小波多尺度积和B样条边缘检测算法研究
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摘要
边缘检测技术在图像工程中占有重要的地位和作用，因为边缘检测是图像分割的核心内容，而图像分割又是从图像处理进入图像分析的关键步骤，也是进一步图像理解的基础。所以对边缘检测的研究一直是图像技术研究中热点和焦点，从而导致边缘检测的算法层出不穷。然而，我们在实际的应用开发中发现，现有的边缘检测算法对目标的检测和识别，多数达不到令人满意的结果，因此,结合实际课题---ICF(惯性约束核聚变)图像处理系统---的需要，本文展开了对边缘检测和目标测量的研究。
高精度地定位靶的空间坐标是ICF的核心技术，解决这个问题的关键是运用图像分割技术高精度地检测、识别和测量靶，所以论文涉及了以下几个主要内容：其一，通过分析小波多尺度边缘检测原理，以及小波变换对边缘和噪声影响的不同规律，提出了小波多尺度积边缘检测算法，该算法能有效地抑制噪声，特别是，在大尺度下利用该算法在不考虑精度的情况下，能有效地识别目标区域；其二，利用B-样条函数对高斯函数的优点，提出了基于Canny算子改进型边缘检测算法，该算法与Canny算子相比，提高了边缘的清晰度和连续性，而且抗噪能力明显增强；其三，高精度的图像测量离不开亚像素分析技术，故对亚像素定位技术作了一定的研究；最后，综合运用上述方法，提出了自动检测、识别圆和测量圆参数算法，在这个算法中，还利用了目标跟踪技术和拟合圆曲线的最小二乘法，其中，针对特殊运用，如跟踪圆曲线上的边缘点，对现有跟踪算法作了一定的改进，使其能过断点，得到更多的圆的边界点。另外，在实际运用中，根据噪声点在边界点周围的分布规律，对拟合圆曲线的最小二乘法做了一定补充，提高了测量圆参数的精度，使其增强了抗噪能力，并为自动检测和测量提供了依据。
最后，本文对ICF图像处理系统的分析、设计、功能作了简单的介绍，同时把自动检测、识别、测量圆的算法运用于实际图片的测量，能达到较理想的结果。
Edge detection technology plays an important role in the Image Engineering, it is core content of Image Segmentation which is key linkage between image analysis and image processing and also the foundation of amage understanding. So edge detection is a hot point for researchers in the field of image process, which results in an amount of algorithms for edge detection. However, in practice of actual application and development, it is discovered that current available edge detection algorithms, which are applied to target detection and recognition, can't obtain satisfying results. Thereby, the researches on edge detection and target measurement combining demand of actual project which is ICF((Inertia Constrain Fusion) image processing system has been explored in this paper.
In ICF system high accuracy position space coordinate of the target is one of the core technique, and the key of resolving this problem depends on the high accuracy detection, recognition and measurement of the target by making use of image segmentation technique. In this thesis several problems are discussed. Firstly, by the analysis of wavelet multi-scale edge detection principle, and different regulation of wavelet transformation to the noise and edge, we bring up wavelet multi-scale product the edge detection algorithm which can availably repress the noise. Especially, the algorithm can effectively recognize the target district at the big scale without considering the accuracy. Secondly, making use of the advantage of the B-Spline function to the Gauss function, we developed Canny-based improvement edge detection algorithm, which can increase the edge clearness and continuity, and has the ability and advantage of anti-noise by comparing with the Canny algorithm. Thirdly, because the analysis technique of sub-pixel is non-substitute in the high accuracy image measurement, the research on the new technique of sub-pixel position is developed in this paper. Finally, we make use of the above method, and bring up the automatic detection, recognition and measurement algorithm.
