小波分析与隐马尔可夫模型在图像处理中的应用
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摘要
图像是人类相互交流和认识客观世界的主要媒体。科学研究和统计表明，人类从外界获得的信息约有75%来自视觉系统。随着计算机的发展，数字图像处理近年来得到极大的重视和长足的发展，已经迅速渗透到人类生活和社会发展的各个方面，使人们传统的生产手段和生活方式发生了巨大的变化。
小波分析是近十多年来迅速发展起来的一门新兴学科，它不仅具有非常丰富的数学内容，而且是一种对应用有巨大潜力、多方面适用的工具。在图像处理方面，小波变换已经在图像压缩、图像去噪、图像增强、图像融合中得到广泛应用。隐马尔可夫模型是20世纪70年代初提出的，现已成为语音识别领域居主导地位的方法。在图像处理方面，隐马尔可夫模型是20世纪90年代初才开始被用于文字图像的识别和纹理图像的分割。
本文主要研究小波分析与隐马尔可夫模型在图像处理中的应用，包括如下两部分：一部分研究小波分析与隐马尔可夫模型相结合在图像分割中的应用，特别是在文本图像分割中的应用；另一部分研究ENO（Essentially Non－Oscillatory）小波变换及其在图像压缩中的应用。主要工作如下：
1． 提出一些基于小波域隐马尔可夫树模型（HMT）的图像分割新算法，每个算法包括详细的分析、算法步骤、计算量评估与实例，结果表明新的HMT分割算法具有可行性与有效性。
2． 介绍ENO小波，并根据Haar小波的自身特点提出一种新的Eno-haar小波变换算法，最后通过实例说明了新算法在信号以及图像压缩中的可行性和有效性。
Image is the main media, by which people communicate and understand the real world. Shown by many scientific researches and statistical results, about 75 percent of information that people acquire from outside root in the visual system. With the development of computers, digital image processing has been recently attached more importance and developed rapidly. It has penetrated into all kinds of aspects in living and social development, moreover has made traditional product means and life style change enormously.
Wavelet analysis that has promptly become a new subject not only has very abundant mathematic knowledge but also is a promising tool to application field. In image processing, wavelet transforms has been applied to image compression, image de-noising, image fusion, etc. Hidden Markov models that were put forward in the seventies of the twentieth century have played a leading role in speech recognition field. In image processing, hidden Markov models didn't be applied to document recognition and texture image segmentation until the nineties of the twentieth.
The dissertation is devoted to the application of wavelet analysis and hidden Markov models to image processing. Two parts are included in the dissertation. In the first part, it is addressed that the combination of wavelet analysis and hidden Markov models is applied to image segmentation, especially to document segmentation. In another part, the essentially non-oscillatory (ENO) wavelet transforms and its application to image compression are addressed. The primary work in the dissertation is in detail:
1. To propose some image segmentation algorithms using wavelet-domain hidden Markov tree models. Each algorithm includes particular analysis, steps, evaluation of computation and many experiments. It is proved by many experiments that these new image segmentation algorithms are feasible and efficient.
2. To introduce ENO wavelet transforms, moreover, to propose a new Eno-haar wavelet transforms according to the inner characteristics of Haar wavelet transforms. And it is proved by many experiments that the new algorithm is feasible to image compression.
小波分析是近十多年来迅速发展起来的一门新兴学科，它不仅具有非常丰富的数学内容，而且是一种对应用有巨大潜力、多方面适用的工具。在图像处理方面，小波变换已经在图像压缩、图像去噪、图像增强、图像融合中得到广泛应用。隐马尔可夫模型是20世纪70年代初提出的，现已成为语音识别领域居主导地位的方法。在图像处理方面，隐马尔可夫模型是20世纪90年代初才开始被用于文字图像的识别和纹理图像的分割。
本文主要研究小波分析与隐马尔可夫模型在图像处理中的应用，包括如下两部分：一部分研究小波分析与隐马尔可夫模型相结合在图像分割中的应用，特别是在文本图像分割中的应用；另一部分研究ENO（Essentially Non－Oscillatory）小波变换及其在图像压缩中的应用。主要工作如下：
1． 提出一些基于小波域隐马尔可夫树模型（HMT）的图像分割新算法，每个算法包括详细的分析、算法步骤、计算量评估与实例，结果表明新的HMT分割算法具有可行性与有效性。
2． 介绍ENO小波，并根据Haar小波的自身特点提出一种新的Eno-haar小波变换算法，最后通过实例说明了新算法在信号以及图像压缩中的可行性和有效性。
Image is the main media, by which people communicate and understand the real world. Shown by many scientific researches and statistical results, about 75 percent of information that people acquire from outside root in the visual system. With the development of computers, digital image processing has been recently attached more importance and developed rapidly. It has penetrated into all kinds of aspects in living and social development, moreover has made traditional product means and life style change enormously.
