小波变换在木材细胞图像边缘检测的应用研究
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摘要
随着木材科学的发展,通过计算机图像处理技术对木材细胞进行分析已成为当今木材研究的一个重要方向。木材细胞图像中的边缘信息是极为有用的,它是进行细胞图像
分割的基础,是反映木材性质重要参数分析的一种快速准确技术环节。本文从传统常用的边缘检测算子的原理入手,对木材细胞图像进行了边缘检测。传统的边缘检测算子大都是基于边缘的灰度不连续性利用梯度局部最大值或二阶导数过零点来检测边缘,容易受噪声干扰；Canny算子计算量大,定位不够精确。基于小波变换的多尺度边缘检测方法弥补了上述不足。
根据边缘检测的评价标准,参照最佳边缘滤波器的设计要求,确定用于边缘检测的小波基函数的一般准则,得出“最佳”边缘检测小波,即二次B样条小波。文中说明了二次样条小波边缘检测算子的优越性,并从数学表达式上推导出二次样条小波是基于Canny最优准则的边缘检测算子。
接下来,我们用二次样条作为小波函数,根据小波变换的木材细胞图像边缘检测原理,采用基于二次样条小波快速多尺度的边缘检测算法。应用此算法对各种木材细胞显微图像进行多尺度边缘检测,其仿真结果比经典的边缘检测算法有明显的改善,得到较好的边缘检测效果,但也存在不完善之处。
最后,本文提出一种基于图像融合的边缘检测算法。首先对源图像进行小波分解,在不同分解层用小波模极大值法对高频子图像进行边缘检测,用数学形态学对低频子图像进行边缘检测,然后采用一定的融合规则将这两个边缘检测图像融合在一起。实验结果表明,这种方法优于单独使用小波模极大值法或数学形态学法,对噪声具有很好的鲁棒性,得到的图像边缘连续、清晰。
Along with the developing of wood science, it has become an important direction of wood research to analysis wood cell by Computer Image Processing. The edge information of cell image is very useful, which is the basis of cell image segment and an accurate approach of all important parameters to reflect wood's property.
In this paper, we introduce the application of some typical image edge detection algorithm, and then determine the methods adapting to wood cell image edge detection. Mostly, traditional arithmetic of image edge detection distill edge using gradient maximum or zero-crossing which base on gray discontinuousness on edge. They are affected easily by noise. Canny arithmetic has shortcomings such as big computing and confirming positions inaccur-ately. Image edge detection based on multi-resolution wavelet transform makes up these shortages before.
According to the criterion of edge detection and consulting the design-aim of optimal edge-filter, we come out with the best edge detection wavelet, namely Quadratic B-Spline wavelet. We not only illustrate the superiority of quadratic spline wavelet edge detection's arithmetic, but also prove quadratic spline wavelet are optimum edge detection's arithmetic based on Canny optimum criterions of edge detection.
Then, according to the application of wavelet transform in wood cell image edge detection, we define quadratic spline as wavelet and put forward the principle of quadratic B-Spline wavelet multi-scale quick edge detection algorithm. Application of the algorithm of the microscopic image of wood cells multi-scale edge detection, the results show that they are improver than traditional edge detection algorithm and get good edge detection effect, but also exist imperfections.
In the last, an edge detection algorithm based on image fusion is proposed. Firstly, the source image is decomposed by wavelet, using wavelet modulus maxima algorithm extracts edges in high-frequency images on the different levels and using mathematical morphological method extracts edges in low-frequency image, then the two edge images are fused according to some fusion rules. The experimental results show that the approach is superior to wavelet modulus maxima algorithm or mathematical morphological method alone and is good robust to noise and the edge is consecutive and clear.
