基于提升小波变换的数字水印技术研究
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摘要
随着计算机网络的快速发展，网络上传输的信息模式发生了翻天覆地的变化，信息的交流变得更加快捷，形式也呈现多样化。尤其是数字图像形式的传播也变得越来越普遍。由于数字内容很容易复制、修改，网络上传播的数字内容存在着大量的盗版和侵权问题，因此知识产权的保护越来越引起重视。数字水印作为信息安全领域的一门新兴学科，已经引起了人们的极大关注。
小波分析由于具有多分辨率和多尺度分析特性，在图像处理方面得到了广泛应用。利用小波分析可以更好地控制水印信息在图像中的分布，从而协调解决稳健性和不可见性之间的矛盾。小波变换的提升方案是构造小波变换的一种新方法，其特点是所有的运算都在空间域进行，从而摆脱了对频域的依赖。由于变换过程中不必依赖傅立叶分析，且容易实现快速算法，所以它广泛的应用于图形图像处理中。
本文主要研究小波提升技术及其在彩色图像数字水印中的应用算法。主要内容如下：
首先，介绍了数字水印的基本特征、原理以及目前国内外的研究现状，包括数字水印的基本特征及分类，归纳了数字水印系统的基本框架，概括性介绍了目前常见的数字水印算法。
其次，分析了人眼视觉系统模型，小波变换的基本原理、Mallat算法以及图像的二维正交小波分解。
然后，介绍了提升小波变换原理及其图像水印中的应用，提出了一种基于提升方案小波的彩色图像数字水印算法。根据人眼视觉特性，在黑暗区域或特别亮的区域，对比度门限(contrast sensitivity threshold)就越高。首先将彩色图像由RGB色彩空间转换成YUV色彩空间，提取Y(亮度)分量，利用亮度特性，将水印可以较大强度地嵌入图像较亮的部分。此算法将空域和频域有效地结合起来。并用仿真实验验证了算法的有效性。
随后，提出了一种基于块分类的提升方案小波的自适应水印算法。该算法首先将彩色图象从RGB色彩空间转化成YUV色彩空间。在YUV模型中提取Y(亮度)分量进行分块，与以往不同的是，本文利用每块的边缘点分布率求出每块的水印嵌入强度，真正做到水印的自适应嵌入。对每一图像块进行提升小波变换。再根据水印嵌入强度因子将水印自适应嵌入到每一块的低频系数中的最大数当中。实验结果表明，此算法易于实现，且具有较好的稳健性。
最后，总结了本人的研究结果并对数字水印的进一步发展进行了展望。
With the fast development of computer network, information model on the transmission has undergone enormous changes, the exchange of information has become more efficient and the form of information has been diversified. Especially, digital images are more and more prevalent. Because digital information can be copied and modified easily,a lot of piracy and copyright issues exist in the digital information that transmitted in the net work. Therefore the protection of intellectual property has become more and more important. Digital watermarking as a new information security has attracted people's attention.
Wavelets have found wide applications in image processing due to its multiresolution and multiscale analysis properties. In addition, the aspect of wavelets is helpful in managing a good distribution or location of the message in the image in terms of robustness versus invisibility. Lifting wavelet is a new method in wavelet construction. Its characteristic is that all computations are processed in spacial domain, independent of frequency domain. Without relying on Fourier analysis, the transformation process can be performed with rapid algorithm, so it's widely used in graphics and video processing.
This thesis focuses on lifting schemes of wavelets and their application algorithms for image digital watermarking. The main contents are outlined as follows:
Firstly, we introduce the essential features, principle and the state of the art of the digital watermark, including essential feature and classification of the digital watermarking, sum up the basic frame of the digital watermark system, and introduce the common digital watermarking algorithms at present.
Secondly, Human Visual System (HVS), fundamental principle of wavelets, Mallat algorithm and two-dimensional wavelet decomposition of image are analyzed.
Then we introduce the algorithm of lifting wavelet and its applications in image digital watermarking, and propose a new watermarking method based on luminance identity. According to human virtual system, the lighter or darker the original image is, the bigger the contrast sensitivity threshold is. We can insert watermarks into the most lightful area of the image based on luminance identity. This method combines area space and frequency space effectively. And the validity of the algorithm is verified. with the artificial experiment.
