利用小波变换的精确直方图规定化技术的研究
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摘要
直方图规定化技术,作为图像增强技术的一个重要工具,尽管在连续域上有了精确结果。但对离散域的数字图像,却很难得到精确结果。
近期,一种基于局部像素灰度的精确排序算法解决了精确直方图规定化问题。但是,鉴于该方法在保留图像细节和运行速度方面的不足,本文提出了一种基于小波技术的精确直方图规定化算法。实验结果表明,本文提出的算法在保留图像细节和提高运行速度方面都较原算法有所改进,并取得了较好的效果。此外,在文中对本文提出的算法的排序失误率,给出了合理的分析模型。
Histogram specification (equalization) is an important tool for tasks such as image enhancement. Although this problem has exact solution for continuous images, in the case of digital images, it is ill posed.
Recently, an exact pixel ordering method based solely on local image intensity was proposed, yet still with some limitations, especially since it ignores the important image edge information. In this paper, we present a wavelet-based method that simultaneously achieves the exact histogram specification and good image enhancement performance. It does so through a carefully designed strict pixel ordering process, during which the wavelet coefficients are fine tuned for the image enhancement purpose. Compared to previous work, this approach takes into account not only local mean intensity values, but also local edge information. Experimental results and comparison with state-of-the-art methods are presented.
近期,一种基于局部像素灰度的精确排序算法解决了精确直方图规定化问题。但是,鉴于该方法在保留图像细节和运行速度方面的不足,本文提出了一种基于小波技术的精确直方图规定化算法。实验结果表明,本文提出的算法在保留图像细节和提高运行速度方面都较原算法有所改进,并取得了较好的效果。此外,在文中对本文提出的算法的排序失误率,给出了合理的分析模型。
Histogram specification (equalization) is an important tool for tasks such as image enhancement. Although this problem has exact solution for continuous images, in the case of digital images, it is ill posed.
Recently, an exact pixel ordering method based solely on local image intensity was proposed, yet still with some limitations, especially since it ignores the important image edge information. In this paper, we present a wavelet-based method that simultaneously achieves the exact histogram specification and good image enhancement performance. It does so through a carefully designed strict pixel ordering process, during which the wavelet coefficients are fine tuned for the image enhancement purpose. Compared to previous work, this approach takes into account not only local mean intensity values, but also local edge information. Experimental results and comparison with state-of-the-art methods are presented.
引文
[1]徐飞,施晓红.Matlab 应用图像处理(第一版)[M].西安:西安电子科技大学出版社.2002.
[2]R.C.Gonzalez,R.E.Wood.Digital Image Processing 2~(nd) Edition[M].Beijing:Publishing House of Electronics Industry.2003.
[3]阮秋琦.数字图像处理学[M].北京:电子工业出版社.2001.
[4]A.Bovik.Handbook of Image and Video Processing,2~(nd) Edition[M].Beijing:Publishing House of Electronics Industry.2006.
[5]D.L.Donoho.De-noising by Soft-thresholding[J].IEEE Transactions on Information Theory.1995,41(3):613-627.
[6]M.Lang,H.Guo,J.E.Odegard,C.S.Burrus,R.O.Wells,Jr.MeVis.Noise Reduction Using An Undecimated Discrete Wavelet Transform[J].IEEE Signal Processing Letters.2002,3(1):10-12..
[7]赵秋宇,王晓红,张德喜.可增强图像细节的改进的直方图均衡化算法[J].信阳师范学院学报(自然科学版).2008,21(4):601-603.
[8]杨词银,黄廉卿.基于幂函数的加权自适应直方图均衡[J].光电子·激光.2002,13(5):515-517.
[9]R.H.Sherrier,G.A.Johnson.Regionally Adaptive Histogram Equalization of the Chest.IEEE Transactions on Medical Imaging.1987,6(1):1-7.
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[11]D.Coltuc,P.Bolon,J.M.Chassery.Exact Histogram Specification.IEEE Transactions on Image Processing[J].2006,15(5):1143-1152.
[12]李华美,汪天富,林江莉,李德玉.基于精确直方图规格化的医学超声图像增强[J].中国医学影像技术.2008,24(2):278-281.
[13]D.Coltuc,P.Bolon.An Inverse Problem:Histogram Equalization[C].Signal Processing Conference 9th.1998:861-864.
