多重分形及其在图像识别中的应用研究
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摘要
多重分形分析是分形理论的深入研究,分形中用单一维数来描述自然界中的几何体,而多重分形则将其扩展至用多个维数来描述自然界中的复杂几何体。多重分形分析作为分形几何领域中的一个重要发展方向,近年来在材料学、地质学、图像处理等学科领域有着广泛的应用。多重分形分析充分考虑了几何体在形成过程中不同层次的分形特征,从而能够比较全面有效地描述物体的分形结构。图像识别是图像处理的重要内容之一,以图像的分类和描述为主要研究内容,也是当今不断发展的重要应用学科。多重分形用于图像处理,已经成为一些科学工作者解决复杂图像处理问题的重要研究手段。
本论文在深入讨论基于多重分形分析的图像去噪和图像边缘提取方法的基础上,进一步分析了图像识别时分形特征应满足的条件,既而提出了基于多重分形分析的图像特征提取算法,利用计算出的多个多重分形谱特征,对四类图像进行了有效的分类识别。实验结果证明,将经过多重分形分析方法提取的图像特征用于图像识别,可以取得较好的识别效果,能够获得较高的识别率。多重分形图像特征为图像识别的研究带来了新的思路,也扩展了多重分形分析在图像处理中的应用,具有一定的理论意义和应用价值。
Multifractal analysis is a further research of the fractal theory. It uses multiple dimensions to descripe the complex geometry of the nature, instead of one dimension in fractal theory. Recently, as a important reseach area of fractal geometry, multifractal analysis is applied widely into many fields of science such as materialogy, geology, image processing and so on. It can fully consider the fractal features of different levels in the forming process of the geometry, and thus, describe the fractal structure of the geometry effectively. Image recognition, which is one of the most important contents of image processing, takes image classification and description as the main research contents, also becoming an applied science with continuous development. Applying multifractal, has become an important reseach method which some scientists use to solve complex problems of image processing.
This thesis first introduces image denoising and image edge extraction methods based on multifractal analysis, and analyses the conditions that fractal features should be met in image recognition. Afterwards a multifractal analysis-based image feature extraction algorithm is proposed, which can calculate sevral multifractal spectrum features of the image. Then the experiment recognize four types of images effectively with the multifractal spectrum features. Experiment result shows that, with the image features extracted by multifactual analysis method, image recognition could get better effect and higher recognition rate. In conclusion, image feature extracted by multifractal analysis method brings new ideas for research of image recognition, and extends the applied range of multifractal analysis in image processing, which shows its theoretical significance and application value.
本论文在深入讨论基于多重分形分析的图像去噪和图像边缘提取方法的基础上,进一步分析了图像识别时分形特征应满足的条件,既而提出了基于多重分形分析的图像特征提取算法,利用计算出的多个多重分形谱特征,对四类图像进行了有效的分类识别。实验结果证明,将经过多重分形分析方法提取的图像特征用于图像识别,可以取得较好的识别效果,能够获得较高的识别率。多重分形图像特征为图像识别的研究带来了新的思路,也扩展了多重分形分析在图像处理中的应用,具有一定的理论意义和应用价值。
Multifractal analysis is a further research of the fractal theory. It uses multiple dimensions to descripe the complex geometry of the nature, instead of one dimension in fractal theory. Recently, as a important reseach area of fractal geometry, multifractal analysis is applied widely into many fields of science such as materialogy, geology, image processing and so on. It can fully consider the fractal features of different levels in the forming process of the geometry, and thus, describe the fractal structure of the geometry effectively. Image recognition, which is one of the most important contents of image processing, takes image classification and description as the main research contents, also becoming an applied science with continuous development. Applying multifractal, has become an important reseach method which some scientists use to solve complex problems of image processing.
This thesis first introduces image denoising and image edge extraction methods based on multifractal analysis, and analyses the conditions that fractal features should be met in image recognition. Afterwards a multifractal analysis-based image feature extraction algorithm is proposed, which can calculate sevral multifractal spectrum features of the image. Then the experiment recognize four types of images effectively with the multifractal spectrum features. Experiment result shows that, with the image features extracted by multifactual analysis method, image recognition could get better effect and higher recognition rate. In conclusion, image feature extracted by multifractal analysis method brings new ideas for research of image recognition, and extends the applied range of multifractal analysis in image processing, which shows its theoretical significance and application value.