高精度地定位靶的空间坐标是ICF的核心技术，解决这个问题的关键是运用图像分割技术高精度地检测、识别和测量靶，所以论文涉及了以下几个主要内容：其一，通过分析小波多尺度边缘检测原理，以及小波变换对边缘和噪声影响的不同规律，提出了小波多尺度积边缘检测算法，该算法能有效地抑制噪声，特别是，在大尺度下利用该算法在不考虑精度的情况下，能有效地识别目标区域；其二，利用B-样条函数对高斯函数的优点，提出了基于Canny算子改进型边缘检测算法，该算法与Canny算子相比，提高了边缘的清晰度和连续性，而且抗噪能力明显增强；其三，高精度的图像测量离不开亚像素分析技术，故对亚像素定位技术作了一定的研究；最后，综合运用上述方法，提出了自动检测、识别圆和测量圆参数算法，在这个算法中，还利用了目标跟踪技术和拟合圆曲线的最小二乘法，其中，针对特殊运用，如跟踪圆曲线上的边缘点，对现有跟踪算法作了一定的改进，使其能过断点，得到更多的圆的边界点。另外，在实际运用中，根据噪声点在边界点周围的分布规律，对拟合圆曲线的最小二乘法做了一定补充，提高了测量圆参数的精度，使其增强了抗噪能力，并为自动检测和测量提供了依据。
最后，本文对ICF图像处理系统的分析、设计、功能作了简单的介绍，同时把自动检测、识别、测量圆的算法运用于实际图片的测量，能达到较理想的结果。
Edge detection technology plays an important role in the Image Engineering, it is core content of Image Segmentation which is key linkage between image analysis and image processing and also the foundation of amage understanding. So edge detection is a hot point for researchers in the field of image process, which results in an amount of algorithms for edge detection. However, in practice of actual application and development, it is discovered that current available edge detection algorithms, which are applied to target detection and recognition, can't obtain satisfying results. Thereby, the researches on edge detection and target measurement combining demand of actual project which is ICF((Inertia Constrain Fusion) image processing system has been explored in this paper.
In ICF system high accuracy position space coordinate of the target is one of the core technique, and the key of resolving this problem depends on the high accuracy detection, recognition and measurement of the target by making use of image segmentation technique. In this thesis several problems are discussed. Firstly, by the analysis of wavelet multi-scale edge detection principle, and different regulation of wavelet transformation to the noise and edge, we bring up wavelet multi-scale product the edge detection algorithm which can availably repress the noise. Especially, the algorithm can effectively recognize the target district at the big scale without considering the accuracy. Secondly, making use of the advantage of the B-Spline function to the Gauss function, we developed Canny-based improvement edge detection algorithm, which can increase the edge clearness and continuity, and has the ability and advantage of anti-noise by comparing with the Canny algorithm. Thirdly, because the analysis technique of sub-pixel is non-substitute in the high accuracy image measurement, the research on the new technique of sub-pixel position is developed in this paper. Finally, we make use of the above method, and bring up the automatic detection, recognition and measurement algorithm.
引文
[1] http://www.llnl.gov/nif/nifworks/pulse.html
[2] Rosenfeld A, Kak A. C. Digital picture processing. New York Academic Press. 1976.
[3] 游素亚，杨静，图像边缘检测技术与发展，新技术：25-28
[4] 徐建华, 图像处理与分析, 科学出版社,1992.
[5] Marr D. C, Hildreth E.C. Theory of edge detection. Proc Roy Soc London, 1980.
[6] J. Shen and S. Castan. An optimal linear operator for step edge detection.CVGIP, 1992.Vol.54: 112-133
[7] J.Canny..A Computational Approach to Edge Detection. IEEE. PAMI 1986, Vol.8.No.6.
[8] Haralick R. M. Digital step edges from zero crossings of second directional derivative. IEEE Trans PAMI, 1984. Vol.6: 58-68.
[9] S. Mallat, Sifen zhong. Characterization of Signals from Multiscale Edges. IEEE.Vol.PAMI. 1992. Vol.14.No.7:710-732
[10] S. Mallat. A Theory for Multiresolution Signal Decomposition：the Wavelet Representation. IEEE.Vol.PAMI.1989. Vol.11.No.7
[11] Serra J. Image analysis and Mathematical Morphology. London Academic, 1982.
