:中国计量科学研究院,2007.
[76]李栋.量子衍生多目标进化算法及其应用研究.[硕士学位论文]:湖南大学图书馆,2008.
[77]姜三平.基于小波变换的图像降噪北京:国防工业出版社,2009.
[78]胡国浩.SAR图像相干斑抑制方法研究.[硕士学位论文]:中国科学院电子学研究所,2007.
[79]Khare A, Khare M, Jeong Y, et al. Despeckling of medical ultrasound images using Daubechies complex wavelet transform. Signal Processing,2009:428-439.
[80]何磊.乘性噪声图像恢复的变分方法.[硕士学位论文]:青岛大学图书馆,2009.
[81]于秋则,朱光喜,柳健等.基于小波域统计建模及显著性修正的SAR图像相干斑抑制.电子与信息学报,2007,29(3):513-516.
[82]郭巍,张平,陈曦等.基于双密度双树复数小波变换的合成孔径雷达图像降噪研究.电子学报,2009,37(12):2747-2752.
[83]高贵,张军,吕信明等.SAR图像乘性噪声模型分析.信号处理,2008,24(2):161-167.
[84]侯建华.基于小波及其统计特性的图像去噪方法研究.[博士学位论文]:华中科技大学图书馆,2007.
[85]Lee J. Digital image enhancement and noise filtering by use of local statistics. IEEE Transactions on pattern analysis and machine intelligence,1980,2:165-168.
[86]Frost V, Stiles J, Shanmugan K, et al. A model for radar images and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on pattern analysis and machine intelligence,1982,4:157-166.
[87]Kuan D, Sawchuk A, Strand T, et al. Adaptive restoration of images with speckle. IEEE Transactions on Acoustics, Speech and Signal Processing,1987,35(3): 373-383.
[88]Crimmins T. Geometric filter for reducing speckle. Optical engineering,1986,25: 651-654.
[89]Lopes A, Nezry E, Touzi R, et al. Structure detection and statistical adaptive speckle filtering in SAR images. International Journal of Remote Sensing,1993, 14(9):1735-1758.
[90]Loupas T, McDicken W, Allan P. An adaptive weighted median filter for speckle suppression inmedical ultrasonic images. IEEE Transactions on Circuits and Systems,1989,36(1):129-135.
[91]Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7): 629-639.
[92]Kacur J, Mikula K. Slow and fast diffusion effects in image processing. Computing and Visualization in Science,2001,3(4):185-195.
[93]Gilboa G, Sochen N, Zeevi Y. Image enhancement and denoising by complex diffusion processes. IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(8):1020-1036.
[94]陈守水.基于偏微分方程的图像降噪及质量评价研究.[博士学位论文]:上海交通大学图书馆,2008.
[95]Schulze M. An edge-enhancing nonlinear filter for reducing multiplicative noise. in:Proceeding of SPIE. San Jose, California:1997.46-56.
[96]Bhuiyan M I H, Ahmad M O, Swamy M N S. Spatially adaptive thresholding in wavelet domain for speckling of ultrasound images. IET Image Processing,2009, 3(3):147-162.
[97]Weaver J, Xu Y, Healy D, et al. Filtering MR images in the wavelet transform domain. Magnetic Resonance in Medicine,1991,21(3):288-295.
[98]Donoho D, JOHNSTONE J. Ideal spatial adaptation by wavelet shrinkage. Biometrika,1994,81(3):425-455.
[99]Donoho D. De-noising by soft-thresholding. IEEE transactions on information theory,1995,41(3):613-627.
[100]Donoho D, Johnstone I. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association,1995,90(432):1200-1224.
[101]Guo H, Odegard J, Lang M, et al. Wavelet based speckle reduction with application to SAR based ATD/R. in:Proceedings of the IEEE International Conference on Image Processiong:1994.75-79.
[102]Gagnon L, Jouan A. Speckle filtering of SAR images-a comparative study between complex-wavelet-based and standard filters. in:Proceedings of SPIE,1997.80-91.
[103]Achim A, Bezerianos A, Tsakalides P. Novel bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Transactions on Medical Imaging,2001,20(8):772-783.
[104]Achim A, Tsakalides P, Bezerianos A. SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling. IEEE Transactions on Geoscience and Remote Sensing,2003,41(8):1773-1784.
[105]Pizurica A, Philips W, Lemahieu I, et al. Despeckling SAR images using wavelets and a new class of adaptive shrinkage estimators. in:International Conference On Image Processing,2001.233-236.
[106]Pizurica A, Philips W, Lemahieu I, et al. A versatile wavelet domain noise filtration technique for medical imaging. IEEE Transactions on Medical Imaging,2003, 22(3):323-331.
[107]Sendur L, Selesnick I. Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Transactions on Signal Processing,2002, 50(11):2744-2756.
[108]Selesnick I, Baraniuk R, Kingsbury N. The dual-tree complex wavelet transform. IEEE Signal Processing Magazine,2005,22(6):123-151.
[109]Kingsbury N. The dual-tree complex wavelet transform:a new efficient tool for image restoration and enhancement. in:Proceedings of EUSIPCO. Rhodes, Greece:1998.319-322.
