基于偏微分方程的图像增强算法研究
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摘要
图像处理是对图像信息加工处理以满足人的视觉心理或应用需求。随着计算机技术的迅速发展,图像处理技术已广泛应用于各个领域。图像增强是图像处理的重点之一,它是根据应用需求加强图像中感兴趣的特性,达到改善视觉效果的目的。由于图像采集设备中电子器件的随机扰动以及周围环境等诸多因素的影响,使获得的图像中含有各种复杂的噪声,图像不同区域对比度不高,存在一定失真。利用图像增强技术对图像进行改善,衰减各类噪声、突出目标轮廓边缘,对后续的图像处理有重要意义。
本文研究以偏微分方程的理论对图像进行增强的算法,分析了将偏微分方程应用于图像增强的思想及其优势,针对偏微分方程理论中较经典的各向异性扩散模型和全变分模型在图像增强方面的应用做了重点研究。论文在分析了各向异性扩散模型、Catte模型和结合前向与后向扩散模型的基础上提出了一种改进模型,即在图像平坦区域采用平滑作用较好的Catte模型,在图像边缘区域采用能够退化边缘的结合前向和后向扩散模型。该改进模型发挥了两种模型的优点,在有效抑制噪声的同时尽可能多的保留图像边缘信息。论文还提出了一种结合自适应全变分模型与冲击滤波器模型的改进算法,该算法既改善了全变分模型所存在阶梯效应,也进一步锐化了图像的边界。论文通过对不同图像的实验仿真,根据峰值信噪比等参数验证了改进模型对图像去噪的有效性。
Image processing is processing the image information to meeting people's visual psychology or application requirements. With the rapid development of the computer technology, image processing technology has been widely used in various fields. Image enhancement is one of the focus of the image processing, it is based on application requirements to stress out interesting features from the image, to achieve the purpose of improving the visual effects. Due to the random perturbation of electronic devices in the image acquisition device and the surrounding environment, making the images contains a variety of complex noise, leading to a certain distortion. Using image enhancement technology to improve the image, decay various types of noise, and highlight the target contour edges is significant to the follow-up image processing.
This paper studies the image enhancement algorithm basing on theory of partial differential equations, analysises it's thinking and advantages by using the partial differential equation on image enhancement, and does deeply analysis for the classic Anisotropic Diffusion Model and the Total Variational Model. The paper proposed an improved enhancement algorithm based on the theories of P-M Model, Catte Model and FAB Model. The improved enhancement algorithm is using Catte Model in the flat area of images and using FAB Model at the edge of images. Another, the paper proposed an improved image enhancement algorithm through combining the Total Variation Model and the Shock Filter Model. The algorithm not only improves ladder effect of the total variation model, but also sharpes the image boundary. Through simulation experiments on different images, this paper proves the validity of the improved model by the peak signal to noise ratio.
本文研究以偏微分方程的理论对图像进行增强的算法,分析了将偏微分方程应用于图像增强的思想及其优势,针对偏微分方程理论中较经典的各向异性扩散模型和全变分模型在图像增强方面的应用做了重点研究。论文在分析了各向异性扩散模型、Catte模型和结合前向与后向扩散模型的基础上提出了一种改进模型,即在图像平坦区域采用平滑作用较好的Catte模型,在图像边缘区域采用能够退化边缘的结合前向和后向扩散模型。该改进模型发挥了两种模型的优点,在有效抑制噪声的同时尽可能多的保留图像边缘信息。论文还提出了一种结合自适应全变分模型与冲击滤波器模型的改进算法,该算法既改善了全变分模型所存在阶梯效应,也进一步锐化了图像的边界。论文通过对不同图像的实验仿真,根据峰值信噪比等参数验证了改进模型对图像去噪的有效性。
Image processing is processing the image information to meeting people's visual psychology or application requirements. With the rapid development of the computer technology, image processing technology has been widely used in various fields. Image enhancement is one of the focus of the image processing, it is based on application requirements to stress out interesting features from the image, to achieve the purpose of improving the visual effects. Due to the random perturbation of electronic devices in the image acquisition device and the surrounding environment, making the images contains a variety of complex noise, leading to a certain distortion. Using image enhancement technology to improve the image, decay various types of noise, and highlight the target contour edges is significant to the follow-up image processing.