[12] Wun-fan Chen, Lu Xiarq. A new algorithm of edge detection for color image: generalized fuzzy operator. Science in China (Series A), 1998. Vol.38, No.3: 468-473
[13] 胡守仁, 神经网络应用技术, 国防科技出版社, 1993.
[14] 章毓晋，图像工程(上，下册)，清华大学出版社，2000
[15] 章毓晋，图像分割，科学出版社，2001.
[16] S. Mallat, 译者：杨力华等，信号处理的小波导引，机械工业出版社，2002
[17] 程正兴，小波分析算法与应用，西安电子科技大学，1997.
[18] 刘贵忠、邸双亮，小波分析及其应用，西安电子科技大学，1992
[19] 阮秋琦， 数字图像处理学，电子工业出版社，2001
[20] 王玉平等， 多尺度B样条小波边缘检测算子，中国科学A辑，1995，Vol.25. No.4:426-437
[21] 陈东义等，一种简化的小波去噪算法，重庆大学学报，1997. Vol.20. No.5:63-67
[22] S. Mallat, Singularity Detection and Processing with Wavelets.IEEE Trans-Actions on Information Theory, 1992, Vol.38. No.2: 617～643
[23] S. Mallat, Singularity Detection and Processing with Wavelets.. IEEE Trans-Actions on Information Theory, 1992, Vol.38. No.2: 617～643
[24] 贾天旭等，中心B样条二进小波多尺度边缘提取，自动化学报，1998. Vol.24. No.2:192-199.
[25] 贾天旭等，基于Bubble小波的多尺度边缘提取，电子学报，1996. Vol.24. No.4:117-121
[26] 魏海等，反对称双正交小波应用于多尺度边缘提取的研究,, 电子学报，2002.Vol.30.No.3:313-3
[27] 贾天旭等，基于一类中心B样条二进小波的多尺度边缘提取, 西安交通大学学报，1996. Vol.30. No.1: 91-113
[28] 徐琼. 边缘检测梯度法的小波实现. 四川轻化工学院学报，1998, Vol.24. No.2：11-14.
[29] 解梅，顾德仁. 使用小波变换的图像边缘检测算法. 电子科技大学学报，1996，Vol.25. No.4：353-356.
[30] A. Rosenfeld. A nonlinear edge detection technique. Proc IEEE, 1970, Vol.5:814-816.
[31] A. Rosenfeld, Y,H. Lee et.al. Edge and curve detection for visual scene analysis. IEEE Trans Comput. 1971, Vol.5. No.20:562-569.
[32] Brian M. Sadler. Analysis of Multi-scale Products for Step Detection and estimation. IEEE Trans on Info theory. 1999. Vol.45. No.3:1043-1051.
[33] I.E Abdou and W.K. Pratt, Quantitative design and evaluation of enhancement/thresholding edge detectors. IEEE Proc, 1979. 67:753-763.
[34] Unser M. AldroubiA, Eden M. On the asymptotic convergence of B-spline wavelets to Gabor function. IEEE Trans Inf. Theory, 1992, Vol.38. No.2:864-872.
[35] 程正兴, 数据拟合, 西安：西安交通大学出版社，1986.
[36] M. F. Hueckel. A operator which locates edges in digitized pictures, JACM, 1971, vol.18:113-125,
[37] M. F. Hueckel.. A local visual operator which recognizes edges and lines, JACM, 1973. vol.20. 634-647,
[38] M. F. Hueckel.. Erratum for 'A local visual operator which recognizes edges and lines', JACM, 1974. vol.21: 350.
[39] A. J. Tabatabai and O. R. Mitchell, Edge location to subpixel values in digital imagery, IEEE Trans PAMI, 1984. vol.6. No.2: 188-201
[40] A. Huertas and G. Medioni, Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks, IEEE Trans PAMI, 1986. vol.8. No.5: 651-664.
[41] A. Englander, Expanding machine vision gauging with subpixel techniques, Sensors-J. Machine Perception. 1987. vol.4. No.6: 9-18.
[42] E. P. Lyvers and O. R. Mitchell, "Subpixel measurements using a moment-based edge operator", IEEE Trans PAMI. 1989. vol.11. No.12: 1293-1308.