分割的基础,是反映木材性质重要参数分析的一种快速准确技术环节。本文从传统常用的边缘检测算子的原理入手,对木材细胞图像进行了边缘检测。传统的边缘检测算子大都是基于边缘的灰度不连续性利用梯度局部最大值或二阶导数过零点来检测边缘,容易受噪声干扰；Canny算子计算量大,定位不够精确。基于小波变换的多尺度边缘检测方法弥补了上述不足。
根据边缘检测的评价标准,参照最佳边缘滤波器的设计要求,确定用于边缘检测的小波基函数的一般准则,得出“最佳”边缘检测小波,即二次B样条小波。文中说明了二次样条小波边缘检测算子的优越性,并从数学表达式上推导出二次样条小波是基于Canny最优准则的边缘检测算子。
接下来,我们用二次样条作为小波函数,根据小波变换的木材细胞图像边缘检测原理,采用基于二次样条小波快速多尺度的边缘检测算法。应用此算法对各种木材细胞显微图像进行多尺度边缘检测,其仿真结果比经典的边缘检测算法有明显的改善,得到较好的边缘检测效果,但也存在不完善之处。
最后,本文提出一种基于图像融合的边缘检测算法。首先对源图像进行小波分解,在不同分解层用小波模极大值法对高频子图像进行边缘检测,用数学形态学对低频子图像进行边缘检测,然后采用一定的融合规则将这两个边缘检测图像融合在一起。实验结果表明,这种方法优于单独使用小波模极大值法或数学形态学法,对噪声具有很好的鲁棒性,得到的图像边缘连续、清晰。
Along with the developing of wood science, it has become an important direction of wood research to analysis wood cell by Computer Image Processing. The edge information of cell image is very useful, which is the basis of cell image segment and an accurate approach of all important parameters to reflect wood's property.
In this paper, we introduce the application of some typical image edge detection algorithm, and then determine the methods adapting to wood cell image edge detection. Mostly, traditional arithmetic of image edge detection distill edge using gradient maximum or zero-crossing which base on gray discontinuousness on edge. They are affected easily by noise. Canny arithmetic has shortcomings such as big computing and confirming positions inaccur-ately. Image edge detection based on multi-resolution wavelet transform makes up these shortages before.
According to the criterion of edge detection and consulting the design-aim of optimal edge-filter, we come out with the best edge detection wavelet, namely Quadratic B-Spline wavelet. We not only illustrate the superiority of quadratic spline wavelet edge detection's arithmetic, but also prove quadratic spline wavelet are optimum edge detection's arithmetic based on Canny optimum criterions of edge detection.
Then, according to the application of wavelet transform in wood cell image edge detection, we define quadratic spline as wavelet and put forward the principle of quadratic B-Spline wavelet multi-scale quick edge detection algorithm. Application of the algorithm of the microscopic image of wood cells multi-scale edge detection, the results show that they are improver than traditional edge detection algorithm and get good edge detection effect, but also exist imperfections.
In the last, an edge detection algorithm based on image fusion is proposed. Firstly, the source image is decomposed by wavelet, using wavelet modulus maxima algorithm extracts edges in high-frequency images on the different levels and using mathematical morphological method extracts edges in low-frequency image, then the two edge images are fused according to some fusion rules. The experimental results show that the approach is superior to wavelet modulus maxima algorithm or mathematical morphological method alone and is good robust to noise and the edge is consecutive and clear.
引文
[1]李坚.木材科学.哈尔滨：东北林业大学出版社,1999：108-121
[2]段瑞玲,李庆祥,李玉和.图像边缘检测方法研究综述[J].光学技术.2005(03)：415-419
[3]Mc Millin Charles W. Application of automation image analysis to wood science[J]. Wood Science,1992,14(3):97-105
[4]Ilic J, Hillis WE. Video image processor for wood anatomical quantification[J]. Holzforschung,1999,37:47-50
[6]Tomoyuuki Maekawa, Minoru Fujita and Hirosi Saiki. Evaluation of two-dimension arrangements of softwood tracheids on transverse sections[J]. Bulletin of the Kyoto University Forests,2003,62:41-48
[7]Jordan B. D. A simple image analysis procedure for fibre wall thickness[J]. JPPS Journal of Pulp and Paper Science,2006,14(2):44-49
[8]Callum A. S. Hill and Dennis Jones. Dimensional changes in Corsican Pine sapwood due to Chemical modification with Linear chain anhydrides. Holzforschung,2006,53(3):267-271
[9]Uagi Watanabe and Misato. Tangential Young's Modulus of Coniferous Early Wood Investigated using Cell models. Wood Science,2008,53(2):209-214
[10]Matti-P. Saren, Ritva Serimaa, Seppo Andersson. Structural Variation of Tracheids in Norway Spruce. Journal of Structural Biology,2009,136:101-109
[11]刘一星,吴玉章,李坚.火炬松木材材性变异规律.东北林业大学学报,1999,27(5)：29-34
[12]王金满,刘一星,赵学增.木材构造计算机视觉分析方法[J].东北林业大学学报,1993,21(2)：52-55
[13]曹军等.基于数字图像处理技术实现木材横纹压缩过程中构造学形态特征的研究[J].森林工程,2000,16(2)：15-18
[14]孙丽萍,管雪梅.木材细胞轮廓提取新方法初探[J].林业机械与木工设备,2004,33(12)：41-42
[15]徐宇.形态分水岭变换在木材细胞图像分割中的应用[D].东北林业大学硕士论文,2008.