[110]Kingsbury N. A dual-tree complex wavelet transform with improved orthogonalityand symmetry properties. in:International Conference on Image Processing:vol.2,2000.375-378.
[111]李玲玲.像素级图像融合方法研究与应用.[博士学位论文]:华中科技大学图书馆,2005.
[112]白衡,王世杰,罗立民等.基于双树复数小波降噪的扩散张量估计.信号处理,2007,23(3):330-335.
[113]李佐胜,姚建刚,杨迎建等.基于MAP估计的复小波域局部自适应绝缘子红外热像去噪方法.仪器仪表学报,2009,30(10):2070-2075.
[114]Chang S, Yu B, Vetterli M. Adaptive wavelet thresholding for image denoising and compression. IEEE Transactions on Image Processing,2000,9(9):1532-1546.
[115]侯建华,熊承义,何翔等.基于小波统计模型的医学超声图像去噪方法研究.中国生物医学工程学报,2009,28(1):31-36.
[116]Xu Y, Weaver J, Healy D, et al. Wavelet transform domain filters:a spatially selective noise filtration technique. IEEE Transactions on Image Processing,1994, 3(6):747-758.
[117]Achim A, Kuruoglu E, Zerubia J. SAR image filtering based on the heavy-tailed Rayleigh model. IEEE Transactions on Image Processing,2006,15(9):2686-2693.
[118]Hao X, Gao S, Gao X. A novel multiscale nonlinear thresholding method for ultrasonic speckle suppressing. IEEE Transactions on Medical Imaging,1999, 18(9):787-794.
[119]Matz S, de Figueiredo R, Co B, et al. A nonlinear image contrast sharpening approach based on Munsell's scale. IEEE Transactions on Image Processing,2006, 15(4):900-909.
[120]Lee Y, Park S. A study of convex/concave edges and edge-enhancing operators basedon the Laplacian. IEEE Transactions on Circuits and Systems,1990,37(7): 940-946.
[121]Munteanu C, Rosa A. Gray-scale image enhancement as an automatic process driven by evolution. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 2004,34(2):1292-1298.
[122]Rosenfeld A, Kak A. Digital picture processing. New York:Academic Press,1982.
[123]Florea C, Vlaicu A, Gordan M, et al. Fuzzy intensification operator based contrast enhancement in the compressed domain. Applied Soft Computing,2009,9(3): 1139-1148.
[124]周激流,吕航.一种基于新型遗传算法的图像自适应增强算法的研究.计算机学报,2001,24(9):959-964.
[125]刘政清,杨华.红外图像降质因素分析及增强效果评价.航天电子对抗,2006,22(6):11-13.
[126]Damera-Venkata N, Kite T, Geisler W, et al. Image quality assessment based on a degradation model. IEEE Transactions on Image Processing,2000,9(4):636-650.
[127]许永峰,张书玲.多阈值图像分割的模糊粒子群优化算法.计算机工程与应用,2008,44(11):182-183.
[128]杨凯,蒋华伟.模糊最大熵多阈值分割的改进算法研究.计算机工程与应用,2009,45(32):174-177.
[129]吴薇.基于最大模糊熵原理的多阈值图像分割新算法.系统工程与电子技术,2005,27(2):357-360.
[130]Pun T. A new method for grey-level picture thresholding using the entropy of the histogram. Signal Processing,1980,2(3):223-237.
[131]Pun T. Entropic thresholding, a new approach. Computer Graphics and Image Processing,1981,16(3):210-239.
[132]Kapur J, Sahoo P, Wong A. A new method for gray-level picture thresholding using the entropy of the histogram. Computer vision, graphics and image processing, 1985,29(3):273-285.
[133]Cheng H, Chen J, Li J. Threshold selection based on fuzzy C-partition entropy approach. Pattern Recognition,1998,31(7):857-870.
[134]Han K, Park K, Lee C, et al. Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. Evolutionary Computation,2001:1422-1429.
[135]焦李成,公茂果,王爽等.自然计算、机器学习与图像理解前沿.西安:西安电子科技大学出版社,2008.
[136]Zadeh L. Fuzzy sets. Information and Control,1965,8(3):338-353.
[137]Tao W, Tian J, Liu J. Image segmentation by three-level thresholding based on maximum fuzzy entropy and genetic algorithm. Pattern Recognition Letters,2003, 24(16):3069-3078.
[138]Tobias O, Seara R. Image segmentation by histogram thresholding using fuzzy sets. IEEE Transactions on Image Processing,2002,11(12):1457-1465.
[139]Zhao M, Fu A, Yan H. A technique of three-level thresholding based on probabilitypartition and fuzzy 3-partition. IEEE Transactions on Fuzzy Systems, 2001,9(3):469-479.
[140]吴薇.图像处理中的模糊技术.现代电子技术,2001,(3):28-30.
[141]王毅,牛奕龙,齐华等.三维医学图像分割的改进量子进化搜索算法.系统仿真学报,2008,20(11):2942-2945.