基于相位信息的图像边缘检测算法研究
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摘要
边缘是图像的基本特征之一，为人们描述或识别目标以及解释图像提供了重要的特征参数。边缘检测是图像处理、图像分析和计算机视觉领域中的经典研究内容之一，是进行模式识别和图像信息提取的基本手段。实际处理的图像都混有噪声，如何消除噪声干扰带来的伪边缘并且同时保证边缘定位的准确性成为边缘检测需要解决的一个重要问题，为此本文进行了基于相位信息的图像边缘检测算法研究。
首先，论文从边缘检测算法的数学思想入手，研究分析了传统边缘检测算法的特点。其中重点分析了这些传统边缘检测算法的抗噪性，在此过程中，本文采用了传统算法对加入了高斯白噪声以后的图像进行边缘检测的分析方法。
其次，论文对基于图像相位信息的边缘检测算法—相位一致性算法进行了分析研究。验证了相位信息在图像处理中的重要性和稳定性后，研究了相位一致性函数。通过分析相位一致性函数与局部能量函数的关系，考虑到图像边缘信息的局部性的特点，选用Gabor小波计算局部能量函数，并使用由局部能量函数求得的相位一致性函数对目标图像进行边缘检测。该方法不需要对图像进行任何先验假设，只是在傅立叶变换域内简单的按相位一致来寻找特征点。该方法不但能够检测到阶跃特征、线特征等亮度特征，而且能够检测到由于人类视觉感知特性而产生的马赫带现象，具有较强的通用性。
最后，论文将基于相位信息的边缘检测算法应用于活塞杆直径测量的边缘检测环节中，结合Hough变换测得了活塞杆的直径。在此基础上，论文分析了该边缘检测算法的实用性，以及在实际应用中的优点和不足。
Edge is one of the basic characters of an image, which offers people important parameters to describe and recognize objects in an image. Edge detection is one of the most fundamental operations in image processing, image analysis and computer vision. It is one of the basic methods for pattern recognition and image information extraction. Images obtained from real-world scenes are generally buried in noise. Both edges and noise may be obtained in an attempt to detect edges from an image with a large amount of noise. How to detect edges reliably and accurately in the presence of noise has remained an important issue in the field of edge detection.
Firstly, the thesis starts with the mathematical thought of image edge detection, and studies on the characteristics of traditional edge-detection algorithm. The focus is the anti-noise property of traditional edge-detection algorithm. During this process, the analytical method makes use of traditional algorithm to detect image in which contains Gaussian White Noise.
Secondly, the thesis researches on an algorithm for image edge detection based on phase information, which is phase congruency. After verifying the importance and stability of phase information in image processing, the thesis studies on phase congruency function. Algorithm for image edge detection based on phase information in wavelet domain is presented. This thesis which analyses the relation between phase congruency function and local energy function chooses Gabor wavelet transform to calculate local energy function, and at last uses phase congruency function to detect object image edge. This method needs hypothesize nothing about images in advance. It is to pick up target image edge based on the signal phase's trend toward consistency in Fourier transform domain. It can not only detect step characteristic and linear feature but also can detect Mach band phenomena on account of the characteristics of human visual perception, so it is possessed of stronger generality.
At last, the thesis makes use of algorithm for image edge detection based on phase information to obtain image edge with piston as detected object, then using Hough transform measures diameter parameter of workpiece. The experimental results prove that the algorithm for image edge detection based on phase information can bring into the effect. Moreover the algorithm effectively detects image edge and exactly gets the diameter parameter. It indicates that the algorithm for image edge detection based on phase information is superior.
