Contourlet变换及其在图像测量中的应用研究
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摘要
图像测量技术是近年来在测量领域中应运而生的一种新的测量技术,它来源于技术实践和社会需要。通过图像测量技术对物体进行在线测量,获取几何参数,实现产品的质量检测。图像测量技术的完善将会推动工程系统的机械化和智能化,提高运行效率,节省人力资源。
图像测量的基本原理是通过处理图像的边缘获得物体的几何参数。精确的确定图像的边缘位置以及合理进行参数计算是提高图像测量精度的关键。传统的边缘提取以及广泛发展的小波边缘提取技术在边缘信息的保持以及边缘平滑上还存在部分不足。此外,边缘点拟合过程中单纯的算法引入引起了参数混乱,对后期参数计算带来了诸多麻烦。针对上述问题,本文选取了Contourlet变换进行边缘提取,并对Hough变换拟合的边缘点直线进行了归一化校正,两者的结合促使测量结果更加理想。
Contourlet变换是多尺度几何分析方法中十分重要的一类,具有良好的时频局部化特性和多分辨率、多方向等分析能力。它能准确地将图像中的边缘轮廓信息捕捉到不同尺度、不同方向的子带中,是检测突变信号强有力的工具。Contourlet变换的引入不仅改善了小波变换在边缘提取中的不足降低了运算复杂度,并且更好实现了边缘信息的非线性逼近。传统的Hough变换在多目标检测时出现多直线,使得直线参数混乱并且端点不明确,影响了后期的参数转换。对此,本文通过概率论知识和多直线信息的有效性进行了归一化校正,恰当的解决了多直线问题。
应用实验是测量器件的内部间距和角度。结果显示,Contourlet变换的边缘提取算法相对小波模极大值边缘提取得到的边缘定位更加精确,复杂度较低,并且噪声干扰更少。在之后的边缘点拟合部分,校正之后的直线更加逼近物体的真实边缘,减小了由于偶然因素出现的虚假直线带来的误差。数据结果可以看出,Contourlet变换边缘提取和Hough变换直线校正的联合处理使得测量误差值相对常用处理方式更低、误差曲线更稳定,最终得到了相对理想的尺寸和角度参数。
Image measurement technology is a new technology came into being in the measurement field recently. It comes from technology practice and social needs. According to the object on-line measurement through image measurement technology, it realized the products quality inspection after getting geometric parameter. The gradual perfection of image measurement technology will promote the mechanization and intelligence of measurement system, improve the operation efficiency, and save human resource.
The basic principle of image measurement is to obtain the geometric parameters of objects through processing image edge. It shows that precise edge position location and reasonable parameter calculation are the keys to improve measurement precision. Traditional edge detection and wavelet edge detection technology that extensive developed still have some shortages at retain edge information and contour smoothing. In addition, simply introducing algorithm on edge point-fitting caused parameters confusion, this will bring many calculation trouble at post treatment. Aiming at these problems, it has selected Contourlet transform in detecting image edge, and then did some normalize correction to the edge-points line that fitted by Hough transform, the combining treatment of the two operation processes further makes measurement result more ideal.
Contourlet transform is one important kinds of multi-scale geometric analysis theory, it have excellent time-frequency localization property and multi-resolution, multi-direction and other analysis ability. This transform can exactly capture the image edge contour information to sub-band in different scales and different directions, so it is a powerful tool in detecting transient signal. The introduction to Contourlet transform not only improved the deficiency about wavelet transform in edge detecting, but better realized nonlinear approximation to edge information. In addition, the appearing multi-line problems by Traditional Hough transform in detecting multi-target cause parameter confusion and endpoint uncertainty, these problems have influenced the later parameter transformation. To this point, it applied normalized correction through knowledge in the probability theory and effectiveness on multi-line information, so it properly solves the multi-line problem.
Application experiment is to measure the interval and angle of the measurement device. The results showed that the edge extraction algorithms based on Contourlet transform performs better than wavelet modulus maxima algorithms in edge location, operational complexity, and anti-interference. In the following edge fitting, the line after being corrected approximate object's real edge better, and reduce the error brought by accidental factor. Results prove that Contourlet transform with Hough transform line-correcting can make the measurement error more lower, and obtain ideal size and angle parameter.
