图像PDE滤波和盲恢复技术的理论研究及其在IVUS图像处理中的应用
|
摘要
随着数字图像和计算机技术的进步,社会对数字图像处理的需求越来越大,数字图像处理技术也逐步应用到各行各业中。数字图像处理的高级应用离不开基础的算法,本文从理论上研究数字图像处理中图像滤波、图像恢复等基本问题,同时研究他们在医学图像处理中的应用。本文包括三个主要部分：
第一部分讨论了一种新的滤波器Guided Filter[15],并且得到了它的PDE等价形式(PGF),实验证明这种滤波器同样能够应用到图像平滑、图像去雾和对比度增强等场景中,而且有更强的物理意义。将这种最新型的滤波技术统一进PDE的框架里,有助于从更本质上理解般滤波器的作用原理和意义,有助于得到新的算法。
第二部分提出了一种新的图像盲恢复算法,对图像的运动模糊和失焦模糊均有较好的恢复效果。运用图像的一部分经过特殊选择的梯度图,用迭代求解的方式计算原图像和点扩展函数。目前的大部分主流图像盲复原方法都需要构造对图像强边缘的预测,而本方法省去了这一步骤,仅通过对现有图像梯度区域的选择,就可以快速有效地估计点扩展函数。由于此点扩展函数的估计模型是近似良态的,对正则项的要求不高,本文据此设计出了更快速的算法。
第三部分中综合利用各种基本的图像处理技术来解决IVUS图像处理中的问题。提出了一种新的IVUS图像血管壁分割算法：先利用本文提出的图像滤波技术(PGF)去除IVUS噪声,同时保持对分割有用的强边缘,然后使用本文以活动轮廓模型为核心的分割算法,从而实现血管内壁的分割。同时,在显示结果的时候利用本文的盲恢复技术对原图像进行增强,这样既可以观察到图像原本被隐藏的细节,又有血管壁的分割结果,有利于疾病的诊断和后续处理及分析的进行。
Digital image processing technique has been applied to many indus-tries. Advanced digital image processing techniques can not be applied without basic algorithm. This paper discuss several basic algorithms including image filter and image restoration, from both views of mathe-matic and engineering. Meanwhile, image processing in medical images, mainly in IVUS images has been discussed. The paper consists of three parts,
In the first part, a newly developed filter which been called Guided Filter is discussed. And, the equivalent form which can be expressed in PDE is proposed. Experiments show that this newly formed technique can be used in many applications, including image smoothing, image de-haze and image contrast enhancement. Moreover, this newly developed style can bring more physical meaning. The Guided Filter is unified into a PDE based framework. This will help us to understand the algorithm more deeply and naturally. Further, this leads to new algorithms.
In the second part, a new image blind deblurring algorithm is pro-posed. The algorithm is a novel and improved method to restore la-tent clear image from a single blurred image using some specifically se-lected image gradients. This algorithm uses an alternative minimization method to optimize the objective function and obtain both the latent image and the point spread function(PSF). Most state-of-the-art blind image restoration methods need a time-consuming and noise-prone step to predict the strong edges of latent images. A great contribution of the proposed method is that such a step is avoided since our method can estimate the PSF efficiently through selected image gradients. Because the estimation model of PSF is well-posed,this paper presents a much faster algorithm to achieve the PSF estimation function.
In the third part, several basic techniques, mostly are the meth-ods proposed in this paper, are combined to solve the problems which appeared in IVUS image process. Firstly, the PGF filter is used to ac-complish the denoising task for the IVUS images. Because of the special characteristics of the PGF filter, the areas which have strong gradients are preserved. Then, the images are thrown into the segmentation algo-rithm which is developed from active contour model. When displaying the results, the blind deblurring technique is applied to synthesis a new image which has both the segment contour and a clear IVUS image. This is very helpful in disease diagnosis.