Wavelet analysis that has promptly become a new subject not only has very abundant mathematic knowledge but also is a promising tool to application field. In image processing, wavelet transforms has been applied to image compression, image de-noising, image fusion, etc. Hidden Markov models that were put forward in the seventies of the twentieth century have played a leading role in speech recognition field. In image processing, hidden Markov models didn't be applied to document recognition and texture image segmentation until the nineties of the twentieth.
The dissertation is devoted to the application of wavelet analysis and hidden Markov models to image processing. Two parts are included in the dissertation. In the first part, it is addressed that the combination of wavelet analysis and hidden Markov models is applied to image segmentation, especially to document segmentation. In another part, the essentially non-oscillatory (ENO) wavelet transforms and its application to image compression are addressed. The primary work in the dissertation is in detail:
1. To propose some image segmentation algorithms using wavelet-domain hidden Markov tree models. Each algorithm includes particular analysis, steps, evaluation of computation and many experiments. It is proved by many experiments that these new image segmentation algorithms are feasible and efficient.
2. To introduce ENO wavelet transforms, moreover, to propose a new Eno-haar wavelet transforms according to the inner characteristics of Haar wavelet transforms. And it is proved by many experiments that the new algorithm is feasible to image compression.
引文
1. Kenneth. R. Castleman. Digital Image Processing, Prentice Hall, 1996.
2. 章毓晋. 图象分割, 科学出版社, 2001.
3. 章毓晋. 图象工程, 清华大学出版社, 1999.
4. Zhang Y J, Gerbrands J J. Objective and quantitative segmentations evaluation and comparison, Signal Processing, 1994, 39: 43~54.
5. 张兆礼, 赵春晖, 梅晓丹. 现代图像处理技术及Matlab实现, 人民邮电出版社, 2001.
6. I. Daubechies, Ten Lectures on Wavelets, Philadelphia: SIAM, 1992.
7. 赵荣椿. 马尔可夫模型及其在语音识别/图像分割中应用的研究, 西北工业大学, 1997.
8. M. S. Crouse and R. G. Baraniuk. Wavelet-based statistical signal processing using Hidden Markov models, IEEE Trans. on Signal Proc.1998, 46(4):886~902.
9. H. Choi and R. G. Baraniuk. Multiscale image segmentation using wavelet-domain hidden Markov models, IEEE Trans. on Image Proc. vol.10,No.9,Sept. 2001,1309~1321.
10. 王新成. 多媒体实用技术, 电子科技大学出版社, 1987.
11. 赵荣椿. 数字图像处理导论, 西北工业大学出版社, 1996.
12. 杨福生. 小波变换的工程分析与应用, 科学出版社, 1999.
13. 程正兴, 小波分析算法与应用, 西安交通大学出版社, 1996.
14. 文成林, 周东华. 多尺度估计理论及其应用, 清华大学出版社, 2002.
15. Hao-Min Zhou. Wavelet Transforms and PDE Techniques in Image Compression, Ph.D. thesis, University of California, Los Angeles, 2000.
16. C. K. Chui, Wavelet: A Mathematical Tool for Signal Analysis, SIAM, 1997.
17. D. Donoho. De-noising by Soft Thresholding, IEEE Trans. Inf. Th. 41(1995), pp.613~627.
18. S. Mallat. A Theory Tour of Signal Processing, Academic Press, 1998.
A.P. Dempster, N.M. Laird, and D.B. Rubin. Maixmum likelihood from incomplete data wia
19. the EM algorithm, J. Roy. Stat. Soc., 1977, 39(1):1~38.
20. M. T. Orchard and K. Ramchandran. An investigation of wavelet-based image coding using an entropy-constrained quantization framework, Data compression Conference'94, 1994, pp.341~350.
21. S. Mallat and S. Zhong. Characterization of signals from signals from multiscale edged, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, pp.710~732, 1992.
22. S. Mallat and W. Hwang. Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory, 1992,38(2):617~643.
23. Kirsch R. Computer determination of the constituent structure of biological images, Computer Biomedical Research, 1971, 4:315~328.
24. 孙山泽. 非参数统计讲义, 北京大学出版社, 2000.
25. 侯玉华, 宋锦萍, 周福娜, 文成林, 杨晓艺. 基于小波域隐马尔科夫模型的文本图像子带分割方法, 电子学报, 2002, 30(8):1180~1183.
26. G. Strang and T. Nguyen. Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996.
27. Hui Chang. Document Image Segmentation and Compression, Ph.D. thesis, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, July 1999.
28. Kirsch R. Computer Determination of the Constituent Structure of Biological Image, Computer Biomedical Research, 1971, 4:315~328.
29. J.K. Romberg, H. Choi, R.G. Baraniuk. Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models, in Proc. of SPIE, Denver, CO, July 1999, vol. 3816, pp. 31~44.
30. S. G. Chang, B. Yu, and M. Vetterli. Spatially Adaptive Wavelet Thresholding with Context modeling for Image Denoising, IEEE Trans. on Image Proc., vol. 9, pp.1522~1531, Sep. 2000.