图像测量的基本原理是通过处理图像的边缘获得物体的几何参数。精确的确定图像的边缘位置以及合理进行参数计算是提高图像测量精度的关键。传统的边缘提取以及广泛发展的小波边缘提取技术在边缘信息的保持以及边缘平滑上还存在部分不足。此外,边缘点拟合过程中单纯的算法引入引起了参数混乱,对后期参数计算带来了诸多麻烦。针对上述问题,本文选取了Contourlet变换进行边缘提取,并对Hough变换拟合的边缘点直线进行了归一化校正,两者的结合促使测量结果更加理想。
Contourlet变换是多尺度几何分析方法中十分重要的一类,具有良好的时频局部化特性和多分辨率、多方向等分析能力。它能准确地将图像中的边缘轮廓信息捕捉到不同尺度、不同方向的子带中,是检测突变信号强有力的工具。Contourlet变换的引入不仅改善了小波变换在边缘提取中的不足降低了运算复杂度,并且更好实现了边缘信息的非线性逼近。传统的Hough变换在多目标检测时出现多直线,使得直线参数混乱并且端点不明确,影响了后期的参数转换。对此,本文通过概率论知识和多直线信息的有效性进行了归一化校正,恰当的解决了多直线问题。
应用实验是测量器件的内部间距和角度。结果显示,Contourlet变换的边缘提取算法相对小波模极大值边缘提取得到的边缘定位更加精确,复杂度较低,并且噪声干扰更少。在之后的边缘点拟合部分,校正之后的直线更加逼近物体的真实边缘,减小了由于偶然因素出现的虚假直线带来的误差。数据结果可以看出,Contourlet变换边缘提取和Hough变换直线校正的联合处理使得测量误差值相对常用处理方式更低、误差曲线更稳定,最终得到了相对理想的尺寸和角度参数。
Image measurement technology is a new technology came into being in the measurement field recently. It comes from technology practice and social needs. According to the object on-line measurement through image measurement technology, it realized the products quality inspection after getting geometric parameter. The gradual perfection of image measurement technology will promote the mechanization and intelligence of measurement system, improve the operation efficiency, and save human resource.
The basic principle of image measurement is to obtain the geometric parameters of objects through processing image edge. It shows that precise edge position location and reasonable parameter calculation are the keys to improve measurement precision. Traditional edge detection and wavelet edge detection technology that extensive developed still have some shortages at retain edge information and contour smoothing. In addition, simply introducing algorithm on edge point-fitting caused parameters confusion, this will bring many calculation trouble at post treatment. Aiming at these problems, it has selected Contourlet transform in detecting image edge, and then did some normalize correction to the edge-points line that fitted by Hough transform, the combining treatment of the two operation processes further makes measurement result more ideal.
Contourlet transform is one important kinds of multi-scale geometric analysis theory, it have excellent time-frequency localization property and multi-resolution, multi-direction and other analysis ability. This transform can exactly capture the image edge contour information to sub-band in different scales and different directions, so it is a powerful tool in detecting transient signal. The introduction to Contourlet transform not only improved the deficiency about wavelet transform in edge detecting, but better realized nonlinear approximation to edge information. In addition, the appearing multi-line problems by Traditional Hough transform in detecting multi-target cause parameter confusion and endpoint uncertainty, these problems have influenced the later parameter transformation. To this point, it applied normalized correction through knowledge in the probability theory and effectiveness on multi-line information, so it properly solves the multi-line problem.
Application experiment is to measure the interval and angle of the measurement device. The results showed that the edge extraction algorithms based on Contourlet transform performs better than wavelet modulus maxima algorithms in edge location, operational complexity, and anti-interference. In the following edge fitting, the line after being corrected approximate object's real edge better, and reduce the error brought by accidental factor. Results prove that Contourlet transform with Hough transform line-correcting can make the measurement error more lower, and obtain ideal size and angle parameter.
引文
[1].吴晓波,杨永琴.图像测量技术的新应用.光学精密工程,1998,6(3):10-15.
[2].李广云.工业测量系统最新进展及应用[J].测绘工程,2001,10(2):36-40.
[3].薛琴1,陈玮1,蒋雯2.数字图像在零件尺寸测量中的应用.计算机与数字工程,2007,35(7).
[4].吴晓波,钟先信,刘厚泉等.高精度图像测量系统[J].光学精密工程,1995,3(1): 28-33.