[16]D. S. Kim, W. H. Lee, I. S. Kweon. Automatic edge detection using 3*3 ideal binary pixel patterns and fuzzy based edge threshold. Pattern Recognition Letters, 2004,(25):101-106
[17]Z. Lei, B. Paul. Edge detection by scale multiplication in wavelet domain. Pattern Recognition Letters,2002,23(14):1771-1784
[18]Q. Tian, X. Li, N. M. Bilgutay. Multiple target detection using split spectrum processing and group delay moving entropy. IEEE Trans on UFFC.2005,42(6):1075-1086
[19]M. Brejl, M. Sonka. Directional 3D edge detection in anisotropic data:detector design and performance assessment. Computer Vision and Image Understanding,2000,(77):84-110
[20]J. M. Geusebroek, A. Dev, R. Boomgarrd, A. W. M. Smeulders, F. Cornelissen, H. Geerts. Color invariant edge detection. Scale Space Theories in Computer Vision, Springer Verlag Gmbh, Berlin.2009,1682:459-464
[21]D. Borghys, V. Lacroix, C. Perneel. Edge and line detection in polarimetric SAR images. Proc. Int. Conf. on Pattern Recognition, Quebec, Canada.2002,2:921-924
[22]李炜,黄心汉.车辆自动识别系统中车牌分割的研究.信号处理,2000,16：41-44
[23]T. Kawaguchi, M. Rizon. Iris detection using intensity and edge information. Pattern Recognition,2003, (36):549-562
[24]邵凌,张立明.一种基于肤色和模板的人脸检测方法.红外与毫米波学报,2000,19(3)：209-214
[25]张书玲,张小华.基于小波变换的边缘检测.西北大学学报(自然科学版),2000,4(2)：93-97
[26]姜长泓,王龙山,尤文等.基于平移不变小波的声发射信号去噪研究[J].仪器仪表学报.2006,27(6)：607-610
[27]Struzik Z R. Wavelet methods in time-series processing [J]. Physics A:Statistical Mechanics and its Application.2001,296(1-2):307-319
[28]章国宝,叶桦,陈维南.基于正交小波变换的多尺度边缘提取.中国图形图像学报,2008,3(8)：651-654
[29]刘斌,彭嘉雄.基于分块的小波多聚焦图像融合方法.华中科技大学图像识别与人工智能研究所,湖北大学数学与计算机科学学院,2005,(25)：78-81
[30]赵学智等.奇异性信号检测时小波基的选择.华南理工大学学报.2000,28(10)：75-80
[31]M. Sun. R. Sclabassi. Symmetric Wavelet Edge Detector of the Minimum Length. International Conference on Image Processing.2006,167(23):2177-2180
[32]狄红卫,张文琴.Canny准则小波边缘检测在图像融合中的应用.光电工程,2005,32(6)：79-82
[33]李在铭等.数字图像处理、压缩与识别技术.成都：电子科技大学出版社2000：135-168
[34]Loupas T, Mcdichen W. N, Allan. An adaptive weighted median filter for speckle suppression in medical ultrasonic images[J]. IEEE Trans on Circuits Cyst,2002,36(1): 129-135
[35]D. Marr, E. Hildreth. Theory of edge detection[J]. Proc. Roy,2008,27:187-217
[36]C. Gonzaez, E. Woods. Digital Image Processing. Second Edition. Publishing House of Electronice Industry,2003:463-474
[37][美]Ingrid Daubechies,李建平,杨万年译.小波十讲.国防工业出版社,2004
[38]S. Mallat, Multifrequency channel decompositions of images and wavelet models, IEEE Transaction in Acoustic Speech and Signal Processing,2001,vol.37:2091-2010
