基于块匹配和边缘导向的图像插值算法
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摘要
随着电子技术的不断发展,数字信息技术的不断提高,数字图像已经涉及到了社会生活越来越多的领域。然而,由于采集条件和采集设备的限制,一般条件和设备仅能获取较低分辨率的数字图像。因此,从已经获取得到的低分辨率图像处理得到较高分辨率的图像有了较大的应用。图像插值技术作为提高图像分辨率的有效途径之一,现已被广泛的应用的诸如医学图像处理、远程遥感图像处理和消费电子图像处理等领域。
传统的经典插值算法,一般是基于低通滤波的思想。这类算法实现简单,算法的复杂度较低,但由于低通滤波思想的限制,不能很好的处理诸如边缘、纹理等图像剧烈跳变的局部细节,容易导致边缘的模糊和锯齿的产生。由于人眼对边缘较敏感,算法效果的好坏很大程度上取决于其对图像边缘的处理,因此人们逐渐提出了基于边缘的图像插值算法,其中具有代表性的为Li等人提出的NEDI算法,该算法基于图像局部协方差具有稳定性和图像局部区域中的像素具有几何对偶性两个假设,通过自适应回归模型来估计局部范围内图像的协方差系数,并通过已知的低分辨率像素和估计得到的协方差系数来进行图像插值。由于其自适应边缘方向插值,因此其能较好避免边缘模糊和边缘锯齿的产生。但是,由于其在插值过程中平等的看待搜索区域中的所有像素,这就导致会引入不满足几何对偶性和局部协方差不变性的像素参与未知像素的估计,使得插值结果有偏差。
本文在充分分析了上面所述的两种不匹配问题：局部协方差不变性不匹配和几何对偶性不匹配的基础上,提出了基于块匹配的图像插值迭代算法,通过块匹配的方式来降低和排除不匹配块对未知像素估计的影响,从而提高图像的插值精度。块匹配思想主要是利用了自然图像中所含有的大量的冗余信息。对应于图像中的每个子块,都可以在其周围寻找到与其相似的其它子块。利用自然图像的这种自相似性可以很好的提高图像处理的效果。
本文的最后从主观实验效果和客观实验数据对比上分析了算法的效果,给出了PSNR值对比结果和SSIM图。实验结果表明本文所提出的方法能更好地抑制人工痕迹产生和保持图像边缘清晰。
With the continuous development of electronic technology and the continuous improvement of digital information technology, the digital image has been involved to more and more areas of social life. However, due to the restrictions of the conditions and the equipments, we can generally get lower resolution digital image. Therefore, get higher resolution image from the low-resolution image processing has been acquired by more and more applications. As an effective way to improve the image resolution, image interpolation technique has been widely applied in areas such as medical image processing, remote sensing image processing, and consumer electronics image processing and other areas.
The existing classical interpolation algorithms are generally based on the idea of the low-pass filter. Such algorithms are simple to be implemented and generally have low complexity. Due to the limitations of the low-pass filter, these algorithms are not good enough to deal with local details such as edges, textures and other image intense transition areas and generally produce fuzzy edges and generate serration. Because eyes are more sensitive to the edge of image, the algorithms are whether good or bad dependent largely on the processed edges of the image, so people gradually proposed the interpolation algorithms based on the edge direction of the image, NEDI is a representative method proposed by Li et al. NEDI is based on two assumptions of local stability property of covariance and geometric duality, and estimated the covariance coefficients via adaptive aggressive model, and estimated high-resolution pixels by low-resolution pixels and the covariance coefficients. Adaptive edge directed interpolation can better avoid blurred edges and prevent jagged edges from generating. However, since during the interpolation process, equally treat all the pixels in search area would introduce mismatched geometrical duality and mismatched local stability property of covariance into the estimation of the unknown pixels, so that the interpolation result will deviate from the actual situation.