[5]. Minh N. Do, Martin Vetterli. The Contourlet Transform: An Efficient Directional Multi-resolution Image Representation. IEEE TRANSACTIONS ON IMAGE PROCESSING, DECEMBER 2005, 14(12):2091-2106.
[6].王建民.二维图像测量机及图像式大尺寸弧长在线测量系统的研究.哈尔滨工业大学博士学位论文, 1998.
[7].陈爱弟,王信义,王忠民.零件尺寸的在线检测方法研究.机器机械制造, 2001,10.
[8].刘上乾,李庆辉. CCD及其应用技术[M].西安:西安电子科技大学出版社,1998.
[9].黄志辉,龙赛琼等.基于图像处理技术的机械零件小孔径尺寸测量方法[ J ].计算机测量与控制, 2006,14 (5)592-594.
[10].吴晓波,安文斗.图像测量系统中的误差分析及提高测量精度的途径.光学精密工程,1997,5(1):133-141.
[11].美Rafael C. Gonzalez, Richard E. Woods and Steven L. Eddins著,阮秋琪等译. Digital Image Processing Using MATLAB:数字图像处理(MATLAB版).北京:电子工业出版社,2005.9.
[12].OTSU N. A threshold selection method from gray-level histograms [J]. IEEE Trans SMC, 1979, 9(1):62-69.
[13].Kapur J N, Sahoo P. K, Wong A K C. A new method for grey-level picture thresholding using the entropy of the histogram[J]. Computer Vision, Graphics, and Image Processing, 1985, 29(3):273-285.
[14].B. Jang & R. T. Chin. Analysis of thinning algorithm using mathematical morphology. IEEE PAMI-12, 1990, 6.
[15]. L.Lam, S.W. Lee and C.Y.Suen. Thinning Methodologies—A Comprehensive survey. IEEE PAMI. 1992, 14(9):869-885.
[16].王郑耀.数字图像的边缘检测[M].西安:西安交通大学出版社,1990,P75-149.
[17].Illingworth J, Kittler J. A survey of the Hough transform [J]. CVGIP: Image Understanding, 1988,44(1):87-116.
[18]. V. F. Leavers. Which Hough transform? CVGIP: Image Understanding, 1993, 58 (2):250–264.
[19].胡占义,杨长江,马颂德. Hough变换的新定义[J].计算机学报, 1997, 20(8):744-752.
[20]. Kalviainen H. Randomized Hough transform: New extensions. Doctoral thesis, Lappeenranta University, 1994.
[21].Ya-Jun Zhang, Zhi-Qiang Liu. Curve detection using a new clustering approach in the Hough space[A]. Procedding of IEEE International Conference on System, Man and Cybernetics [C]. Nashiville, Tennessee: IEEE Computer Society Press, 2000, 4: 2746-2751.
[22].Kazuhito Murakami and Tadashi Naruse. High-Speed Line Detection Method Using Hough Transform in Local Area. Systems and Computers in Japan, 2001, 32(10).
[23].A. Bonci, T. Leo, and S. Longhi. A Bayesian approach to the Hough transform for line detection. In IEEE Transactions on Systems, Man, and Cybernetics (Part A), 2005, 35: 945–955.
[24].焦李成,谭山.图像的多尺度几何分析:回顾和展望[ J ].电子学报, 2003, 31 (12A) : 1975-1981.
[25].成礼智,王红霞,罗永.小波的理论与应用.北京,科学出版社,2004年9月:200-219.
[26].程正兴,林勇平.小波分析在图像处理中的应用.工程数学学报,2001年12月:60-85.
[27].钱伟.小波理论在图象技术中的应用研究[J].模式识别与智能系统,2006,(11).
[28].D L Donoho, M R Duncan. Digital Curvelet Transform: Strategy, Implementation and Experiment [C]. Bellingham Washington: Proc of Aerosense 2000, Wavelet Applications VII, 2000, P12-29.
[29].R Eslami, H Radha. On Low Bit-rate Coding Using the Contourlet Transform[C]. Pacific Grove: Asilomar Conference on Signals, System and Computers, 2003.
[30].V Chappelier, C Guillemot, SMarinkovic. Image Coding with Iterated Contourlet and Wavelet Transforms[C]. IEEE International Conference on Image Processing, 2004, P3157-3160.