[39]S. Mallat, S. Zhong, Characterization of signals from multiscale edges, Pattern Analysis and Machine Intelligence, IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,14(7):710-732
[40]P. Maria. B. Panagiota. Image Processing, The Fundamentals. China Machine Press, 2005,215-223
[41]K. Castleman. Digital Image Processing. USA, New Jersey:Prentice Hal, Englewood Cliffs.2006:125-140
[42]S. K. Pal, R. A. King. On edge detection of x-ray images using fuzzy sets[J]. IEEE Trans on PAMI,2003,5(1):69-77
[43]洪文松,陈武凡.实现图像边缘检测的改进广义模糊算子法[J].中国图像图形学报,1999,4(2)：143-147
[44]E. C. Hildreth. The detection of intensity changes by computer and biological vision system[J]. CVGIP,2003,22(1):1-27
[45]杨海军,梁德群.一种基于信息测度和神经网络的边缘检测方法[J].电子学报,2001,29(1)：51-53
[46]L. O. Chua, L. Yang. Cellular neural networks:Theory[J]. IEEE Trans. Circuits System, 2008,35(10):1257-1272
[47]Vijiaks, etal. Fingerprint feature extraction by fuzzy logic and neural networks[A],2009: 1138-1142
[48]范立南.基于多结构元形态边缘检测与不变矩特征模式识别[D].沈阳：东北大学,2004
[49]章毓晋.图像处理和分析.北京：清华大学出版社,2002,181-187
[50]张汗灵.MATLAB在图像处理中的应用[M].北京：清华大学出版社,2008：301-323
[51]胡学龙,许开宇.数字图像处理[M].北京：电子工业出版社,2006：171-173
[2]段瑞玲,李庆祥,李玉和.图像边缘检测方法研究综述[J].光学技术.2005(03)：415-419
[3]Mc Millin Charles W. Application of automation image analysis to wood science[J]. Wood Science,1992,14(3):97-105
[4]Ilic J, Hillis WE. Video image processor for wood anatomical quantification[J]. Holzforschung,1999,37:47-50
[6]Tomoyuuki Maekawa, Minoru Fujita and Hirosi Saiki. Evaluation of two-dimension arrangements of softwood tracheids on transverse sections[J]. Bulletin of the Kyoto University Forests,2003,62:41-48
[7]Jordan B. D. A simple image analysis procedure for fibre wall thickness[J]. JPPS Journal of Pulp and Paper Science,2006,14(2):44-49
[8]Callum A. S. Hill and Dennis Jones. Dimensional changes in Corsican Pine sapwood due to Chemical modification with Linear chain anhydrides. Holzforschung,2006,53(3):267-271
[9]Uagi Watanabe and Misato. Tangential Young's Modulus of Coniferous Early Wood Investigated using Cell models. Wood Science,2008,53(2):209-214
[10]Matti-P. Saren, Ritva Serimaa, Seppo Andersson. Structural Variation of Tracheids in Norway Spruce. Journal of Structural Biology,2009,136:101-109
[11]刘一星,吴玉章,李坚.火炬松木材材性变异规律.东北林业大学学报,1999,27(5)：29-34
[12]王金满,刘一星,赵学增.木材构造计算机视觉分析方法[J].东北林业大学学报,1993,21(2)：52-55
[13]曹军等.基于数字图像处理技术实现木材横纹压缩过程中构造学形态特征的研究[J].森林工程,2000,16(2)：15-18
[14]孙丽萍,管雪梅.木材细胞轮廓提取新方法初探[J].林业机械与木工设备,2004,33(12)：41-42
[15]徐宇.形态分水岭变换在木材细胞图像分割中的应用[D].东北林业大学硕士论文,2008.