首先，论文从边缘检测算法的数学思想入手，研究分析了传统边缘检测算法的特点。其中重点分析了这些传统边缘检测算法的抗噪性，在此过程中，本文采用了传统算法对加入了高斯白噪声以后的图像进行边缘检测的分析方法。
其次，论文对基于图像相位信息的边缘检测算法—相位一致性算法进行了分析研究。验证了相位信息在图像处理中的重要性和稳定性后，研究了相位一致性函数。通过分析相位一致性函数与局部能量函数的关系，考虑到图像边缘信息的局部性的特点，选用Gabor小波计算局部能量函数，并使用由局部能量函数求得的相位一致性函数对目标图像进行边缘检测。该方法不需要对图像进行任何先验假设，只是在傅立叶变换域内简单的按相位一致来寻找特征点。该方法不但能够检测到阶跃特征、线特征等亮度特征，而且能够检测到由于人类视觉感知特性而产生的马赫带现象，具有较强的通用性。
最后，论文将基于相位信息的边缘检测算法应用于活塞杆直径测量的边缘检测环节中，结合Hough变换测得了活塞杆的直径。在此基础上，论文分析了该边缘检测算法的实用性，以及在实际应用中的优点和不足。
Edge is one of the basic characters of an image, which offers people important parameters to describe and recognize objects in an image. Edge detection is one of the most fundamental operations in image processing, image analysis and computer vision. It is one of the basic methods for pattern recognition and image information extraction. Images obtained from real-world scenes are generally buried in noise. Both edges and noise may be obtained in an attempt to detect edges from an image with a large amount of noise. How to detect edges reliably and accurately in the presence of noise has remained an important issue in the field of edge detection.
Firstly, the thesis starts with the mathematical thought of image edge detection, and studies on the characteristics of traditional edge-detection algorithm. The focus is the anti-noise property of traditional edge-detection algorithm. During this process, the analytical method makes use of traditional algorithm to detect image in which contains Gaussian White Noise.
Secondly, the thesis researches on an algorithm for image edge detection based on phase information, which is phase congruency. After verifying the importance and stability of phase information in image processing, the thesis studies on phase congruency function. Algorithm for image edge detection based on phase information in wavelet domain is presented. This thesis which analyses the relation between phase congruency function and local energy function chooses Gabor wavelet transform to calculate local energy function, and at last uses phase congruency function to detect object image edge. This method needs hypothesize nothing about images in advance. It is to pick up target image edge based on the signal phase's trend toward consistency in Fourier transform domain. It can not only detect step characteristic and linear feature but also can detect Mach band phenomena on account of the characteristics of human visual perception, so it is possessed of stronger generality.
At last, the thesis makes use of algorithm for image edge detection based on phase information to obtain image edge with piston as detected object, then using Hough transform measures diameter parameter of workpiece. The experimental results prove that the algorithm for image edge detection based on phase information can bring into the effect. Moreover the algorithm effectively detects image edge and exactly gets the diameter parameter. It indicates that the algorithm for image edge detection based on phase information is superior.
引文
[1] Wesley E．Snyder，Hairong Qi．机器视觉教程．北京：机械工业出版社，2005．9．
[2] 高文，陈熙霖．计算机视觉．北京：清华大学出版社，1999．6．
[3] 贾云得．机器视觉．北京：科学出版社，2000．3．
[4] 章毓晋．图像处理和分析．北京：清华大学出版社，1999．2．
[5] 张晶．图像边缘检测算法的研究：(硕士学位论文)．山东：山东大学，2006．
[6] 刘贵忠，邸双亮．小波分析及其应用，西安电子科技大学，1997．
[7] 盛国芳，焦李成．基于遗传算法的最佳熵阈值的图像分割．计算机工程与应用．2003，30(12)：103-105．
[8] 张璟，郭春秋，聂雪等．快速、准确的图像阈值分割新方法．西安文理学院学报．2006，9(3)：54-58．
[9] 甘金来．图像边缘检测算法的比较研究：(硕士学位论文)．四川：电子科技大学，2005．
[10] 陈延标，夏良正．数字图像处理．北京：人民邮电出版社，1990．9．
[11] 朱铮涛，黎绍发，杨敏等．基于机器视觉的气门杆几何参数测量方法研究．组合机床与自动化加工技术．2004，49(5)：104-107．
[12] 邹定海，叶声华，王春和等．用于在线测量的视觉检测系统[J]．仪器仪表学报，1995，16(4)：337-341．
[13] 魏伟波，芮筱亭．图像边缘检测方法研究．计算机工程与应用．2006，24(30)：88-91．
[14] 傅一平．基于Gabor和小波的边缘检测理论、快速算法与实时应用研究：(博士学位论文)．浙江大学．2004．
[15] 叶枫．基于灰度图像的边缘检测方法研究：(硕士论文)西北工业大学．2003．
[16] D. Marr. Vision-A Computational Investigation into the Human Representation and Processing of Visual Information, W.H. Freeman and Company, San Francisco, 1982.