G. Fan and X.-G. Xia. A Joint Multi-context and Multiscale Approach to Bayesian Image
31. Segmentation, IEEE Tran. on Geoscience and Remote Sensing, Vol 39, No. 12, pp.2680 ~2688, Dec. 2001.
32. G. Fan and X.-G. Xia. Improved Hidden Markov Models in the Wavelet-Domain, IEEE Trans. on Signal Processing, Vol. 49, No. 1, pp.115~120, Jan. 2001.
33. G. Fan and X.-G. Xia. Texture Analysis and Synthesis Using Wavlet-Domain Hidden Markov Models, in Proceedings of the 5th IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, June 2001.
2. 章毓晋. 图象分割, 科学出版社, 2001.
3. 章毓晋. 图象工程, 清华大学出版社, 1999.
4. Zhang Y J, Gerbrands J J. Objective and quantitative segmentations evaluation and comparison, Signal Processing, 1994, 39: 43~54.
5. 张兆礼, 赵春晖, 梅晓丹. 现代图像处理技术及Matlab实现, 人民邮电出版社, 2001.
6. I. Daubechies, Ten Lectures on Wavelets, Philadelphia: SIAM, 1992.
7. 赵荣椿. 马尔可夫模型及其在语音识别/图像分割中应用的研究, 西北工业大学, 1997.
8. M. S. Crouse and R. G. Baraniuk. Wavelet-based statistical signal processing using Hidden Markov models, IEEE Trans. on Signal Proc.1998, 46(4):886~902.
9. H. Choi and R. G. Baraniuk. Multiscale image segmentation using wavelet-domain hidden Markov models, IEEE Trans. on Image Proc. vol.10,No.9,Sept. 2001,1309~1321.
10. 王新成. 多媒体实用技术, 电子科技大学出版社, 1987.
11. 赵荣椿. 数字图像处理导论, 西北工业大学出版社, 1996.
12. 杨福生. 小波变换的工程分析与应用, 科学出版社, 1999.
13. 程正兴, 小波分析算法与应用, 西安交通大学出版社, 1996.
14. 文成林, 周东华. 多尺度估计理论及其应用, 清华大学出版社, 2002.
15. Hao-Min Zhou. Wavelet Transforms and PDE Techniques in Image Compression, Ph.D. thesis, University of California, Los Angeles, 2000.
16. C. K. Chui, Wavelet: A Mathematical Tool for Signal Analysis, SIAM, 1997.
17. D. Donoho. De-noising by Soft Thresholding, IEEE Trans. Inf. Th. 41(1995), pp.613~627.
18. S. Mallat. A Theory Tour of Signal Processing, Academic Press, 1998.
A.P. Dempster, N.M. Laird, and D.B. Rubin. Maixmum likelihood from incomplete data wia
19. the EM algorithm, J. Roy. Stat. Soc., 1977, 39(1):1~38.
20. M. T. Orchard and K. Ramchandran. An investigation of wavelet-based image coding using an entropy-constrained quantization framework, Data compression Conference'94, 1994, pp.341~350.
21. S. Mallat and S. Zhong. Characterization of signals from signals from multiscale edged, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, pp.710~732, 1992.
22. S. Mallat and W. Hwang. Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory, 1992,38(2):617~643.
23. Kirsch R. Computer determination of the constituent structure of biological images, Computer Biomedical Research, 1971, 4:315~328.
24. 孙山泽. 非参数统计讲义, 北京大学出版社, 2000.
25. 侯玉华, 宋锦萍, 周福娜, 文成林, 杨晓艺. 基于小波域隐马尔科夫模型的文本图像子带分割方法, 电子学报, 2002, 30(8):1180~1183.
26. G. Strang and T. Nguyen. Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996.
27. Hui Chang. Document Image Segmentation and Compression, Ph.D. thesis, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, July 1999.
28. Kirsch R. Computer Determination of the Constituent Structure of Biological Image, Computer Biomedical Research, 1971, 4:315~328.
29. J.K. Romberg, H. Choi, R.G. Baraniuk. Bayesian Tree-Structured Image Modeling using Wavelet-domain Hidden Markov Models, in Proc. of SPIE, Denver, CO, July 1999, vol. 3816, pp. 31~44.
30. S. G. Chang, B. Yu, and M. Vetterli. Spatially Adaptive Wavelet Thresholding with Context modeling for Image Denoising, IEEE Trans. on Image Proc., vol. 9, pp.1522~1531, Sep. 2000.
G. Fan and X.-G. Xia. A Joint Multi-context and Multiscale Approach to Bayesian Image
31. Segmentation, IEEE Tran. on Geoscience and Remote Sensing, Vol 39, No. 12, pp.2680 ~2688, Dec. 2001.
32. G. Fan and X.-G. Xia. Improved Hidden Markov Models in the Wavelet-Domain, IEEE Trans. on Signal Processing, Vol. 49, No. 1, pp.115~120, Jan. 2001.
33. G. Fan and X.-G. Xia. Texture Analysis and Synthesis Using Wavlet-Domain Hidden Markov Models, in Proceedings of the 5th IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, June 2001.