Afterwards, an adaptive color image watermarking algorithm is proposed, which is based on block classification and lifting scheme wavelet. First we change the original image from RGB color space to YUV color space, then extract Y component and split it into blocks. According to the visual masking features of HVS, watermarking insert scale factor of every block was calculated. Based on the lifting scheme wavelet, watermarking components were inserted into the largest coefficient of low-frequency coefficients adaptively according to the masked scales. The experimental results demonstrate that this method can be carried out simply and has good robusticity.
小波分析由于具有多分辨率和多尺度分析特性，在图像处理方面得到了广泛应用。利用小波分析可以更好地控制水印信息在图像中的分布，从而协调解决稳健性和不可见性之间的矛盾。小波变换的提升方案是构造小波变换的一种新方法，其特点是所有的运算都在空间域进行，从而摆脱了对频域的依赖。由于变换过程中不必依赖傅立叶分析，且容易实现快速算法，所以它广泛的应用于图形图像处理中。
本文主要研究小波提升技术及其在彩色图像数字水印中的应用算法。主要内容如下：
首先，介绍了数字水印的基本特征、原理以及目前国内外的研究现状，包括数字水印的基本特征及分类，归纳了数字水印系统的基本框架，概括性介绍了目前常见的数字水印算法。
其次，分析了人眼视觉系统模型，小波变换的基本原理、Mallat算法以及图像的二维正交小波分解。
然后，介绍了提升小波变换原理及其图像水印中的应用，提出了一种基于提升方案小波的彩色图像数字水印算法。根据人眼视觉特性，在黑暗区域或特别亮的区域，对比度门限(contrast sensitivity threshold)就越高。首先将彩色图像由RGB色彩空间转换成YUV色彩空间，提取Y(亮度)分量，利用亮度特性，将水印可以较大强度地嵌入图像较亮的部分。此算法将空域和频域有效地结合起来。并用仿真实验验证了算法的有效性。
随后，提出了一种基于块分类的提升方案小波的自适应水印算法。该算法首先将彩色图象从RGB色彩空间转化成YUV色彩空间。在YUV模型中提取Y(亮度)分量进行分块，与以往不同的是，本文利用每块的边缘点分布率求出每块的水印嵌入强度，真正做到水印的自适应嵌入。对每一图像块进行提升小波变换。再根据水印嵌入强度因子将水印自适应嵌入到每一块的低频系数中的最大数当中。实验结果表明，此算法易于实现，且具有较好的稳健性。
最后，总结了本人的研究结果并对数字水印的进一步发展进行了展望。
With the fast development of computer network, information model on the transmission has undergone enormous changes, the exchange of information has become more efficient and the form of information has been diversified. Especially, digital images are more and more prevalent. Because digital information can be copied and modified easily,a lot of piracy and copyright issues exist in the digital information that transmitted in the net work. Therefore the protection of intellectual property has become more and more important. Digital watermarking as a new information security has attracted people's attention.
Wavelets have found wide applications in image processing due to its multiresolution and multiscale analysis properties. In addition, the aspect of wavelets is helpful in managing a good distribution or location of the message in the image in terms of robustness versus invisibility. Lifting wavelet is a new method in wavelet construction. Its characteristic is that all computations are processed in spacial domain, independent of frequency domain. Without relying on Fourier analysis, the transformation process can be performed with rapid algorithm, so it's widely used in graphics and video processing.
This thesis focuses on lifting schemes of wavelets and their application algorithms for image digital watermarking. The main contents are outlined as follows:
Firstly, we introduce the essential features, principle and the state of the art of the digital watermark, including essential feature and classification of the digital watermarking, sum up the basic frame of the digital watermark system, and introduce the common digital watermarking algorithms at present.
Secondly, Human Visual System (HVS), fundamental principle of wavelets, Mallat algorithm and two-dimensional wavelet decomposition of image are analyzed.
Then we introduce the algorithm of lifting wavelet and its applications in image digital watermarking, and propose a new watermarking method based on luminance identity. According to human virtual system, the lighter or darker the original image is, the bigger the contrast sensitivity threshold is. We can insert watermarks into the most lightful area of the image based on luminance identity. This method combines area space and frequency space effectively. And the validity of the algorithm is verified. with the artificial experiment.