[17] 赵春江，施文康，邓勇．基于模糊推理的边界检测方法[J]．光学精密工程，2003，11(3)：309-313．
[18] A.V. Oppenheim and J.s. Lim. The importance of phase in signals. In Proceedings of the IEEE, 1981, 529-541.
[19] M.C. Morrone and R.A. Owens. Feature detection from local energy[J].Pattern Recognition Letters. 1987 6:303-313.
[20] 蔡毓，刘贵忠，侯兴松．基于二进小波变换的实信号的多尺度Hilbert变换和瞬时频率提取[J]．电子与信息学报，2002，8：1028-1034．
[21] Owens R A, Venkatesh S, Rose J. Edge detection is a projection[J]. Pattern Recognition Letter, 1989,9:223-244.
[22] S. Venkatesh and R.A. Owens. An energy feature detection scheme. In the International Conference on Image Procession. 1989, 553-557.
[23] J. Morlet, G. arens, E. Foureau and D. Giard. Wave propagation and sampling theory. Part 2: Sampling theory and complex waves. Geophysics 1982, 47(1):222-236.
[24] J.G. Daugman. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by tow-dimensional visual cortical filters. Journal of the Optical Society of American. 1985 2(7):1160-1169.
[25] 张鸿宾，王晴．Gabor小波在检测纹理边界及相位展开中的应用．计算机学报．1998，21(12)：1096-1102．
[26] 姚卫，李振华，贺安之．用Gabor小波作干涉波前重建．光学学报．1999，19(6)：805-810．
[27] 薛健．Gabor变换的理论应用研究：(博士学位论文)．北京：北方交通大学，1996．
[28] 肖志涛，国澄明，于明，唐红梅．Log Gabor函数在人类视觉系统特性研究中的应用．信号处理，2002，18(5)：399-402．
[29] Z.T. Xiao, C.M. Guo, M. Yu. Research on log Gabor Wavelet and its Application in Image Edge Detection. In Proceedings: 6th International Conference on Signal Process. Beijing, China, Aug. 2002:592-595.
[30] M.A. Webster, R.L. De Valois. Relationship between spatial-frequency and orientation tuning of striate-cortex cells. Journal of The Optical society of America 1985, A2 (7):1124-1132.
[31] S.J. Anderson, D.C. Burr. Spatial and temporal selectivity of the human motion detection system. Vision Research 1985, 25(8):1147-1154.
[32] D.J. Field. Relations between the statistics of natural images and the response properties of cortical cells. Journal of the Optical Society of American. 1987 A4 (12):2379-2394.
[33] P. Kovesi. Invariant measure of image features from phase information. PhD thesis. Univ of Western Australia. 1996.
[34] C. Ronse. On idempotence and related requirements in edge detection. IEEE Trans. Pattern Analysis and Machine Intelligence. Vol. 15, No. 5, May 1993:484-491.