[43] K. Jensen and D. Anastassiou, Sub-pixel edge localization and the interpolation of still images, IEEE Trans. Image Processing, 1995. vol.4. No.3: 285-295.
[44] Xiangdong Liu and R. W. Ehrich, Sub-pixel edge location in binary images using dithering, IEEE Trans. PAMI, 1995. vol.17. No.6: 629-634.
[45] 章毓晋，傅倬. 利用切线方向信息检测亚像素边缘,模式识别与人工智能，1997，vol.10. No.1: 69-74.
[46] 王建明，浦昭邦，尹继学. 空间矩亚像素细分算法的研究. 光学技术，1999，vol.20. No.4
[47] 孔丹，李介谷. 基于空间矩的灰度边缘亚像元度量精度分析. 红外与激光工程，1998, No.2
[48] 周丽娟, 柳池等，图像边界自动跟踪的边缘提取算法，哈尔滨理工大学学报，1997, Vol.2. No.5: 50-53.
[49] Samuel.M.Thomas ，Y.T.Chan，A Simple Approach for the Estimation of Circular Arc Center and Its Radius.
[50] 田社平等，平面圆圆心及半径的最小二乘拟合，实用测试技术，1995, No.5: 23-25。
[51] 孔兵等，基于圆拟合的激光光斑中心检测算法，红外与激光工程，2002. vol.3. No.3: 275-279
[2] Rosenfeld A, Kak A. C. Digital picture processing. New York Academic Press. 1976.
[3] 游素亚，杨静，图像边缘检测技术与发展，新技术：25-28
[4] 徐建华, 图像处理与分析, 科学出版社,1992.
[5] Marr D. C, Hildreth E.C. Theory of edge detection. Proc Roy Soc London, 1980.
[6] J. Shen and S. Castan. An optimal linear operator for step edge detection.CVGIP, 1992.Vol.54: 112-133
[7] J.Canny..A Computational Approach to Edge Detection. IEEE. PAMI 1986, Vol.8.No.6.
[8] Haralick R. M. Digital step edges from zero crossings of second directional derivative. IEEE Trans PAMI, 1984. Vol.6: 58-68.
[9] S. Mallat, Sifen zhong. Characterization of Signals from Multiscale Edges. IEEE.Vol.PAMI. 1992. Vol.14.No.7:710-732
[10] S. Mallat. A Theory for Multiresolution Signal Decomposition：the Wavelet Representation. IEEE.Vol.PAMI.1989. Vol.11.No.7
[11] Serra J. Image analysis and Mathematical Morphology. London Academic, 1982.
[12] Wun-fan Chen, Lu Xiarq. A new algorithm of edge detection for color image: generalized fuzzy operator. Science in China (Series A), 1998. Vol.38, No.3: 468-473
[13] 胡守仁, 神经网络应用技术, 国防科技出版社, 1993.
[14] 章毓晋，图像工程(上，下册)，清华大学出版社，2000
[15] 章毓晋，图像分割，科学出版社，2001.
[16] S. Mallat, 译者：杨力华等，信号处理的小波导引，机械工业出版社，2002
[17] 程正兴，小波分析算法与应用，西安电子科技大学，1997.
[18] 刘贵忠、邸双亮，小波分析及其应用，西安电子科技大学，1992
[19] 阮秋琦， 数字图像处理学，电子工业出版社，2001
[20] 王玉平等， 多尺度B样条小波边缘检测算子，中国科学A辑，1995，Vol.25. No.4:426-437
[21] 陈东义等，一种简化的小波去噪算法，重庆大学学报，1997. Vol.20. No.5:63-67
[22] S. Mallat, Singularity Detection and Processing with Wavelets.IEEE Trans-Actions on Information Theory, 1992, Vol.38. No.2: 617～643
[23] S. Mallat, Singularity Detection and Processing with Wavelets.. IEEE Trans-Actions on Information Theory, 1992, Vol.38. No.2: 617～643
[24] 贾天旭等，中心B样条二进小波多尺度边缘提取，自动化学报，1998. Vol.24. No.2:192-199.