Afterwards, an adaptive color image watermarking algorithm is proposed, which is based on block classification and lifting scheme wavelet. First we change the original image from RGB color space to YUV color space, then extract Y component and split it into blocks. According to the visual masking features of HVS, watermarking insert scale factor of every block was calculated. Based on the lifting scheme wavelet, watermarking components were inserted into the largest coefficient of low-frequency coefficients adaptively according to the masked scales. The experimental results demonstrate that this method can be carried out simply and has good robusticity.
引文
[1] 孙圣和，陆哲明．数字水印处理技术．电子学报，2000，28(8)：85～90．
[2] Reticolas F.A.R, Anderson R.J., Kuhn M.G.., Information Hiding-A survey.Proceedings of IEEE, 1999,87(7): 1062～1078.
[3] Moulin R, Osullivan J. A., Information-theoretic analysis of information hiding. IEEE Trans. Inf. Theory, 2003, 49(3): 563～593.
[4] Podilchuk C., Zeng W., Image-Adaptive watermarking using visual models. IEEE Journal of Selected Areas on Communications, 1998, 16(4): 525～539.
[5] Watson A. B., DCT quantization matrices visually optimized for individual images. SPIE: Human Vision, Visual Processing and Digital Display Ⅳ. 1993, 1913: 201～216.
[6] Huang J. W., Shi Y. Q., An adaptive image watermarking scheme based on visual masking. IEEE Electronics Letters, 1998, 34(8): 748～750.
[7] Wang H. M., Su RC., Kuo C. J., Wavelet based digital image watermarking. Optics Express. Vol. 3, No 12, 1998: 491-496.
[8] Wei Lu, Hong-Tao, Lu Fu-Lai Chung, Chaos-based spread spectrum robust watermarking in DWT domain, Proc. International Conference On Machine Learning And Cybernetics, Aug 2005.
[9] 马社祥，刘贵忠，曾召华，基于小波变换的数字水印及版权保护，电子与信息学报，Vol．23，No．11，1102-1109，Nov 2001．
[10] Delaigle J., Vleechouwer C., Macq B., Watermarking algorithm based on a human visual model. Signal Processing, 1998, 66(3): 319～335.
[11] Shao Y., Wu G. and Lin X., A wavelet based adaptive watermarking algorithm. Inter. Conf. Info-tech and Info-net (ICII' 01), 2001, 3: 384～389,
[12] Huang J. W., Shi Y. Q., Embedding image watermarking in DC component [J]. IEEE Transactions on Circuits and Systems for Video Technology, 2000, 10(6): 974～979.
[13] 黄达人，刘九芬，黄继武 小波变换域图像水印嵌入对策和算法[J]，软件学报，2002，13(7)：1290～1298．
[14] 楼偶俊，王相海提升方案小波和DCT下的图像盲水印算法[J]，计算机辅助设计与图形学学报，2005，17(4)：846～851．
[15] 黄继武，Shi Yun Q．，姚若河，基于块分类的自适应图像水印算法[J]，中国图象图形学报，1999，4(8)：640～643．
[16] 钮心忻，杨义先，基于小波变换的水印隐藏与检测算法[J]，计算机学报， 2000,23 (1) :21-27.
[17] 齐东旭,分形及其应用,北京：科学出版社,1994, 143-145.
[18] Zhu B.B., Swanson M.D. , Tewfik A.H., When Seeing Isn't Believing[J], Signal Processing Magazine, IEEE, 21(2), Mar 2004.
[19] Barni M., Bartolini F. ,Data hiding for fighting piracy[J], Signal Processing Magazine, IEEE, 21(2), Mar 2004.
[20] Hordan R.V., On digital image watermarking robust to geometric transformations licks. Proceeding of the 2000 International Conference on Image Proceeding, 2000, 3,691 -693.
[21] Barni M., Bartolini F., Cappellini V, Piva A., Salucco F. ,Textbased geometric normalization for robust wartermarking of digital maps. Proceeding of the 2001 IEEE international Conference on Image Processing, 2001,1,1082-1085.
[22] Caldeli R., Barni M., Bartolini F., Piva A., Geometric-invariant robust watermarking through constellation matching in the frequency domain. Proceedings of the 2000 IEEE international Conference on Image Processing, 2000,2,65-68.
[23] Lin C-Y, Wu M., Bloom J. A., Cox I. J., Miller M. L, Lui Y.M., Rotation, scale and translation resilient watermarking for images. IEEE Transactions on Image Processing, 2001,10(5):767-782.