第一部分讨论了一种新的滤波器Guided Filter[15],并且得到了它的PDE等价形式(PGF),实验证明这种滤波器同样能够应用到图像平滑、图像去雾和对比度增强等场景中,而且有更强的物理意义。将这种最新型的滤波技术统一进PDE的框架里,有助于从更本质上理解般滤波器的作用原理和意义,有助于得到新的算法。
第二部分提出了一种新的图像盲恢复算法,对图像的运动模糊和失焦模糊均有较好的恢复效果。运用图像的一部分经过特殊选择的梯度图,用迭代求解的方式计算原图像和点扩展函数。目前的大部分主流图像盲复原方法都需要构造对图像强边缘的预测,而本方法省去了这一步骤,仅通过对现有图像梯度区域的选择,就可以快速有效地估计点扩展函数。由于此点扩展函数的估计模型是近似良态的,对正则项的要求不高,本文据此设计出了更快速的算法。
第三部分中综合利用各种基本的图像处理技术来解决IVUS图像处理中的问题。提出了一种新的IVUS图像血管壁分割算法：先利用本文提出的图像滤波技术(PGF)去除IVUS噪声,同时保持对分割有用的强边缘,然后使用本文以活动轮廓模型为核心的分割算法,从而实现血管内壁的分割。同时,在显示结果的时候利用本文的盲恢复技术对原图像进行增强,这样既可以观察到图像原本被隐藏的细节,又有血管壁的分割结果,有利于疾病的诊断和后续处理及分析的进行。
Digital image processing technique has been applied to many indus-tries. Advanced digital image processing techniques can not be applied without basic algorithm. This paper discuss several basic algorithms including image filter and image restoration, from both views of mathe-matic and engineering. Meanwhile, image processing in medical images, mainly in IVUS images has been discussed. The paper consists of three parts,
In the first part, a newly developed filter which been called Guided Filter is discussed. And, the equivalent form which can be expressed in PDE is proposed. Experiments show that this newly formed technique can be used in many applications, including image smoothing, image de-haze and image contrast enhancement. Moreover, this newly developed style can bring more physical meaning. The Guided Filter is unified into a PDE based framework. This will help us to understand the algorithm more deeply and naturally. Further, this leads to new algorithms.
In the second part, a new image blind deblurring algorithm is pro-posed. The algorithm is a novel and improved method to restore la-tent clear image from a single blurred image using some specifically se-lected image gradients. This algorithm uses an alternative minimization method to optimize the objective function and obtain both the latent image and the point spread function(PSF). Most state-of-the-art blind image restoration methods need a time-consuming and noise-prone step to predict the strong edges of latent images. A great contribution of the proposed method is that such a step is avoided since our method can estimate the PSF efficiently through selected image gradients. Because the estimation model of PSF is well-posed,this paper presents a much faster algorithm to achieve the PSF estimation function.
In the third part, several basic techniques, mostly are the meth-ods proposed in this paper, are combined to solve the problems which appeared in IVUS image process. Firstly, the PGF filter is used to ac-complish the denoising task for the IVUS images. Because of the special characteristics of the PGF filter, the areas which have strong gradients are preserved. Then, the images are thrown into the segmentation algo-rithm which is developed from active contour model. When displaying the results, the blind deblurring technique is applied to synthesis a new image which has both the segment contour and a clear IVUS image. This is very helpful in disease diagnosis.
引文
[1]医学图像处理技术,马丽明,李艳婷,黄兆佳,叶兆斌,现代医院2007年11月第7卷第11期
[2]Image analysis techniques for automated IVUS contour detection, Maria Papadogiorgaki, Vasileios Mezarism Yiannis S. Chatzizisis, George D. Gi-annoglou and Ioannis Kompatsiaris, Ultrasound in Medicine and Biology, Vol.34, Issue 9, pp.1482-1498, September 2008.
[3]Mathematical problems in image processing. Partial Differential Equations and the Calculus of Variations, Gilles Aubert, Pierre Kornprobst, Springer Science+Business Media, LLC. Second Edition,2006. Applied Mathemat-ical Sciences, Band 147. P118.
[4]Image selective smoothing and edge detection by nonlinear diffusion, Catte F, Lions P-L, Morel J-M, Coll T, SIAM Journal on Numerical Analysis, Vol.29, no.1, pp.182-193,1992.
[5]Image selective smoothing and edge detection by nonlinear diffution, Luis Alvarez, Pierre-Louis Lions, J-M Morel, SIAM Journal on Numerical Anal-ysis, Vol.29, no.3, pp.845-866,1992.