This paper studies the image enhancement algorithm basing on theory of partial differential equations, analysises it's thinking and advantages by using the partial differential equation on image enhancement, and does deeply analysis for the classic Anisotropic Diffusion Model and the Total Variational Model. The paper proposed an improved enhancement algorithm based on the theories of P-M Model, Catte Model and FAB Model. The improved enhancement algorithm is using Catte Model in the flat area of images and using FAB Model at the edge of images. Another, the paper proposed an improved image enhancement algorithm through combining the Total Variation Model and the Shock Filter Model. The algorithm not only improves ladder effect of the total variation model, but also sharpes the image boundary. Through simulation experiments on different images, this paper proves the validity of the improved model by the peak signal to noise ratio.
引文
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[19]朱正煌.基于偏微分方程的图像处理技术[J].南京邮电大学硕士学位论文,2008
[20]张亶,陈刚.基于偏微分方程的图像处理[M].北京:高等教育出版社,2004.
[21]杨新,李俊.图像偏微分方程的原理与应用[M].上海:上海交通大学出版社,2003.
[22]朱秀昌,刘峰,胡栋.数字图像处理与图像通信[M].北京:北京邮电大学出版社,2002.
[23]王桥.数字图像处理[M].北京:科学出版社,2009.
[24]冯象初,王卫卫.图像处理的变分和偏微分方程方法[M].北京:科学出版社,2009.
[25]吴斌,吴亚东,张红英.基于变分偏微分方程的图像复原技术[M].北京:北京大学出版社,2008.
[26]何明一,卫保国.数字图像处理[M].北京:科学出版社,2008.
[27]秦襄培.MATLAB图像处理与界面编程宝典[M].电子工业出版社,2009.
[28]王洪元.MATLAB语言及其在电子信息工程中的应用[M].北京:清华大学出版社,2004.
[29]杨高波.MATLAB图像/视频处理应用及实例[M].北京:电子工业出版社,2010.
[30]A.Sarti, K.Mikula, F.Sgallari, C.Lamberti. Evolutionary partial differential equations for biomedical image processing[J],Computers and Biomedical Research,Apr.2002,Vol.35,No.2, 77-91.
[31]S.Bettahar, A.B.Stambouli. Shock filter coupled to curvature diffusion for image denoising and sharpening[J], Image and Vision Computing, Nov.2008, Vol.26, No.11, 1481-1489.
[32]B.Dzaja, M.Bonkovic, S.Bovan. Filtering vs. Nonlinear estimation procedures for image enhancement[J], WSEAS Transactions on Computers, Sep.2009, 1543-1553.
[33]V.B.Surya Prasath ,A.Singh. Controlled Inverse Diffusion Models for Image Restoration and Enhancement[J], ICETET, Jul.2008, 90-97.
[34]F.Zhang, L.C.Zhang. Multiscale Nonlinear Diffusion and Shock Filter for Ultrasound Image Enhancement[J], Computer Vision and Pattern Recognition, Jun.2006, 1972-1977.
[2]Perona P, Malik J, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Machine Intell. Vol. 12. no.7, July 1990, pp720-727.
[3]You, Y.-L., Kaveh, M., Fourth-order partial differential equations for noise removal. IEEE Transactions on Image Processing, Volume 9, Issue 10, Oct.2000, Page(s):1723-1730.
[4]Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [Physica D]. 1992, 60: 259-268.
[5]FCatte,P Lions, J Morel, T Coll. Image selective smoothing and edge deteetion by nonlinear[J]. SLAM Journal on Numerical Analysis, 1992,29(l):182-193.
[6]G Gilboa, N Soehen, YY Zeevi. Forward-and-backward diffusion processes for adaptive image enhancement and denoising[J]. IEEE Trans. Image Processing, 2002, 11(7):689一703.
[7]M.Fortier, D.Ziou. A global approach for solving evolutive heat transfer for image denoising and inpainting[J], IEEE Transactions on Image Processing, 2006, Vol.15, No.9, 2558-2573.
[8]Y.Chen, P.Bose. On the incorporation of time-delay regularization into curvature-based diffusion[J], Journal of Mathematical Imaging and Vision, 2001, Vol.14, No.2, 149-164.