[14]D.Coltuc, P.Bolon.Strict Ordering On Discrete Images and Applications[C].Proceedings of IEEE International Conference on Image Processing.1999, 3(3):150-153.
[15]D.Coltuc, P.Bolon.Color Image Watermarking In HSI Space[C].IEEE International Conference on Image Processing.2000, 3(3):698-701.
[16]A.Rosenfeld, A.C.Kak.Digital Picture Processing[M].Upper Saddle River, New Jersey, Prentice-Hall.1982.
[17]J.P.Rolland, V.Vo, B.Bloss, C.K.Abbey.Fast Algorithm for Histogram Matching Applications to Texture Synthesis[J].Journal of Electronic Imaging.2000, 9(1): 39-45.
[18]J.A.Stark.Adaptive Image Contrast Enhancement Using Generalization of Histogram Equalization[J].IEEE Transactions on Signal Processing.2000, 9(5): 889-896.
[19]V.Caselles, J.L.Lisani, J.M.Morel, G.Sapiro.Shape Preserving Local Histogram Modification[J].IEEE Transactions on Signal Processing.1999, 8(2): 220-230.
[20]Y.J.Zhang.Improving the Accuracy of Direct Histogram Specification [J].Electronics Letters 1992, 28(3): 213-214.
[21]E.L.Hall.Almost Uniform Distribution for Computer Image Enhancement[J].IEEE Transactions on Computer.1974, 23(2): 207-208.
[22]S.Mallat.A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.1989, 11(7): 674-693.
[23]S.Mallat.A Wavelet Tour of Signal Processing 2nd Edition[M].Beijing: China Machine Press.2003.
[24]M.S.Crouse, R.D.Nowak, R.G.Baraniuk.Wavelet-Based Statistical Signal Processing Using Hidden Markov Models[J].IEEE Transactions on Signal Processing.1998, 46(4): 886-902.
[25]Y.Wan, R.D.Nowak.A Wavelet-Based Statistical Model for Image Restoration[C].IEEE International Conference on Image Processing.2001, 1(1): 598-601.
[26]J.Y.Kim, L.S.Kim, S.H.Hwang.An Advanced Contrast Enhancement Using Partially Overlapped Sub-Block Histogram Equalization[J].IEEE Transactions on Circuits System Video Technology.2001, 11(4): 475-484.
[27]H.C.Zhu, H.Y.Francis, F.K.Lam.Image Contrast Enhancement by Constrained Local Histogram Equalization[J].Computer Vision and Image Understand.1999, 73(2): 281-290.
[28]E.P.Simoncelli, E.H.Adelson.Noise Removal via Bayesian Wavelet Coring[C].Proceedings of IEEE International Conference Image Processing.1996, 1(1): 379-382.
[29]A.P.Dempster, N.M.Laird, D.B.Rubin.Maximum Likelihood from Incomplete Data via the EM Algorithm[J].Journal of the Royal Statistical Society.1977, 39(1): 1-38.
[30]G.J.McLachlan, T.Krishnan.The EM Algorithm and Extensions[M].New York: Wiley.1997.
[31]R.O.Duda, P.E.Hart, D.G.Stork.Pattern Classification 2~(nd) Edition[M].Beijing: China Machine Press.2004.
[2]R.C.Gonzalez,R.E.Wood.Digital Image Processing 2~(nd) Edition[M].Beijing:Publishing House of Electronics Industry.2003.
[3]阮秋琦.数字图像处理学[M].北京:电子工业出版社.2001.
[4]A.Bovik.Handbook of Image and Video Processing,2~(nd) Edition[M].Beijing:Publishing House of Electronics Industry.2006.
[5]D.L.Donoho.De-noising by Soft-thresholding[J].IEEE Transactions on Information Theory.1995,41(3):613-627.
[6]M.Lang,H.Guo,J.E.Odegard,C.S.Burrus,R.O.Wells,Jr.MeVis.Noise Reduction Using An Undecimated Discrete Wavelet Transform[J].IEEE Signal Processing Letters.2002,3(1):10-12..
[7]赵秋宇,王晓红,张德喜.可增强图像细节的改进的直方图均衡化算法[J].信阳师范学院学报(自然科学版).2008,21(4):601-603.