[16]D. S. Kim, W. H. Lee, I. S. Kweon. Automatic edge detection using 3*3 ideal binary pixel patterns and fuzzy based edge threshold. Pattern Recognition Letters, 2004,(25):101-106
[17]Z. Lei, B. Paul. Edge detection by scale multiplication in wavelet domain. Pattern Recognition Letters,2002,23(14):1771-1784
[18]Q. Tian, X. Li, N. M. Bilgutay. Multiple target detection using split spectrum processing and group delay moving entropy. IEEE Trans on UFFC.2005,42(6):1075-1086
[19]M. Brejl, M. Sonka. Directional 3D edge detection in anisotropic data:detector design and performance assessment. Computer Vision and Image Understanding,2000,(77):84-110
[20]J. M. Geusebroek, A. Dev, R. Boomgarrd, A. W. M. Smeulders, F. Cornelissen, H. Geerts. Color invariant edge detection. Scale Space Theories in Computer Vision, Springer Verlag Gmbh, Berlin.2009,1682:459-464
[21]D. Borghys, V. Lacroix, C. Perneel. Edge and line detection in polarimetric SAR images. Proc. Int. Conf. on Pattern Recognition, Quebec, Canada.2002,2:921-924
[22]李炜,黄心汉.车辆自动识别系统中车牌分割的研究.信号处理,2000,16：41-44
[23]T. Kawaguchi, M. Rizon. Iris detection using intensity and edge information. Pattern Recognition,2003, (36):549-562
[24]邵凌,张立明.一种基于肤色和模板的人脸检测方法.红外与毫米波学报,2000,19(3)：209-214
[25]张书玲,张小华.基于小波变换的边缘检测.西北大学学报(自然科学版),2000,4(2)：93-97
[26]姜长泓,王龙山,尤文等.基于平移不变小波的声发射信号去噪研究[J].仪器仪表学报.2006,27(6)：607-610
[27]Struzik Z R. Wavelet methods in time-series processing [J]. Physics A:Statistical Mechanics and its Application.2001,296(1-2):307-319
[28]章国宝,叶桦,陈维南.基于正交小波变换的多尺度边缘提取.中国图形图像学报,2008,3(8)：651-654
[29]刘斌,彭嘉雄.基于分块的小波多聚焦图像融合方法.华中科技大学图像识别与人工智能研究所,湖北大学数学与计算机科学学院,2005,(25)：78-81
[30]赵学智等.奇异性信号检测时小波基的选择.华南理工大学学报.2000,28(10)：75-80
[31]M. Sun. R. Sclabassi. Symmetric Wavelet Edge Detector of the Minimum Length. International Conference on Image Processing.2006,167(23):2177-2180
[32]狄红卫,张文琴.Canny准则小波边缘检测在图像融合中的应用.光电工程,2005,32(6)：79-82
[33]李在铭等.数字图像处理、压缩与识别技术.成都：电子科技大学出版社2000：135-168
[34]Loupas T, Mcdichen W. N, Allan. An adaptive weighted median filter for speckle suppression in medical ultrasonic images[J]. IEEE Trans on Circuits Cyst,2002,36(1): 129-135
[35]D. Marr, E. Hildreth. Theory of edge detection[J]. Proc. Roy,2008,27:187-217
[36]C. Gonzaez, E. Woods. Digital Image Processing. Second Edition. Publishing House of Electronice Industry,2003:463-474
[37][美]Ingrid Daubechies,李建平,杨万年译.小波十讲.国防工业出版社,2004
[38]S. Mallat, Multifrequency channel decompositions of images and wavelet models, IEEE Transaction in Acoustic Speech and Signal Processing,2001,vol.37:2091-2010
[39]S. Mallat, S. Zhong, Characterization of signals from multiscale edges, Pattern Analysis and Machine Intelligence, IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,14(7):710-732
[40]P. Maria. B. Panagiota. Image Processing, The Fundamentals. China Machine Press, 2005,215-223
[41]K. Castleman. Digital Image Processing. USA, New Jersey:Prentice Hal, Englewood Cliffs.2006:125-140
[42]S. K. Pal, R. A. King. On edge detection of x-ray images using fuzzy sets[J]. IEEE Trans on PAMI,2003,5(1):69-77
[43]洪文松,陈武凡.实现图像边缘检测的改进广义模糊算子法[J].中国图像图形学报,1999,4(2)：143-147
[44]E. C. Hildreth. The detection of intensity changes by computer and biological vision system[J]. CVGIP,2003,22(1):1-27
[45]杨海军,梁德群.一种基于信息测度和神经网络的边缘检测方法[J].电子学报,2001,29(1)：51-53
[46]L. O. Chua, L. Yang. Cellular neural networks:Theory[J]. IEEE Trans. Circuits System, 2008,35(10):1257-1272
[47]Vijiaks, etal. Fingerprint feature extraction by fuzzy logic and neural networks[A],2009: 1138-1142
[48]范立南.基于多结构元形态边缘检测与不变矩特征模式识别[D].沈阳：东北大学,2004
[49]章毓晋.图像处理和分析.北京：清华大学出版社,2002,181-187
[50]张汗灵.MATLAB在图像处理中的应用[M].北京：清华大学出版社,2008：301-323
[51]胡学龙,许开宇.数字图像处理[M].北京：电子工业出版社,2006：171-173
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