This paper fully considered the two mismatched problems proposed above, mis-matched local stability property of covariance and mismatched geometric duality. And proposed a new iterative algorithm based on block-matched for images interpolation. Through the algorithm of block-matched, the effect of mismatched blocks in estimation of high resolution pixels can be reduced and excluded. Block-matched algorithms are mainly depending on the redundant information of nature images. As each sub-block can find similar sub-blocks around itself, which can be used to improve the effect of image processing, this has been widely used in image denoising, image restoration and image interpolation and other image processing areas.
At the end of this paper, we compare the effect of the BMEDI algorithm via objective and subjective experiment data. We show the PSNR values and SSIM images. Experimental results show that the new algorithm can suppress the artifacts and preserve image edge much better.
传统的经典插值算法,一般是基于低通滤波的思想。这类算法实现简单,算法的复杂度较低,但由于低通滤波思想的限制,不能很好的处理诸如边缘、纹理等图像剧烈跳变的局部细节,容易导致边缘的模糊和锯齿的产生。由于人眼对边缘较敏感,算法效果的好坏很大程度上取决于其对图像边缘的处理,因此人们逐渐提出了基于边缘的图像插值算法,其中具有代表性的为Li等人提出的NEDI算法,该算法基于图像局部协方差具有稳定性和图像局部区域中的像素具有几何对偶性两个假设,通过自适应回归模型来估计局部范围内图像的协方差系数,并通过已知的低分辨率像素和估计得到的协方差系数来进行图像插值。由于其自适应边缘方向插值,因此其能较好避免边缘模糊和边缘锯齿的产生。但是,由于其在插值过程中平等的看待搜索区域中的所有像素,这就导致会引入不满足几何对偶性和局部协方差不变性的像素参与未知像素的估计,使得插值结果有偏差。
本文在充分分析了上面所述的两种不匹配问题：局部协方差不变性不匹配和几何对偶性不匹配的基础上,提出了基于块匹配的图像插值迭代算法,通过块匹配的方式来降低和排除不匹配块对未知像素估计的影响,从而提高图像的插值精度。块匹配思想主要是利用了自然图像中所含有的大量的冗余信息。对应于图像中的每个子块,都可以在其周围寻找到与其相似的其它子块。利用自然图像的这种自相似性可以很好的提高图像处理的效果。
本文的最后从主观实验效果和客观实验数据对比上分析了算法的效果,给出了PSNR值对比结果和SSIM图。实验结果表明本文所提出的方法能更好地抑制人工痕迹产生和保持图像边缘清晰。
With the continuous development of electronic technology and the continuous improvement of digital information technology, the digital image has been involved to more and more areas of social life. However, due to the restrictions of the conditions and the equipments, we can generally get lower resolution digital image. Therefore, get higher resolution image from the low-resolution image processing has been acquired by more and more applications. As an effective way to improve the image resolution, image interpolation technique has been widely applied in areas such as medical image processing, remote sensing image processing, and consumer electronics image processing and other areas.
The existing classical interpolation algorithms are generally based on the idea of the low-pass filter. Such algorithms are simple to be implemented and generally have low complexity. Due to the limitations of the low-pass filter, these algorithms are not good enough to deal with local details such as edges, textures and other image intense transition areas and generally produce fuzzy edges and generate serration. Because eyes are more sensitive to the edge of image, the algorithms are whether good or bad dependent largely on the processed edges of the image, so people gradually proposed the interpolation algorithms based on the edge direction of the image, NEDI is a representative method proposed by Li et al. NEDI is based on two assumptions of local stability property of covariance and geometric duality, and estimated the covariance coefficients via adaptive aggressive model, and estimated high-resolution pixels by low-resolution pixels and the covariance coefficients. Adaptive edge directed interpolation can better avoid blurred edges and prevent jagged edges from generating. However, since during the interpolation process, equally treat all the pixels in search area would introduce mismatched geometrical duality and mismatched local stability property of covariance into the estimation of the unknown pixels, so that the interpolation result will deviate from the actual situation.