[24] Ni Z., Sung E., Shi Y. Q. Enhancing robustness of digital watermarking against geometric attack based on fractal transform. The 2000 IEEE International Conference on Multimedia and Expo, 2002,2,1033-1036.
[25] Choi H., Kim H., Kim T. ,Robust sinusoidal watermark for images. Electronic Letters, 22 July 1999,35(15):1238-1239.
[26] Agung I .W., Sweeney P., Method for combating random geometric attack on image watermarking. Electronics Letter, 29 March 2001,37(7):420-421.
[27] Ingemar Cox, Matthew L.Miller, Jeffrey Bloom. Digital Watermarking. Mogran Kaufemann Publishers, 2001.
[28] Pitas I., A method for signature casting on digital image. Proc. Of international conference on image processing. 1996,(3):215-218.
[29] Hsu C. I. , Wu J. L. ,Multiresolution watermarking . for digital image. IEEE Trans On Circuits and Systems II: Analog and Digital Signal Processing. 1998:67-68.
[30] Sweldens W. ,The lifting scheme: A new philosophy in biorthogonal wavelet constructions [A].Proceedings of SPIE,San Diego,CA, 1995,2569:68-79.
[31] Wang Chunsheng, Cheng Yiming, Wang Yixiao., An adaptive digital watermarking algorithm based on the classification of image blocks [J]. Computer Engineering and Applocation,2002,38(21):106-110.
[32] Hsu C-T, Wu J-L., Hidden signature in images. IEEE Trans. on Image Processing. 1999,8(1):58-68.
[33] Xia X.G., Design of prefilters for discrete multiwavelet transforms. IEEE Trans. on Signal Processing. 1996,44(1):25-35.
[34] Xia X.G., GBoncelet C, Aree G.R., Wavelet transform based watermark for digital images. Optics Express. 1998,3(12):497-511.
[35] Bao Paul, Ma Xiaohu, Image adaptive watermarking using wavelet domain singular value decomposition. IEEE Trans. 2005,15(1):96-102.
[36] Bender W., Gruhl D., Morimoto N., Techniques for data hiding. Proc. SPIE, vol. 2420,San Jose, CA, Feb. 1995,40.
[37] Pitas I., Kaskalis T. H., Applying signatures on digital images. Proc. IEEE Workshop Nolinear Image and Signal Proceeding, Neos Marmaros, Greece, June 1996,460.
[38] Lam E.Y., Goodman J.W.,A mathematical analysis of the DCT coefficient distributions for images{j}, IEEE Transactions on Image Processing,2000, 9(10):1661-1666.
[39] Muller F. ,Distribution shape of two dimensional DCT coefficients for nature image[J]. Electronics Letter, 1993,29(2): 1935-1936.
[40] Jayant N., Johnston J., Safranek R., Signal compression based on model of human perception. Proceeding of the IEEE, 1993,81(10).
[41] Nick G, Redmill D., Image and video watermark coding for noisy channels, Proc. SPIE Conference' 97, April 1997.
[42] Xie Liehua, Gonzabo A., Joint wavelet compression and authentication watermarking, Proc. IEEE International Conference On Image Processing, 1998.
[43] Fridrich J., Symmetric ciphers based on two-dimensional chaotic maps,. International Journal Of Bifurcation And Chaos, Vol.8,1259-1284,1998.
[44] Mao Yaobin, Chen Guanrong, Lian Shiguo, A novel fast image encryption scheme based on 3D chaotic baker maps, International Journal Of Bifurcation And Chaos, Vol.14, No.10,2004.
[45] Huang Jianyong, Yang Changsheng, Image Digital Watermarking Algorithm Using Multiresolution Wavelet Transform, Proc. IEEE SMC 2004,2977 - 2982 Oct 2004.
[46] Ganglong Duan, Yan Zhang, Jiwen Lu, A multilevel image-adaptive digital watermarking algorithm based on chaotic sequences and ICA, Proc. SCIT'2005,142-146,2005.
[47] Cox I.J.,Kilian J.,Leighton T.,Shamoon T.,Secure spread spectrum watermarking for multimedia. IEEE Trans. on Image Processing. 1997, 6(12):1673～687.