[31].吴晓波.图像边缘特性分析[J].光学精密工程, 1999, 7(1): 59-62.
[32].曾欢,王浩.图像边缘检测算法的性能比较与分析[J].现代电子技术, 2006,14: 53-55.
[33].常鹏.一种基于小波变换的多尺度边缘检测方法[J].模式识别与人工智能, 1996, 9(3) : 251-257.
[34].姬光荣,王国宇等.基于小波变换的多尺度边缘检测.中国图象图形学报,1998年10月,P717-720.
[35].李彦斌.基于小波理论的数字图像边缘检测算法研究[J].检测技术与自动化装置, 2006,(3).
[36].龚思思,李也白.小波变换的模极大值在图像边缘检测中的应用研究, 2008,7.
[37].王坤鹏,杨东勇.双正交小波滤波器构造及其应用与图像边缘检测[J].微计算机信息, 2005,( 20).
[38].TU Chun-liang , Hwang Wen-liang , Ho Jinn. Analysis of singularities From Modulus Maxima of Complex Wavelets[J]. IEEE Trans. on information theory, 2005, 51 (3):1049-1062.
[39].Jiayu Chen, Hong Sun. Multi-resolution Edge Detection Based on Alpha-stable Model in SAR Images Using Translation-Invariance Contourlet Transform. 2006 IEEE International Symposium on Signal Processing and Information Technology, 2006, P264-270.
[40].张悦庭,尹忠科,王建英.一种新的图像边缘检测方法.电子信息学报,2008,30(6): 1295-1299.
[41].Phoong See-May, Kim C W, Vaidyanathan P P, and Ansari R. A new class of two-channel biorthogonal filter banks and wavelet bases[J]. IEEE Trans. on Signal Processing, 1995, 43(3): 649-665.
[42].Zhao Yifan, Xia Liangzheng.Contourlet-based Feature Extraction on TextureImages.2008 International Conference on Computer Science and Software Engineering, 2008, P221:224.
[2].李广云.工业测量系统最新进展及应用[J].测绘工程,2001,10(2):36-40.
[3].薛琴1,陈玮1,蒋雯2.数字图像在零件尺寸测量中的应用.计算机与数字工程,2007,35(7).
[4].吴晓波,钟先信,刘厚泉等.高精度图像测量系统[J].光学精密工程,1995,3(1): 28-33.
[5]. Minh N. Do, Martin Vetterli. The Contourlet Transform: An Efficient Directional Multi-resolution Image Representation. IEEE TRANSACTIONS ON IMAGE PROCESSING, DECEMBER 2005, 14(12):2091-2106.
[6].王建民.二维图像测量机及图像式大尺寸弧长在线测量系统的研究.哈尔滨工业大学博士学位论文, 1998.
[7].陈爱弟,王信义,王忠民.零件尺寸的在线检测方法研究.机器机械制造, 2001,10.
[8].刘上乾,李庆辉. CCD及其应用技术[M].西安:西安电子科技大学出版社,1998.
[9].黄志辉,龙赛琼等.基于图像处理技术的机械零件小孔径尺寸测量方法[ J ].计算机测量与控制, 2006,14 (5)592-594.
[10].吴晓波,安文斗.图像测量系统中的误差分析及提高测量精度的途径.光学精密工程,1997,5(1):133-141.
[11].美Rafael C. Gonzalez, Richard E. Woods and Steven L. Eddins著,阮秋琪等译. Digital Image Processing Using MATLAB:数字图像处理(MATLAB版).北京:电子工业出版社,2005.9.
[12].OTSU N. A threshold selection method from gray-level histograms [J]. IEEE Trans SMC, 1979, 9(1):62-69.
[13].Kapur J N, Sahoo P. K, Wong A K C. A new method for grey-level picture thresholding using the entropy of the histogram[J]. Computer Vision, Graphics, and Image Processing, 1985, 29(3):273-285.
[14].B. Jang & R. T. Chin. Analysis of thinning algorithm using mathematical morphology. IEEE PAMI-12, 1990, 6.
[15]. L.Lam, S.W. Lee and C.Y.Suen. Thinning Methodologies—A Comprehensive survey. IEEE PAMI. 1992, 14(9):869-885.
[16].王郑耀.数字图像的边缘检测[M].西安:西安交通大学出版社,1990,P75-149.