This paper fully considered the two mismatched problems proposed above, mis-matched local stability property of covariance and mismatched geometric duality. And proposed a new iterative algorithm based on block-matched for images interpolation. Through the algorithm of block-matched, the effect of mismatched blocks in estimation of high resolution pixels can be reduced and excluded. Block-matched algorithms are mainly depending on the redundant information of nature images. As each sub-block can find similar sub-blocks around itself, which can be used to improve the effect of image processing, this has been widely used in image denoising, image restoration and image interpolation and other image processing areas.
At the end of this paper, we compare the effect of the BMEDI algorithm via objective and subjective experiment data. We show the PSNR values and SSIM images. Experimental results show that the new algorithm can suppress the artifacts and preserve image edge much better.
引文
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[2]余松煜,周源华,吴时光。数字图像处理[M]。北京：电子工业出版社,1989。
[3]余松煌,张文军,孙军编著。现代图像处理、压缩与识别技术,科学出版社,43-59,1998
[4]Maeland E. On the comparison of interpolation methods. IEEE Trans Med Imag, 1988,7:213-217
[5]Parker J A, Kenyon R V, Troxel D E. Comparison of interpolating methods for image resampling. IEEE Trans Med Imag,1983, MI-2:31-39
[6]Park S K, Schowengerdt R A. Image reconstruction by parametric cubic convolution. Comput Vision Graph Image Proc,1983,23:258-272
[7]Keys R. Cubic convolution interpolation for digital image processing. IEEE Trans, on Acoustics, Speech and Signal Processing,1981,29(6):1153-1160.
[8]Meijering E H W, Niessen W J, Viergever M A. Piecewise polynomial kernels for image interpolation:A generalization of cubic convolution. In:Proc IEEE Int Conf Image Processing, Kobe, Japan,1999.647-651
[9]Hsieh H, Andrews H C. Cubic splines for image interpolation and digital filtering. IEEE Trans Acoust Speech Signal Proc,1981,26:508-517
[10]Unser M, Aldroubi A, Eden M. Fast B-spline transforms for continuous image representation and interpolation. IEEE Trans Patt Anal Mach Intell,1991,13: 277-285
[11]H. Takeda, S. Farsiu, and P. Milanfar, "Kernel regression for image processing and reconstruction," IEEE Trans. Image Process., vol.16, no.2, pp.349-366, Feb.2007.
[12]Morse B S, Schwartzwald D. Isophote-based interpolation. In:Proc. of the'98 Int'l Conf. on Image Processing (ICIP'98).Chicago:IEEE Computer Society Press,1998.227-231.
[13]Muresan DD, Parks TW. Adaptively quadratic (AQua) image interpolation. IEEE Trans, on Image Processing,2004,13(5):690-698.
[14]Battiato S, Gallo G Stanco F. A locally adaptive zooming algorithm for digital images. Image and Vision Computing,2002,20(11):805-812.
[15]Takahashi Y, Taguchi A. An enlargement method of digital images with the prediction of high-frequency components. In:IEEE Int'l Conf. on Acoustics, Speech, and Signal Processing (ICASSP2002). Orlando:IEEE Computer Society Press,2002. IV-3700-IV-3703.
[16]Atkins CB, Bouman CA, Allebach JP. Optimal image scaling using pixel classification. In:Proc. of the'01 Int'l Conf. on Image Processing (ICIP'01). Thessaloniki,2001.864-867.
[17]Freeman WT, Jones TR, Pasztor EC. Example-based super-resolution. IEEE Computer Graphics and Applications,2002,22(2):56-65
[18]Glasner D, Bagon S, Irani M. Super-resolution from a single image. In:IEEE 12th International Conference on Computer Vision (ICCV'09). Kyoto:IEEE Computer Society Press,2009.349-356.
[19]Chang H, Yeung DY, Xiong YM. Super-resolution through neighbor embedding. In:IEEE Computer Society Conf. on Computer Vision and Pattern Recognition (CVPR'04). Washington:IEEE Computer Society Press,2004,1-275-1-282.