[48] 王丽娜，于戈，王国仁，基于混沌特性改进的小波数字水印算法，电子学报，Vol．29，No．10，1424-1426,2001．
[49] 刘卫国，科学计算与MATLAB语言，中国铁道出版社，2000．
[50] 陈桂明，应用MATLAB语言处理数字信号与数字图像，科学出版社，2000．
[51] 李建平，唐远炎．小波分析方法的应用，重庆大学出版社，2001．
[52] Stephane Mallat著，杨力华、戴道清等译，信号处理的小波导引(第二版)，机械工业出版社，2002．
[2] Reticolas F.A.R, Anderson R.J., Kuhn M.G.., Information Hiding-A survey.Proceedings of IEEE, 1999,87(7): 1062～1078.
[3] Moulin R, Osullivan J. A., Information-theoretic analysis of information hiding. IEEE Trans. Inf. Theory, 2003, 49(3): 563～593.
[4] Podilchuk C., Zeng W., Image-Adaptive watermarking using visual models. IEEE Journal of Selected Areas on Communications, 1998, 16(4): 525～539.
[5] Watson A. B., DCT quantization matrices visually optimized for individual images. SPIE: Human Vision, Visual Processing and Digital Display Ⅳ. 1993, 1913: 201～216.
[6] Huang J. W., Shi Y. Q., An adaptive image watermarking scheme based on visual masking. IEEE Electronics Letters, 1998, 34(8): 748～750.
[7] Wang H. M., Su RC., Kuo C. J., Wavelet based digital image watermarking. Optics Express. Vol. 3, No 12, 1998: 491-496.
[8] Wei Lu, Hong-Tao, Lu Fu-Lai Chung, Chaos-based spread spectrum robust watermarking in DWT domain, Proc. International Conference On Machine Learning And Cybernetics, Aug 2005.
[9] 马社祥，刘贵忠，曾召华，基于小波变换的数字水印及版权保护，电子与信息学报，Vol．23，No．11，1102-1109，Nov 2001．
[10] Delaigle J., Vleechouwer C., Macq B., Watermarking algorithm based on a human visual model. Signal Processing, 1998, 66(3): 319～335.
[11] Shao Y., Wu G. and Lin X., A wavelet based adaptive watermarking algorithm. Inter. Conf. Info-tech and Info-net (ICII' 01), 2001, 3: 384～389,
[12] Huang J. W., Shi Y. Q., Embedding image watermarking in DC component [J]. IEEE Transactions on Circuits and Systems for Video Technology, 2000, 10(6): 974～979.
[13] 黄达人，刘九芬，黄继武 小波变换域图像水印嵌入对策和算法[J]，软件学报，2002，13(7)：1290～1298．
[14] 楼偶俊，王相海提升方案小波和DCT下的图像盲水印算法[J]，计算机辅助设计与图形学学报，2005，17(4)：846～851．
[15] 黄继武，Shi Yun Q．，姚若河，基于块分类的自适应图像水印算法[J]，中国图象图形学报，1999，4(8)：640～643．
[16] 钮心忻，杨义先，基于小波变换的水印隐藏与检测算法[J]，计算机学报， 2000,23 (1) :21-27.
[17] 齐东旭,分形及其应用,北京：科学出版社,1994, 143-145.
[18] Zhu B.B., Swanson M.D. , Tewfik A.H., When Seeing Isn't Believing[J], Signal Processing Magazine, IEEE, 21(2), Mar 2004.
[19] Barni M., Bartolini F. ,Data hiding for fighting piracy[J], Signal Processing Magazine, IEEE, 21(2), Mar 2004.
[20] Hordan R.V., On digital image watermarking robust to geometric transformations licks. Proceeding of the 2000 International Conference on Image Proceeding, 2000, 3,691 -693.
[21] Barni M., Bartolini F., Cappellini V, Piva A., Salucco F. ,Textbased geometric normalization for robust wartermarking of digital maps. Proceeding of the 2001 IEEE international Conference on Image Processing, 2001,1,1082-1085.
[22] Caldeli R., Barni M., Bartolini F., Piva A., Geometric-invariant robust watermarking through constellation matching in the frequency domain. Proceedings of the 2000 IEEE international Conference on Image Processing, 2000,2,65-68.