[6]图像偏微分方程的原理及应用第六章,杨新,上海交通大学出版社,2003
[7]Image denoising and segementation via nonlinear diffusion, Yunmei Chen, BC Vemuri, Li Wang, Computers and Mathematics with Applications, Vol.39, no.5-6, pp.131-149, Mar 2000.
[8]Bilateral Filtering and Anisotropic Diffusion:Towards a Unified View-point, Danny Barash, Scale-Space and Morphology in Computer Vision Lecture Notes in Computer Science,2006, Vol 2106/2006,273-280.
[9]A common framework for nonlinear diffusion, adaptive smoothing, bilat-eral filtering and mean shift, Danny Barash, Dorin Comaniciu, Image and Vision Computing, Vol.22, Issue 1, pp.73-81, January 2004.
[10]Analysis of the Bilateral Filter, Michael Elad, Signals, Systems and Com-puters,2002. Conference Record of the Thirty-Sixth Asilomar Conference on, Vol.1, pp.483-487, Nov.2002.
[11]The staircasing effect in neighborhood filters and its solution, Antoni Buades, Bartomeu Coll, and Jean-Michel Morel, IEEE Transactions on Image Processing, vol.15, issue 6, pp.1499-1505,2006.
[12]Neighborhood filters and PDE's, Antoni Buades, Antoni Buades, Jean-Michel Morel, Numerische Mathematik Volume 105, Number 1,1-34.
[13]A closed form solution to natural image matting, Anat Levin, Dani Lischinski, Yair Weiss,IEEE Transactions on Pattern Analysis and Ma-chine Intelligence, vol.30, no.2, pp.228-242, February 2008.
[14]Single image haze removal using dark channel prior, Kaiming He, Jian Sun, Xiaoou Tang, IEEE Transactions on Pattern Analysis and Machine Intelligence,31 Aug.2010.
[15]Guided Image Filtering, Kaiming He, Jian Sun, and Xiaoou Tang, Com-puter Vision-ECCV 2010 Lecture Notes in Computer Science,2010, Vol-ume 6311/2010,1-14.
[16]PSF Estimation using Sharp Edge Prediction, Neel Joshi, Richard Szeliski, and David J. Kriegman, IEEE Conference on Computer Vision and Pattern Recognition, pp.1-8,2008.
[17]Fast Motion Deblurring, Sunghyun Cho and Seungyong Lee, ACM Trans-actions on Graphics(SIGGRAPH ASIA 2009), Vol.28, No.5,2009.
[18]High-quality motion deblurring from a single image, Qi Shan, Jiaya Jia, and Aseem Agarwala, ACM Transactions on Graphics (SIGGRAPH), Vol.27, No.3,2008.
[19]Removing camera shake from a single photograph,Rob Fergus, Barun Singh. Aaron Hertzmann, Sam T. Roweis, William T. Freeman, ACM Transactions on Graphics, Vol.25, No.3,787-794,2006.
[20]Blind image deconvolution revisited, D. Kundur and D. Hatzinakos, IEEE Signal Processing Magazine, Vol.13, No.6, pp.61-63,1996.
[21]Interative blind deconvolution method and its applications, G. R. Ayers and J. C. Dainty, Optics Letters, Vol.13, No.7, pp.547-549,1988.
[22]Understanding and evaluating blind deconvolution algorithms, Anat Levin, Yair Weiss, Fredo Durand, and William T. Freeman, IEEE Con-ference on Computer Vision and Pattern Recognition, pp.1964-1971,2009.
[23]http://home.postech.ac.kr/-sodomau/
[24]http://www.cse.cuhk.edu.hk/-leojia/projects/motion_deblurring/index.html
[2]Image analysis techniques for automated IVUS contour detection, Maria Papadogiorgaki, Vasileios Mezarism Yiannis S. Chatzizisis, George D. Gi-annoglou and Ioannis Kompatsiaris, Ultrasound in Medicine and Biology, Vol.34, Issue 9, pp.1482-1498, September 2008.
[3]Mathematical problems in image processing. Partial Differential Equations and the Calculus of Variations, Gilles Aubert, Pierre Kornprobst, Springer Science+Business Media, LLC. Second Edition,2006. Applied Mathemat-ical Sciences, Band 147. P118.