[17].Illingworth J, Kittler J. A survey of the Hough transform [J]. CVGIP: Image Understanding, 1988,44(1):87-116.
[18]. V. F. Leavers. Which Hough transform? CVGIP: Image Understanding, 1993, 58 (2):250–264.
[19].胡占义,杨长江,马颂德. Hough变换的新定义[J].计算机学报, 1997, 20(8):744-752.
[20]. Kalviainen H. Randomized Hough transform: New extensions. Doctoral thesis, Lappeenranta University, 1994.
[21].Ya-Jun Zhang, Zhi-Qiang Liu. Curve detection using a new clustering approach in the Hough space[A]. Procedding of IEEE International Conference on System, Man and Cybernetics [C]. Nashiville, Tennessee: IEEE Computer Society Press, 2000, 4: 2746-2751.
[22].Kazuhito Murakami and Tadashi Naruse. High-Speed Line Detection Method Using Hough Transform in Local Area. Systems and Computers in Japan, 2001, 32(10).
[23].A. Bonci, T. Leo, and S. Longhi. A Bayesian approach to the Hough transform for line detection. In IEEE Transactions on Systems, Man, and Cybernetics (Part A), 2005, 35: 945–955.
[24].焦李成,谭山.图像的多尺度几何分析:回顾和展望[ J ].电子学报, 2003, 31 (12A) : 1975-1981.
[25].成礼智,王红霞,罗永.小波的理论与应用.北京,科学出版社,2004年9月:200-219.
[26].程正兴,林勇平.小波分析在图像处理中的应用.工程数学学报,2001年12月:60-85.
[27].钱伟.小波理论在图象技术中的应用研究[J].模式识别与智能系统,2006,(11).
[28].D L Donoho, M R Duncan. Digital Curvelet Transform: Strategy, Implementation and Experiment [C]. Bellingham Washington: Proc of Aerosense 2000, Wavelet Applications VII, 2000, P12-29.
[29].R Eslami, H Radha. On Low Bit-rate Coding Using the Contourlet Transform[C]. Pacific Grove: Asilomar Conference on Signals, System and Computers, 2003.
[30].V Chappelier, C Guillemot, SMarinkovic. Image Coding with Iterated Contourlet and Wavelet Transforms[C]. IEEE International Conference on Image Processing, 2004, P3157-3160.
[31].吴晓波.图像边缘特性分析[J].光学精密工程, 1999, 7(1): 59-62.
[32].曾欢,王浩.图像边缘检测算法的性能比较与分析[J].现代电子技术, 2006,14: 53-55.
[33].常鹏.一种基于小波变换的多尺度边缘检测方法[J].模式识别与人工智能, 1996, 9(3) : 251-257.
[34].姬光荣,王国宇等.基于小波变换的多尺度边缘检测.中国图象图形学报,1998年10月,P717-720.
[35].李彦斌.基于小波理论的数字图像边缘检测算法研究[J].检测技术与自动化装置, 2006,(3).
[36].龚思思,李也白.小波变换的模极大值在图像边缘检测中的应用研究, 2008,7.
[37].王坤鹏,杨东勇.双正交小波滤波器构造及其应用与图像边缘检测[J].微计算机信息, 2005,( 20).
[38].TU Chun-liang , Hwang Wen-liang , Ho Jinn. Analysis of singularities From Modulus Maxima of Complex Wavelets[J]. IEEE Trans. on information theory, 2005, 51 (3):1049-1062.
[39].Jiayu Chen, Hong Sun. Multi-resolution Edge Detection Based on Alpha-stable Model in SAR Images Using Translation-Invariance Contourlet Transform. 2006 IEEE International Symposium on Signal Processing and Information Technology, 2006, P264-270.
[40].张悦庭,尹忠科,王建英.一种新的图像边缘检测方法.电子信息学报,2008,30(6): 1295-1299.
[41].Phoong See-May, Kim C W, Vaidyanathan P P, and Ansari R. A new class of two-channel biorthogonal filter banks and wavelet bases[J]. IEEE Trans. on Signal Processing, 1995, 43(3): 649-665.
[42].Zhao Yifan, Xia Liangzheng.Contourlet-based Feature Extraction on TextureImages.2008 International Conference on Computer Science and Software Engineering, 2008, P221:224.