[2] 高文，陈熙霖．计算机视觉．北京：清华大学出版社，1999．6．
[3] 贾云得．机器视觉．北京：科学出版社，2000．3．
[4] 章毓晋．图像处理和分析．北京：清华大学出版社，1999．2．
[5] 张晶．图像边缘检测算法的研究：(硕士学位论文)．山东：山东大学，2006．
[6] 刘贵忠，邸双亮．小波分析及其应用，西安电子科技大学，1997．
[7] 盛国芳，焦李成．基于遗传算法的最佳熵阈值的图像分割．计算机工程与应用．2003，30(12)：103-105．
[8] 张璟，郭春秋，聂雪等．快速、准确的图像阈值分割新方法．西安文理学院学报．2006，9(3)：54-58．
[9] 甘金来．图像边缘检测算法的比较研究：(硕士学位论文)．四川：电子科技大学，2005．
[10] 陈延标，夏良正．数字图像处理．北京：人民邮电出版社，1990．9．
[11] 朱铮涛，黎绍发，杨敏等．基于机器视觉的气门杆几何参数测量方法研究．组合机床与自动化加工技术．2004，49(5)：104-107．
[12] 邹定海，叶声华，王春和等．用于在线测量的视觉检测系统[J]．仪器仪表学报，1995，16(4)：337-341．
[13] 魏伟波，芮筱亭．图像边缘检测方法研究．计算机工程与应用．2006，24(30)：88-91．
[14] 傅一平．基于Gabor和小波的边缘检测理论、快速算法与实时应用研究：(博士学位论文)．浙江大学．2004．
[15] 叶枫．基于灰度图像的边缘检测方法研究：(硕士论文)西北工业大学．2003．
[16] D. Marr. Vision-A Computational Investigation into the Human Representation and Processing of Visual Information, W.H. Freeman and Company, San Francisco, 1982.
[17] 赵春江，施文康，邓勇．基于模糊推理的边界检测方法[J]．光学精密工程，2003，11(3)：309-313．
[18] A.V. Oppenheim and J.s. Lim. The importance of phase in signals. In Proceedings of the IEEE, 1981, 529-541.
[19] M.C. Morrone and R.A. Owens. Feature detection from local energy[J].Pattern Recognition Letters. 1987 6:303-313.
[20] 蔡毓，刘贵忠，侯兴松．基于二进小波变换的实信号的多尺度Hilbert变换和瞬时频率提取[J]．电子与信息学报，2002，8：1028-1034．
[21] Owens R A, Venkatesh S, Rose J. Edge detection is a projection[J]. Pattern Recognition Letter, 1989,9:223-244.
[22] S. Venkatesh and R.A. Owens. An energy feature detection scheme. In the International Conference on Image Procession. 1989, 553-557.
[23] J. Morlet, G. arens, E. Foureau and D. Giard. Wave propagation and sampling theory. Part 2: Sampling theory and complex waves. Geophysics 1982, 47(1):222-236.
[24] J.G. Daugman. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by tow-dimensional visual cortical filters. Journal of the Optical Society of American. 1985 2(7):1160-1169.
[25] 张鸿宾，王晴．Gabor小波在检测纹理边界及相位展开中的应用．计算机学报．1998，21(12)：1096-1102．
[26] 姚卫，李振华，贺安之．用Gabor小波作干涉波前重建．光学学报．1999，19(6)：805-810．
[27] 薛健．Gabor变换的理论应用研究：(博士学位论文)．北京：北方交通大学，1996．
[28] 肖志涛，国澄明，于明，唐红梅．Log Gabor函数在人类视觉系统特性研究中的应用．信号处理，2002，18(5)：399-402．
[29] Z.T. Xiao, C.M. Guo, M. Yu. Research on log Gabor Wavelet and its Application in Image Edge Detection. In Proceedings: 6th International Conference on Signal Process. Beijing, China, Aug. 2002:592-595.
[30] M.A. Webster, R.L. De Valois. Relationship between spatial-frequency and orientation tuning of striate-cortex cells. Journal of The Optical society of America 1985, A2 (7):1124-1132.
[31] S.J. Anderson, D.C. Burr. Spatial and temporal selectivity of the human motion detection system. Vision Research 1985, 25(8):1147-1154.
[32] D.J. Field. Relations between the statistics of natural images and the response properties of cortical cells. Journal of the Optical Society of American. 1987 A4 (12):2379-2394.
[33] P. Kovesi. Invariant measure of image features from phase information. PhD thesis. Univ of Western Australia. 1996.
[34] C. Ronse. On idempotence and related requirements in edge detection. IEEE Trans. Pattern Analysis and Machine Intelligence. Vol. 15, No. 5, May 1993:484-491.