[23] Lin C-Y, Wu M., Bloom J. A., Cox I. J., Miller M. L, Lui Y.M., Rotation, scale and translation resilient watermarking for images. IEEE Transactions on Image Processing, 2001,10(5):767-782.
[24] Ni Z., Sung E., Shi Y. Q. Enhancing robustness of digital watermarking against geometric attack based on fractal transform. The 2000 IEEE International Conference on Multimedia and Expo, 2002,2,1033-1036.
[25] Choi H., Kim H., Kim T. ,Robust sinusoidal watermark for images. Electronic Letters, 22 July 1999,35(15):1238-1239.
[26] Agung I .W., Sweeney P., Method for combating random geometric attack on image watermarking. Electronics Letter, 29 March 2001,37(7):420-421.
[27] Ingemar Cox, Matthew L.Miller, Jeffrey Bloom. Digital Watermarking. Mogran Kaufemann Publishers, 2001.
[28] Pitas I., A method for signature casting on digital image. Proc. Of international conference on image processing. 1996,(3):215-218.
[29] Hsu C. I. , Wu J. L. ,Multiresolution watermarking . for digital image. IEEE Trans On Circuits and Systems II: Analog and Digital Signal Processing. 1998:67-68.
[30] Sweldens W. ,The lifting scheme: A new philosophy in biorthogonal wavelet constructions [A].Proceedings of SPIE,San Diego,CA, 1995,2569:68-79.
[31] Wang Chunsheng, Cheng Yiming, Wang Yixiao., An adaptive digital watermarking algorithm based on the classification of image blocks [J]. Computer Engineering and Applocation,2002,38(21):106-110.
[32] Hsu C-T, Wu J-L., Hidden signature in images. IEEE Trans. on Image Processing. 1999,8(1):58-68.
[33] Xia X.G., Design of prefilters for discrete multiwavelet transforms. IEEE Trans. on Signal Processing. 1996,44(1):25-35.
[34] Xia X.G., GBoncelet C, Aree G.R., Wavelet transform based watermark for digital images. Optics Express. 1998,3(12):497-511.
[35] Bao Paul, Ma Xiaohu, Image adaptive watermarking using wavelet domain singular value decomposition. IEEE Trans. 2005,15(1):96-102.
[36] Bender W., Gruhl D., Morimoto N., Techniques for data hiding. Proc. SPIE, vol. 2420,San Jose, CA, Feb. 1995,40.
[37] Pitas I., Kaskalis T. H., Applying signatures on digital images. Proc. IEEE Workshop Nolinear Image and Signal Proceeding, Neos Marmaros, Greece, June 1996,460.
[38] Lam E.Y., Goodman J.W.,A mathematical analysis of the DCT coefficient distributions for images{j}, IEEE Transactions on Image Processing,2000, 9(10):1661-1666.
[39] Muller F. ,Distribution shape of two dimensional DCT coefficients for nature image[J]. Electronics Letter, 1993,29(2): 1935-1936.
[40] Jayant N., Johnston J., Safranek R., Signal compression based on model of human perception. Proceeding of the IEEE, 1993,81(10).
[41] Nick G, Redmill D., Image and video watermark coding for noisy channels, Proc. SPIE Conference' 97, April 1997.
[42] Xie Liehua, Gonzabo A., Joint wavelet compression and authentication watermarking, Proc. IEEE International Conference On Image Processing, 1998.
[43] Fridrich J., Symmetric ciphers based on two-dimensional chaotic maps,. International Journal Of Bifurcation And Chaos, Vol.8,1259-1284,1998.
[44] Mao Yaobin, Chen Guanrong, Lian Shiguo, A novel fast image encryption scheme based on 3D chaotic baker maps, International Journal Of Bifurcation And Chaos, Vol.14, No.10,2004.
[45] Huang Jianyong, Yang Changsheng, Image Digital Watermarking Algorithm Using Multiresolution Wavelet Transform, Proc. IEEE SMC 2004,2977 - 2982 Oct 2004.
[46] Ganglong Duan, Yan Zhang, Jiwen Lu, A multilevel image-adaptive digital watermarking algorithm based on chaotic sequences and ICA, Proc. SCIT'2005,142-146,2005.
[47] Cox I.J.,Kilian J.,Leighton T.,Shamoon T.,Secure spread spectrum watermarking for multimedia. IEEE Trans. on Image Processing. 1997, 6(12):1673～687.
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