引文
[1]Jian Zhao. SAR Image Denoising Based on Wavelet-fractal Analysis[J]. Journal of Systems Engineering and Electronic,2007, V18(1):12-15
[2]Jian Zhao, Bianzhang Yu. Research and Development on Image Processing of Wavelet and Fractal Based[C]. Dynamics of Continuous, Discrete and Impulsive Systems B: Applications and Algorithms,2006,13:987-991
[3]赵健,雷蕾,蒲小勤.分形理论及其在信号处理中的应用[M].北京：清华大学出版社,2008
[4]Mandelbrot B. B.. The Fractal Geometry of Nature[M]. NewYork:W. H. Freeman and Co.,1983
[5]赵耀,王红星,袁保宗.分形图像编码研究的进展[J].电子学报,2000,28(4)：95-101,106
[6]Jang E., Kinsner W.. Multifractal wavelet compression of fingerprints[C]. IEEE Conference on Communications, Power and Computing,1997:313-321
[7]Davis G. M.. A Wavelet-Based Analysis of Fractal Image Compression[J]. IEEE Transactions on Image Processing,1998, V7(2):141-154
[8]Chen Feng, Guangrong Ji, Junna Cheng, et al. Image Edge Detection Based on Improved Local Fractal Dimension[C]. The 2008 Fourth International Conference on Natural Computation,2008, V4:640-643
[9]赵健,杨川,俞卞章.多重分形分析图像边缘提取算法[J].光子学报,2003,32(1)：61-64
[10]Toennies K. D., Schnabel J. A.. Edge Detection Using the Local Fractal dimension[C]. IEEE Seventh Symposium on Computer-based Medical Systems,1994:34-39
[11]Potlaplli H., Luo R. C..Fractal-Based Classification of Natural Textures[J]. IEEE Transactions On Industrial Electronics,1998, V45(1):142-150
[12]Ghazel M., Freeman G. H., Vrscay E. R., et al. Fractal Image Denoising[J]. IEEE Transactions On Image Processing,2003, V12(12):1560-1578
[13]Malviya A.. Fractal based spatial domain techniques for image de-noising[C]. IEEE International Conference on Audio, Language and Image Processing,2008:1511-1516
[14]李会方.多重分形理论及其在图象处理中应用的研究[D].西北工业大学,2004
[15]Berthe K., Jing Yun hua, Yang Yang. Efficient image compression based on combination of fuzzy fractal theory[C]. IEEE Conference on Computers, Communications, Control and Power Engineering,2002, V1:573-577
[16]谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京：科学出版社,1997
[17]赵健,宋祖勋,俞卞章.基于多重分形分析的SAR图像消噪增强研究[J].西北工业大学学报,2003,21(1)：30-34
[18]黄斌,彭真明,张启衡.基于增强分形特征的人造目标检测[J].光电工程,2006,33(10)：9-12
[19]Vehel J. L., Mignot P.. Multifractal Segmentation of Images[J]. Fractals,1994, V2(3): 371-378
[20]Voorons M., Germain M., Benie G. B., et al. Segmentation of high resolution images based on the multifractal analysi[C]. IEEE International Conference on Geoscience and Remote Sensing Symposium,2003, V6:3531-3533
[21]Grazzini J., Turiel A., Yalia H.. Presegmentation of high-resolution satellite images with a multifractal reconstruction scheme based on an entropy criterium[C]. IEEE International Conference on Image Processing,2005, V1:1-649-52
[22]Lassouaoui N., LHamami. Genetic algorithms and multifractal segmentation of cervical cell images[C]. Seventh International Symposium on Signal Processing and Its Applications,2003, V2:1-4
[23]Uma K., Ramakrishnan K. R., Ananthakrishna G.. Image analysis using multifractals[C]. IEEE International Conference on Acoustics, Speech, and Signal Processing.,1996, V4: 2188-2190
[24]El Boustani A., Siddiqui S., Kinsner W., et al. A multifractal analysis for SAR images segmentation[C]. Canadian Conference on Electrical and Computer Engineering,2004, V3:1427-1430
[25]Ivanov P. Ch., Amaral L. A. N., Goldberger N. A., et al. Multifractality in human heartbeat dynamics[J]. Nature 399,1999:461-465
[26]Soemintapura K., Langi A. Z. R.. Wavelet-multifractal processing of signals[C]. IEEE Asia-Pacific Conference on Circuits and Systems,1998:65-68
[27]Kinsner W., Vincent Cheung, Cannons K., et al. Signal classification through multifractal analysis and complex domain neural networks[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part C:Applications and Reviews,2006, V36(2): 196-203
[28]王祖林,周荫清.多重分形谱及其计算[J].北京航天航空大学学报,2000,26(3)：256-258
[29]李彤,商朋见.多重分形在掌纹识别中的研究[J].物理学报,2007,56(8)：4393-4400
