基于径向希尔伯特变换的图像边缘增强特性研究
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摘要
研究了基于螺旋相位频谱滤波器滤波的径向希尔伯特变换对不同边缘分布图像的增强特性.给出了拓扑荷n=1的有限孔径螺旋相位滤波器点扩散函数的解析表达式,并利用圆孔、汉字和人像等三幅不同边缘分布密度的图像进行了边缘增强的模拟计算.结果表明,基于螺旋相位频谱滤波的径向希尔伯特变换会使边缘增强图像具有立体浮雕效果,并且随着输入图像的边缘分布密度变大,立体浮雕效果会越显著.通过理论分析得出,这一现象是由螺旋相位滤波器点扩散函数中的次极大分布与输入图像边缘卷积引起的.这一结论为图像的信息处理提供了一些有利的手段.
The properties of edge enhancement for different marginal distribution density image based on radial Hilbert transform with a spiral phase filter were studied.The analytical expression to describe the point spread function of a finite-radius spiral phase filter with topological charge n=1 was given and the edge enhancement for different marginal distribution image such as circular aperture,Chinese character and portraits were simulated.The results show that the edge enhanced images using radial Hilbert transform have three-dimensional relief effect,and the more intensive marginal distribution of input image,the more significant relief effect.Theoretical analysis found that this property derives from convolution between the input image and subsidiary maximum in the point spread function.This conclusion will be beneficial as a way for image processing.
The properties of edge enhancement for different marginal distribution density image based on radial Hilbert transform with a spiral phase filter were studied.The analytical expression to describe the point spread function of a finite-radius spiral phase filter with topological charge n=1 was given and the edge enhancement for different marginal distribution image such as circular aperture,Chinese character and portraits were simulated.The results show that the edge enhanced images using radial Hilbert transform have three-dimensional relief effect,and the more intensive marginal distribution of input image,the more significant relief effect.Theoretical analysis found that this property derives from convolution between the input image and subsidiary maximum in the point spread function.This conclusion will be beneficial as a way for image processing.
引文
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[2]CHEN Guo-jin,ZHU Miao-fen,SHI Hu-li,et al.Identification of image definition based on minimum isotropywavelet[J].Acta Photonica Sinica,2008,37(2):395-399.陈国金,朱妙芬,施浒立,等.基于最小各向同性小波滤波的图像清晰度识别[J].光子学报,2008,37(2):395-399.
[3]CHEN Xue-hua,HE Zhen-hua,HUANG De-ji.Seismic dataedge detection based on higher-order pseudo Hilbert transform[J].Progress in Geophysics,2008,23(4):1106-1110.陈学华,贺振华,黄德济.地震资料的高阶伪希尔伯特变换边缘检测[J].地球物理学进展,2008,23(4):1106-1110.
[4]CHEN Xue-hua,HE Zhen-hua,HUANG De-ji.High-orderpseudo Hilbert transform and application in edge detection[J].Journal of Data Acquisition&Processing,2008,23(2):224-227.陈学华,贺振华,黄德济.高阶伪希尔伯特变换在边缘检测中的应用[J].数据采集与处理,2008,23(2):224-227.
[5]DAVIS J A,McNAMARA D E,COTTRELL D M,et al.Imageprocessing with the radial Hilbert transform:theory andexperiments[J].Optics Letters,2000,25(2):99-101.
[6]GUO C S,ZHANG Y,HAN Y J,et al.Generation of opticalvortices with arbitrary shape and array via helical phase spatialfiltering[J].Optics Communications,2006,259(2):449-454.
[7]SITU G,WARBER M,PEDRINI G,et al.Phase contrastenhancement in microscopy using spiral phase filtering[J].Optics Communications,2010,283(7):1273-1277.
[8]JESACHER A,FURHAPTER S,BERNET S,et al.Shadoweffects in spiral phase contrast microscopy[J].PhysicalReview Letters,2005,94(23):233902-4.
[9]FURHAPTER S,JESACHER A,BERNET S,et al.Spiralphase contrast imaging in microscopy[J].Optics Express,2005,13(3):689-694.
[10]GUO C S,ZHANG Y,HAN Y J,et al.Generation of opticalvortices with arbitrary shape and array via helical phasespatial filtering[J].Optics Communications,2006,259(2):449-454.
[11]BOKOR N,IKETAKI Y.Laguerre-Gaussian radial Hilberttransform for edge-enhancement Fourier transform X-raymicroscopy[J].Optics Express,2009,17(7):5533-5539.
[12]YI Tao,CAO Lei-feng,YANG Guo-hong,et al.Edgeenhancement imaging using spiral zone plate[J].High PowerLaser and Particle Beams,2010,22(9):2075-2078.易涛,曹磊峰,杨国洪等.利用螺旋型波带片进行边缘增强成像[J].强激光与粒子束,2010,22(9):2075-2078.
[13]SITU G,PEDRINI G,OSTEN W.Spiral phase filtering andorientation-selective edge detection/enhancement[J].JOSAA,2009,26(8):1789-1798.
[14]LIU Ting-ting,HONG Zheng-ping,GUO Cheng-shan.Common path pahse-shifting digital holography based on aspiral phase filtering[J].Journal of Optoelectronics Laser,2008,19(1):96-99.刘婷婷,洪正平,国承山.基于螺旋相位滤波器的共路相移数字全息术[J].光电子.激光,2008,19(1):96-99.
[15]FOO G,PALACIOS D M,SWARTZLANDER G A.Opticalvortex coronagraph[J].Optics Letters,2005,30(24):3308-3310.
[16]GUO C S,HAN Y J,XU J B.Radial Hilbert transform withLaguerre-Gaussian spatial filters[J].Opt Lett,2006,31(10):1394-1396.
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