[9]W.B.Luo. Efficient removal of impulse noise from digital images[J], IEEE Transactions on Consumer Electronics, 2006, Vol.52, No.2, 523-527.
[10]Osher S, Rudin L.Feature Oriented Image Enhancement Using Shock Filters[J]. SIAM J Numer Anal, 1990,27(4):919-940.
[11]G.Gilboa,N.Soehen, Y.Y.Zeevi. Variational Denoising of Partly Textured Images by Spatially Varying Constraints. IEEE Transactions on image processing, 2006, 15(8): 2281-2289
[12]L. Alvarez, L. Mazorra, Signal and image restoration using shock filters and anisotropic diffusion, SIAM Journal on Numerical Analysis, 1994, Vol.31, 590-605
[13]W.Z.Shao, Z.H.Wei. Edge-and-corner preserving regularization for image interpolation and reconstruction[J], Image and Vision Computing, Dec.2008, Vol.26, No.12, 1591-1606.
[14]R.P.Fedkiw, G.Sapiro, C.W.Shu. Shock capturing,level sets,and PDE based methods in computer vision and image processing:a review of Osher's contributions[J], Journal of Computational Physics, Mar.2003, Vol.185, No.2, 309-341.
[15]B.Tremblais, B.Augereau. A fast multi-scale edge detection algorithm[J], Pattern Recognition Letters, Apr.2004, Vol.25, No.6, 603-618.
[16]P.H.Money, S.H.Kang. Total variation minimizing blind deconvolution with shock filter reference[J], Image and Vision Computing, Feb.2008, Vol.26, No.2, 302-314.
[17]G.Chantas, N.P.Galatsanos, R.Molina, A.K.Katsaggelos. Variational Bayesian image restoration with a product of spatially weighted total variation image priors [J], IEEE Transactions on Image Processing, Feb.2010, Vol.19, No.2, 351-362.
[18]G.V.Borisenko, A.M.Denisov. A diffusion method for image filtering and sharpening[J], Programming and Computing Software, Sep.2008, Vol.34, No.5, 260-270.
[19]朱正煌.基于偏微分方程的图像处理技术[J].南京邮电大学硕士学位论文,2008
[20]张亶,陈刚.基于偏微分方程的图像处理[M].北京:高等教育出版社,2004.
[21]杨新,李俊.图像偏微分方程的原理与应用[M].上海:上海交通大学出版社,2003.
[22]朱秀昌,刘峰,胡栋.数字图像处理与图像通信[M].北京:北京邮电大学出版社,2002.
[23]王桥.数字图像处理[M].北京:科学出版社,2009.
[24]冯象初,王卫卫.图像处理的变分和偏微分方程方法[M].北京:科学出版社,2009.
[25]吴斌,吴亚东,张红英.基于变分偏微分方程的图像复原技术[M].北京:北京大学出版社,2008.
[26]何明一,卫保国.数字图像处理[M].北京:科学出版社,2008.
[27]秦襄培.MATLAB图像处理与界面编程宝典[M].电子工业出版社,2009.
[28]王洪元.MATLAB语言及其在电子信息工程中的应用[M].北京:清华大学出版社,2004.
[29]杨高波.MATLAB图像/视频处理应用及实例[M].北京:电子工业出版社,2010.
[30]A.Sarti, K.Mikula, F.Sgallari, C.Lamberti. Evolutionary partial differential equations for biomedical image processing[J],Computers and Biomedical Research,Apr.2002,Vol.35,No.2, 77-91.
[31]S.Bettahar, A.B.Stambouli. Shock filter coupled to curvature diffusion for image denoising and sharpening[J], Image and Vision Computing, Nov.2008, Vol.26, No.11, 1481-1489.
[32]B.Dzaja, M.Bonkovic, S.Bovan. Filtering vs. Nonlinear estimation procedures for image enhancement[J], WSEAS Transactions on Computers, Sep.2009, 1543-1553.
[33]V.B.Surya Prasath ,A.Singh. Controlled Inverse Diffusion Models for Image Restoration and Enhancement[J], ICETET, Jul.2008, 90-97.
[34]F.Zhang, L.C.Zhang. Multiscale Nonlinear Diffusion and Shock Filter for Ultrasound Image Enhancement[J], Computer Vision and Pattern Recognition, Jun.2006, 1972-1977.