[30]李军,庄镇泉,高清维,等.基于多重分形分析的图像边缘检测算法[J].电路与系统学报,2001,6(3)：16-19
[31]Shouyun Liang, Qunmin Wang, Xiumei Zhong. Research of fractal dimension characteristics on debris flow gully & valley form[C]. The 2nd International Conference on Power Electronics and Intelligent Transportation System,2009:27-30
[32]He C., Yang S.X., Huang X.. Progressive decoding method for fractal image compression[J]. Vision, Image and Signal Processing,2004, V151(3):207-213
[33]Jian Lu, Yuru Zou, Zhongxing Ye. Enhanced Fractal-Wavelet Image Denoising[C]. International Colloquium on Computing, Communication, Control, and Management, 2008,V1:115-119
[34]Xi Yufei, Liu Tianyou, Wu Xiaoyang. Application of Fractal Technique in Nonlinear Geophysical Signal Processing[C]. International Congress on Image and Signal Processing,2009:1-4
[35]Cao Wenlun, Shi Zhongke, Feng Jianhu. Traffic Image Classification Method Based on Fractal Dimension[C]. IEEE 5th International Conference on Cognitive Informatics, 2006, V2:903-907
[36]Shilian Xu, Jiaru Yang, Yanqin Wang, et al. Application of fractal art for the package decoration design[C]. IEEE 10th International Conference on Computer-Aided Industrial Design & Conceptual Design,2009:705-709
[37]Kinsner W., Dansereau R.. A Relative Fractal Dimension Spectrum as a Complexity Measure[C]. IEEE 5th International Conference on Cognitive Informatics,2006, V1: 200-208
[38]赵健.小波与分形理论在图像处理中的应用研究[D].西北工业大学,2003
[39]Best S.R.. The fractal loop antenna:a comparison of fractal and non-fractal geometries[C]. IEEE International Symposium on Antennas and Propagation Society, 2001, V3:146-149
[40]Faghfouri A., Kinsner W.. Local and global analysis of multifractal singularity spectrum through wavelets[C]. Canadian Conference on Electrical and Computer Engineering, 2005:2163-2169
[41]Brown G., Michon G., Peyriere J.. On the multifractal analysis of measures[J]. Journal of Stat Phys.,1992,66:775-790
[42]李会方,俞卞章.基于小波的多重分形图像去噪新算法[J].光学精密工程,2004,6(12)：305-308
[43]李在铭.数字图像处理、压缩与识别技术[M].西安：电子科技大学出版社,2000
[2]Jian Zhao, Bianzhang Yu. Research and Development on Image Processing of Wavelet and Fractal Based[C]. Dynamics of Continuous, Discrete and Impulsive Systems B: Applications and Algorithms,2006,13:987-991
[3]赵健,雷蕾,蒲小勤.分形理论及其在信号处理中的应用[M].北京：清华大学出版社,2008
[4]Mandelbrot B. B.. The Fractal Geometry of Nature[M]. NewYork:W. H. Freeman and Co.,1983
[5]赵耀,王红星,袁保宗.分形图像编码研究的进展[J].电子学报,2000,28(4)：95-101,106
[6]Jang E., Kinsner W.. Multifractal wavelet compression of fingerprints[C]. IEEE Conference on Communications, Power and Computing,1997:313-321
[7]Davis G. M.. A Wavelet-Based Analysis of Fractal Image Compression[J]. IEEE Transactions on Image Processing,1998, V7(2):141-154
[8]Chen Feng, Guangrong Ji, Junna Cheng, et al. Image Edge Detection Based on Improved Local Fractal Dimension[C]. The 2008 Fourth International Conference on Natural Computation,2008, V4:640-643
[9]赵健,杨川,俞卞章.多重分形分析图像边缘提取算法[J].光子学报,2003,32(1)：61-64
[10]Toennies K. D., Schnabel J. A.. Edge Detection Using the Local Fractal dimension[C]. IEEE Seventh Symposium on Computer-based Medical Systems,1994:34-39
[11]Potlaplli H., Luo R. C..Fractal-Based Classification of Natural Textures[J]. IEEE Transactions On Industrial Electronics,1998, V45(1):142-150
[12]Ghazel M., Freeman G. H., Vrscay E. R., et al. Fractal Image Denoising[J]. IEEE Transactions On Image Processing,2003, V12(12):1560-1578
[13]Malviya A.. Fractal based spatial domain techniques for image de-noising[C]. IEEE International Conference on Audio, Language and Image Processing,2008:1511-1516
[14]李会方.多重分形理论及其在图象处理中应用的研究[D].西北工业大学,2004
[15]Berthe K., Jing Yun hua, Yang Yang. Efficient image compression based on combination of fuzzy fractal theory[C]. IEEE Conference on Computers, Communications, Control and Power Engineering,2002, V1:573-577
[16]谢和平,薛秀谦.分形应用中的数学基础与方法[M].北京：科学出版社,1997