[4]Image selective smoothing and edge detection by nonlinear diffusion, Catte F, Lions P-L, Morel J-M, Coll T, SIAM Journal on Numerical Analysis, Vol.29, no.1, pp.182-193,1992.
[5]Image selective smoothing and edge detection by nonlinear diffution, Luis Alvarez, Pierre-Louis Lions, J-M Morel, SIAM Journal on Numerical Anal-ysis, Vol.29, no.3, pp.845-866,1992.
[6]图像偏微分方程的原理及应用第六章,杨新,上海交通大学出版社,2003
[7]Image denoising and segementation via nonlinear diffusion, Yunmei Chen, BC Vemuri, Li Wang, Computers and Mathematics with Applications, Vol.39, no.5-6, pp.131-149, Mar 2000.
[8]Bilateral Filtering and Anisotropic Diffusion:Towards a Unified View-point, Danny Barash, Scale-Space and Morphology in Computer Vision Lecture Notes in Computer Science,2006, Vol 2106/2006,273-280.
[9]A common framework for nonlinear diffusion, adaptive smoothing, bilat-eral filtering and mean shift, Danny Barash, Dorin Comaniciu, Image and Vision Computing, Vol.22, Issue 1, pp.73-81, January 2004.
[10]Analysis of the Bilateral Filter, Michael Elad, Signals, Systems and Com-puters,2002. Conference Record of the Thirty-Sixth Asilomar Conference on, Vol.1, pp.483-487, Nov.2002.
[11]The staircasing effect in neighborhood filters and its solution, Antoni Buades, Bartomeu Coll, and Jean-Michel Morel, IEEE Transactions on Image Processing, vol.15, issue 6, pp.1499-1505,2006.
[12]Neighborhood filters and PDE's, Antoni Buades, Antoni Buades, Jean-Michel Morel, Numerische Mathematik Volume 105, Number 1,1-34.
[13]A closed form solution to natural image matting, Anat Levin, Dani Lischinski, Yair Weiss,IEEE Transactions on Pattern Analysis and Ma-chine Intelligence, vol.30, no.2, pp.228-242, February 2008.
[14]Single image haze removal using dark channel prior, Kaiming He, Jian Sun, Xiaoou Tang, IEEE Transactions on Pattern Analysis and Machine Intelligence,31 Aug.2010.
[15]Guided Image Filtering, Kaiming He, Jian Sun, and Xiaoou Tang, Com-puter Vision-ECCV 2010 Lecture Notes in Computer Science,2010, Vol-ume 6311/2010,1-14.
[16]PSF Estimation using Sharp Edge Prediction, Neel Joshi, Richard Szeliski, and David J. Kriegman, IEEE Conference on Computer Vision and Pattern Recognition, pp.1-8,2008.
[17]Fast Motion Deblurring, Sunghyun Cho and Seungyong Lee, ACM Trans-actions on Graphics(SIGGRAPH ASIA 2009), Vol.28, No.5,2009.
[18]High-quality motion deblurring from a single image, Qi Shan, Jiaya Jia, and Aseem Agarwala, ACM Transactions on Graphics (SIGGRAPH), Vol.27, No.3,2008.
[19]Removing camera shake from a single photograph,Rob Fergus, Barun Singh. Aaron Hertzmann, Sam T. Roweis, William T. Freeman, ACM Transactions on Graphics, Vol.25, No.3,787-794,2006.
[20]Blind image deconvolution revisited, D. Kundur and D. Hatzinakos, IEEE Signal Processing Magazine, Vol.13, No.6, pp.61-63,1996.
[21]Interative blind deconvolution method and its applications, G. R. Ayers and J. C. Dainty, Optics Letters, Vol.13, No.7, pp.547-549,1988.
[22]Understanding and evaluating blind deconvolution algorithms, Anat Levin, Yair Weiss, Fredo Durand, and William T. Freeman, IEEE Con-ference on Computer Vision and Pattern Recognition, pp.1964-1971,2009.
[23]http://home.postech.ac.kr/-sodomau/
[24]http://www.cse.cuhk.edu.hk/-leojia/projects/motion_deblurring/index.html