[8]杨词银,黄廉卿.基于幂函数的加权自适应直方图均衡[J].光电子·激光.2002,13(5):515-517.
[9]R.H.Sherrier,G.A.Johnson.Regionally Adaptive Histogram Equalization of the Chest.IEEE Transactions on Medical Imaging.1987,6(1):1-7.
[10]R.B.Paranjape,W.M.Morrow,R.M.Rangayyan.Adaptive Neighborhood Histogram Equalization for Image Enhancement[J].Graphic Models and Image Processing.1992,54(3):259-267.
[11]D.Coltuc,P.Bolon,J.M.Chassery.Exact Histogram Specification.IEEE Transactions on Image Processing[J].2006,15(5):1143-1152.
[12]李华美,汪天富,林江莉,李德玉.基于精确直方图规格化的医学超声图像增强[J].中国医学影像技术.2008,24(2):278-281.
[13]D.Coltuc,P.Bolon.An Inverse Problem:Histogram Equalization[C].Signal Processing Conference 9th.1998:861-864.
[14]D.Coltuc, P.Bolon.Strict Ordering On Discrete Images and Applications[C].Proceedings of IEEE International Conference on Image Processing.1999, 3(3):150-153.
[15]D.Coltuc, P.Bolon.Color Image Watermarking In HSI Space[C].IEEE International Conference on Image Processing.2000, 3(3):698-701.
[16]A.Rosenfeld, A.C.Kak.Digital Picture Processing[M].Upper Saddle River, New Jersey, Prentice-Hall.1982.
[17]J.P.Rolland, V.Vo, B.Bloss, C.K.Abbey.Fast Algorithm for Histogram Matching Applications to Texture Synthesis[J].Journal of Electronic Imaging.2000, 9(1): 39-45.
[18]J.A.Stark.Adaptive Image Contrast Enhancement Using Generalization of Histogram Equalization[J].IEEE Transactions on Signal Processing.2000, 9(5): 889-896.
[19]V.Caselles, J.L.Lisani, J.M.Morel, G.Sapiro.Shape Preserving Local Histogram Modification[J].IEEE Transactions on Signal Processing.1999, 8(2): 220-230.
[20]Y.J.Zhang.Improving the Accuracy of Direct Histogram Specification [J].Electronics Letters 1992, 28(3): 213-214.
[21]E.L.Hall.Almost Uniform Distribution for Computer Image Enhancement[J].IEEE Transactions on Computer.1974, 23(2): 207-208.
[22]S.Mallat.A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.1989, 11(7): 674-693.
[23]S.Mallat.A Wavelet Tour of Signal Processing 2nd Edition[M].Beijing: China Machine Press.2003.
[24]M.S.Crouse, R.D.Nowak, R.G.Baraniuk.Wavelet-Based Statistical Signal Processing Using Hidden Markov Models[J].IEEE Transactions on Signal Processing.1998, 46(4): 886-902.
[25]Y.Wan, R.D.Nowak.A Wavelet-Based Statistical Model for Image Restoration[C].IEEE International Conference on Image Processing.2001, 1(1): 598-601.
[26]J.Y.Kim, L.S.Kim, S.H.Hwang.An Advanced Contrast Enhancement Using Partially Overlapped Sub-Block Histogram Equalization[J].IEEE Transactions on Circuits System Video Technology.2001, 11(4): 475-484.
[27]H.C.Zhu, H.Y.Francis, F.K.Lam.Image Contrast Enhancement by Constrained Local Histogram Equalization[J].Computer Vision and Image Understand.1999, 73(2): 281-290.
[28]E.P.Simoncelli, E.H.Adelson.Noise Removal via Bayesian Wavelet Coring[C].Proceedings of IEEE International Conference Image Processing.1996, 1(1): 379-382.
[29]A.P.Dempster, N.M.Laird, D.B.Rubin.Maximum Likelihood from Incomplete Data via the EM Algorithm[J].Journal of the Royal Statistical Society.1977, 39(1): 1-38.
[30]G.J.McLachlan, T.Krishnan.The EM Algorithm and Extensions[M].New York: Wiley.1997.
[31]R.O.Duda, P.E.Hart, D.G.Stork.Pattern Classification 2~(nd) Edition[M].Beijing: China Machine Press.2004.