[17]赵健,宋祖勋,俞卞章.基于多重分形分析的SAR图像消噪增强研究[J].西北工业大学学报,2003,21(1)：30-34
[18]黄斌,彭真明,张启衡.基于增强分形特征的人造目标检测[J].光电工程,2006,33(10)：9-12
[19]Vehel J. L., Mignot P.. Multifractal Segmentation of Images[J]. Fractals,1994, V2(3): 371-378
[20]Voorons M., Germain M., Benie G. B., et al. Segmentation of high resolution images based on the multifractal analysi[C]. IEEE International Conference on Geoscience and Remote Sensing Symposium,2003, V6:3531-3533
[21]Grazzini J., Turiel A., Yalia H.. Presegmentation of high-resolution satellite images with a multifractal reconstruction scheme based on an entropy criterium[C]. IEEE International Conference on Image Processing,2005, V1:1-649-52
[22]Lassouaoui N., LHamami. Genetic algorithms and multifractal segmentation of cervical cell images[C]. Seventh International Symposium on Signal Processing and Its Applications,2003, V2:1-4
[23]Uma K., Ramakrishnan K. R., Ananthakrishna G.. Image analysis using multifractals[C]. IEEE International Conference on Acoustics, Speech, and Signal Processing.,1996, V4: 2188-2190
[24]El Boustani A., Siddiqui S., Kinsner W., et al. A multifractal analysis for SAR images segmentation[C]. Canadian Conference on Electrical and Computer Engineering,2004, V3:1427-1430
[25]Ivanov P. Ch., Amaral L. A. N., Goldberger N. A., et al. Multifractality in human heartbeat dynamics[J]. Nature 399,1999:461-465
[26]Soemintapura K., Langi A. Z. R.. Wavelet-multifractal processing of signals[C]. IEEE Asia-Pacific Conference on Circuits and Systems,1998:65-68
[27]Kinsner W., Vincent Cheung, Cannons K., et al. Signal classification through multifractal analysis and complex domain neural networks[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part C:Applications and Reviews,2006, V36(2): 196-203
[28]王祖林,周荫清.多重分形谱及其计算[J].北京航天航空大学学报,2000,26(3)：256-258
[29]李彤,商朋见.多重分形在掌纹识别中的研究[J].物理学报,2007,56(8)：4393-4400
[30]李军,庄镇泉,高清维,等.基于多重分形分析的图像边缘检测算法[J].电路与系统学报,2001,6(3)：16-19
[31]Shouyun Liang, Qunmin Wang, Xiumei Zhong. Research of fractal dimension characteristics on debris flow gully & valley form[C]. The 2nd International Conference on Power Electronics and Intelligent Transportation System,2009:27-30
[32]He C., Yang S.X., Huang X.. Progressive decoding method for fractal image compression[J]. Vision, Image and Signal Processing,2004, V151(3):207-213
[33]Jian Lu, Yuru Zou, Zhongxing Ye. Enhanced Fractal-Wavelet Image Denoising[C]. International Colloquium on Computing, Communication, Control, and Management, 2008,V1:115-119
[34]Xi Yufei, Liu Tianyou, Wu Xiaoyang. Application of Fractal Technique in Nonlinear Geophysical Signal Processing[C]. International Congress on Image and Signal Processing,2009:1-4
[35]Cao Wenlun, Shi Zhongke, Feng Jianhu. Traffic Image Classification Method Based on Fractal Dimension[C]. IEEE 5th International Conference on Cognitive Informatics, 2006, V2:903-907
[36]Shilian Xu, Jiaru Yang, Yanqin Wang, et al. Application of fractal art for the package decoration design[C]. IEEE 10th International Conference on Computer-Aided Industrial Design & Conceptual Design,2009:705-709
[37]Kinsner W., Dansereau R.. A Relative Fractal Dimension Spectrum as a Complexity Measure[C]. IEEE 5th International Conference on Cognitive Informatics,2006, V1: 200-208
[38]赵健.小波与分形理论在图像处理中的应用研究[D].西北工业大学,2003
[39]Best S.R.. The fractal loop antenna:a comparison of fractal and non-fractal geometries[C]. IEEE International Symposium on Antennas and Propagation Society, 2001, V3:146-149
[40]Faghfouri A., Kinsner W.. Local and global analysis of multifractal singularity spectrum through wavelets[C]. Canadian Conference on Electrical and Computer Engineering, 2005:2163-2169
[41]Brown G., Michon G., Peyriere J.. On the multifractal analysis of measures[J]. Journal of Stat Phys.,1992,66:775-790
[42]李会方,俞卞章.基于小波的多重分形图像去噪新算法[J].光学精密工程,2004,6(12)：305-308
[43]李在铭.数字图像处理、压缩与识别技术[M].西安：电子科技大学出版社,2000