[25] 贾天旭等，基于Bubble小波的多尺度边缘提取，电子学报，1996. Vol.24. No.4:117-121
[26] 魏海等，反对称双正交小波应用于多尺度边缘提取的研究,, 电子学报，2002.Vol.30.No.3:313-3
[27] 贾天旭等，基于一类中心B样条二进小波的多尺度边缘提取, 西安交通大学学报，1996. Vol.30. No.1: 91-113
[28] 徐琼. 边缘检测梯度法的小波实现. 四川轻化工学院学报，1998, Vol.24. No.2：11-14.
[29] 解梅，顾德仁. 使用小波变换的图像边缘检测算法. 电子科技大学学报，1996，Vol.25. No.4：353-356.
[30] A. Rosenfeld. A nonlinear edge detection technique. Proc IEEE, 1970, Vol.5:814-816.
[31] A. Rosenfeld, Y,H. Lee et.al. Edge and curve detection for visual scene analysis. IEEE Trans Comput. 1971, Vol.5. No.20:562-569.
[32] Brian M. Sadler. Analysis of Multi-scale Products for Step Detection and estimation. IEEE Trans on Info theory. 1999. Vol.45. No.3:1043-1051.
[33] I.E Abdou and W.K. Pratt, Quantitative design and evaluation of enhancement/thresholding edge detectors. IEEE Proc, 1979. 67:753-763.
[34] Unser M. AldroubiA, Eden M. On the asymptotic convergence of B-spline wavelets to Gabor function. IEEE Trans Inf. Theory, 1992, Vol.38. No.2:864-872.
[35] 程正兴, 数据拟合, 西安：西安交通大学出版社，1986.
[36] M. F. Hueckel. A operator which locates edges in digitized pictures, JACM, 1971, vol.18:113-125,
[37] M. F. Hueckel.. A local visual operator which recognizes edges and lines, JACM, 1973. vol.20. 634-647,
[38] M. F. Hueckel.. Erratum for 'A local visual operator which recognizes edges and lines', JACM, 1974. vol.21: 350.
[39] A. J. Tabatabai and O. R. Mitchell, Edge location to subpixel values in digital imagery, IEEE Trans PAMI, 1984. vol.6. No.2: 188-201
[40] A. Huertas and G. Medioni, Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks, IEEE Trans PAMI, 1986. vol.8. No.5: 651-664.
[41] A. Englander, Expanding machine vision gauging with subpixel techniques, Sensors-J. Machine Perception. 1987. vol.4. No.6: 9-18.
[42] E. P. Lyvers and O. R. Mitchell, "Subpixel measurements using a moment-based edge operator", IEEE Trans PAMI. 1989. vol.11. No.12: 1293-1308.
[43] K. Jensen and D. Anastassiou, Sub-pixel edge localization and the interpolation of still images, IEEE Trans. Image Processing, 1995. vol.4. No.3: 285-295.
[44] Xiangdong Liu and R. W. Ehrich, Sub-pixel edge location in binary images using dithering, IEEE Trans. PAMI, 1995. vol.17. No.6: 629-634.
[45] 章毓晋，傅倬. 利用切线方向信息检测亚像素边缘,模式识别与人工智能，1997，vol.10. No.1: 69-74.
[46] 王建明，浦昭邦，尹继学. 空间矩亚像素细分算法的研究. 光学技术，1999，vol.20. No.4
[47] 孔丹，李介谷. 基于空间矩的灰度边缘亚像元度量精度分析. 红外与激光工程，1998, No.2
[48] 周丽娟, 柳池等，图像边界自动跟踪的边缘提取算法，哈尔滨理工大学学报，1997, Vol.2. No.5: 50-53.
[49] Samuel.M.Thomas ，Y.T.Chan，A Simple Approach for the Estimation of Circular Arc Center and Its Radius.
[50] 田社平等，平面圆圆心及半径的最小二乘拟合，实用测试技术，1995, No.5: 23-25。
[51] 孔兵等，基于圆拟合的激光光斑中心检测算法，红外与激光工程，2002. vol.3. No.3: 275-279