[20]Jensen K, Anastassiou D. Subpixel edge localization and the interpolation of still images. IEEE Trans, on Image Processing,1995,4(3):285-295.
[21]H. A. Aly and E. Dubois. Image up-sampling using totalvariation regularization with a new observation model. IEEE Trans, on IP,14(10):1647-1659,2005.
[22]R. Fattal. Upsampling via imposed edges statistics. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2007),26(3):95:1-95:8,2007.
[23]Q. Shan, Z. Li, J. Jia, and C. K. Tang. Fast image/video upsampling. ACM Transactions on Graphics (SIGGRAPH ASIA),2008.
[24]ALY, H. DUBOIS,E. Image up-sampling using total-variation regularization with a new observation model. IEEE Trans. Image Processing 14,10,1647-1659. 2005.
[25]Pumar M A. Zooming of terrain imagery using fractal-based interpolation. Comput Graphic,1996,20:171-176
[26]Munoz A, Blu T, Unser M. Least-squares image resizing using finite differences. IEEE Trans Image Proc,2001,10:1365-1378
[27]Unser M, Aldroubi A, Eden M. Enlargement or reduction of digital images with minimum loss of information. IEEE Trans Image Proc,1995,4:247-258
[28]B.S.Morse and D. Schwartzwald. Image magnification using level-set reconstruction. In CVPR, volume 1, pages 333-340,2001.
[29]W. Dong, L. Zhang, G. Shi, and X.Wu, "Nonlocal back-projection for adaptive image enlargement," in Proc. IEEE Int. Conf. Image Process., Cairo, Egypt, Nov. 7-10,2009, pp.349-352.
[30]Allebach J, Wong PW. Edge-Directed interpolation. In:Proc. of the'96 Int'l Conf. on Image Processing (ICIP'96). Lausanne:IEEE Computer Society Press,1996.707-710.
[31]L. Zhang and X. Wu, Image interpolation via directional filtering and data fusion, IEEE Trans. Image Process., vol.15, no.8, pp.2226-2238, Aug.2006.
[32]H. Shi, Canny edge based image expansion, Circuits and Systems,2002. ISCAS 2002. IEEE International Symposium on. Vol.1,1-785-I-788
[33]Wu XL, Zhang XJ. Image interpolation using texture orientation map and kernel Fisher discriminant. In:IEEE Int'l Conf. on Image Processing (ICIP'05). Genoa: IEEE Computer Society Press,2005.1-49-52.
[34]Zhang L, Wu XL. An edge-guided image interpolation algorithm via directional filtering and data fusion. IEEE Trans, on Image Processing,2006,15(8):2226-2238.
[35]F. Malgouyres and F. Guichard, "Edge direction preserving image zooming:A mathematical and numerical analysis," SI AM J. Numer. Anal., vol.39, pp.1-37, 2001.
[36]Li M, Nguyen TQ. Markov random field model-based edge-directed image interpolation. IEEE Trans, on Image Processing,2008,17(7):1121-1128.
[37]Zhe W, Ma KK, Cai CH. Edge-contrast-guided image interpolation using directional variation field diffusion. In:17th IEEE Int'l Conf. on Image Processing (ICIP'10). Hong Kong,2010:2005-2008.
[38]Mishiba K, Suzuki T, Ikehara M. Edge-adaptive image interpolation using constrained least squares. In:17th IEEE Int'l Conf. on Image Processing (ICIP'10). Hong Kong,2010:2837-2840.
[39]Li X, Orchard MT. New edge-directed interpolation. IEEE Trans, on Image Processing,2001,10(10):1521-1527.
[40]Zhang X, Wu X. Image interpolation by adaptive 2-D autoregressive modeling and soft-decision estimation. IEEE Trans Image Proc,2008,17:887-896
[41]Mishiba K, Suzuki T, Ikehara M. Edge-Adaptive image interpolation using constrained least squares. In:Proc. of the 2010 Int'l Conf. on Image Processing (ICIP 2010). Hong Kong:IEEE Computer Society Press,2010.2837-2840.
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