一种基于梯度和零交叉点的图像边缘检测新方法_英文_

第27卷 第8期2006年8月仪器仪表学报Chinese Journal of Scient ific InstrumentVo l 27No 8A ug 2006New method for image edge detection basedon gradient and zero crossing*Zhao Zhig ang Wan Jiaona(I nf or mation E ngineer ing Colleg e of Qing dao Univ ers ity,Qing dao266071,China)Abstract A new method for image edg e detection is proposed based on local m ax imum o f the first derivativ e and zero cr ossing of the seco nd derivative.Although there are many traditional methods for edge detection,es pecially som e metho ds based o n zero crossings,mo st o f them are sensitive to no ise,so that the im ag e edge can 't be detected clear ly.T he pr opo sed algo rithm can avoid such disadvantages.This method calculates the first de r iv ative and finds out the local maximum,then calculates the seco nd derivativ e and g ets the zero cr ossing.After com paring the results,those points w ho se second der iv ative is zero crossing but first derivative is not local m ax im um are deleted,because maybe these edge po ints are pr oduced by noise.T he ex periment r esults show that this new method reaches no t only perfect edg e detection result but also good r obustness to noise.Key words image edg e detection gr adient zero cr ossing一种基于梯度和零交叉点的图像边缘检测新方法赵志刚 万娇娜(青岛大学信息工程学院 青岛 266071)摘要 本文提出了一种基于一阶导数局部极大值和二阶导数零交叉点的图像边缘检测方法。

许多传统的边缘检测方法,尤其是一些基于二阶导数零交叉点的方法,对于信号中的噪声比较敏感使得边缘信息不能完全准确地检测出来,而本方法可以较好地解决这些问题。

本文提出的算法是先计算出像素一阶导数的局部极大值以及二阶导数对应的零交叉点,将两者进行比较,删除那些二阶导数是零交叉点但一阶导数不是局部极大值的像素点,最后把剩下像素连接起来,即是图像边缘。

实验研究结果表明该方法具有良好的边缘检测效果和鲁棒性。

关键词 图像边缘检测 梯度 零交叉点中图分类号 T N391.41 文献标识码 A 国家标准学科分类代码 520.601 IntroductionEdge det ect ion is one of t he basic research t opics for long in the field of image processing.Because of the im port ance of edge det ect ion in modern research areas such as SAR image processing,medical image processing,et c. where it is being used ext ensively,it is a very act ive field of invest igat ion nowadays.Edge of an image is defined as a set of locally con nect ed picture elements(pixels)w hich are characterized by t heir rapid int ensit y variations.Generally,an edge is the boundary bet ween tw o regions w it h relat ively dist inct gray level properties[1-2].Since edg es carry import ant in formation,and t he edge has been widely used in solid ima ging,image segment at ion and patt ern recognition,edge det ect ion is an essential aspect in image analysis.In some t radit ional met hods,signal border is usually understood as the point where signal bounds,i.e.where*本文于2005年5月收到。

822 仪 器 仪 表 学 报第27卷the f irst derivat ive of the signal achieves local maxima [3]orthe second derivative at t he gradient direct ion which is also zero crossings.T his paper will show you a brand new method using both know ledge of gradient and zero crossings f or edge de t ect ion.2 The Theory of Some Traditional Edge Detec tion Methods and Knowledge RelatedIn the case of 1 D signal,t he edge det ect ion is based on the local maxima of 1 order derivat ive,and gradient is the measurement of the function changes.Similarly,the obvious change of image int ensity can be expressed by gra dient function.G radient is the 2 D equivalent form of 1 order derivative,defined as a vect or: G (x ,y)=G xG y= f x f y(1)wit h two import ant characterist ics:(1)T he direct ion of vect or G(x,y)is the direct ion of f(x,y)increasing most quickly;(2)T he amplit ude of gradient vector is|G (x ,y)|=G 2x+G 2y(2)and usually w e use absolute value t o approach t he sw ing ofgradient:|G (x ,y)|=|G x |+|G y |(3)or|G (x ,y)| max (|G x |,|G y |)(4)T hrough t he analysis of vect or,we know that t he direction of gradient can be defined as: a(x,y )=arct an (G y /G x )(5)Generally,we consider the pix els whose value of gra dient is local maxima as the edg e pixels.It is because the pixels at t he edge have rapid int ensit y variat ions.It means that the pix el can be det ect ed as an edge when the magni t ude of the f irst derivat ive is greater t han a given t hresh old.A ccording to the mathemat ic knowledge,w e know that local maxima of the first derivat ive means zero cross ings of t he second derivat ive.It means t hat the edge pix els have both max ima of t he first derivative and the second derivative zero crossings.T he relat ion among t he image funct ion,the first derivative and the second derivative areshown in F ig.1.T he second derivative is posit ive for the part of t he transition associated wit h t he dark side of t he edge,nega tive for t hat part of the transit ion associat ed with t he light side of the edge,and zero in areas of const ant gray level.It has a zero crossing at t he midpoint of a t ransit ion in gray level.T herefore,the pixel can be det ect ed as an edge at the zero crossing of it s second derivat ive,but this met hod is sensit ive to noise.F ig.1 T he R elatio n amo ng the Image F unctio n,the First Der ivative and the Seco nd Derivativ eSome previous classical algorithms are based on gra dient and local maxima,such as Sobel met hod,Prew it t met hod and Roberts met hod w hich find edges using their own approximation t o t he derivat ive,and ret urn edges at those point s where t he gradient of t he original image is maximum.However t hese methods can not get perfectible result s of t hose boundaries of curves.T hey are eff ect ivefor beeline boundary rat her t han curve boundary. Similarly,t here are also many algorithms based on second derivative and zero crossings for edge det ect ion,such as the LoG (laplacian of gaussian)met hod which finds edges by looking for zero crossings aft er filtering t he original image with a LoG filter,and the zero cross met h od w hich f inds edges by looking f or zero crossings aft er fil tering t he original image with a filt er you specify.Howev er,t hese met hods do have great effect on edge det ect ion,almost all of them are sensit ive t o noise.Which means that while t he image adds noise,t hese algorit hms may not get t he exact boundary of t he original image [3 4].3 The Thought of New Algorithm and Experi ment ResultsAccording to t he analysis above,a new method f or第8期Zhao Zhig ang et al:N ew method for imag e edge detection based on g radient and zer o cro ssing823edge detection based on bot h the gradient methods and thethought of zero crossings is present ed.So that it can notonly det ect t he edge but also have good robustness tonoise.T he algorithm for edge det ect ion has five st eps:(1)U se LoG f ilt er t ransact t he original image,namethe t ransacted image as G;(2)Compute the second derivat ive of pixels of G,andrecord t hose zero cross point s t hen record them as H.And the Gaussian gradient operator can be ex pressed byformula below:2G(x,y)=12!4x2+y2!2-2exp-x2+y22!2(6)we use it through st ep1and step2t o smooth the im age and calculat e t he second derivat ive in order t o find out the zero crossings.(3)Calculat e t he first derivat ive of pixels of G,and find those pixels whose value of the first derivative is lo cally maxima,compare them w it h given threshold and make those greater than t he threshold as H;(4)Compare H and H,delet e t hose point s whose second derivative are zero but first derivat ive is not locally maxima,t hen make the lef t points as the edg e named T.(5)Get t he f inal edge det ect ion output,and algorit hm is finished.In the same environment,w e use M atlab t o compile programs t o det ect the image edge and compare the result s of different algorit hms.We detect t he edge of a bacilli image which w e find from web based on the new met hod,and give the result s through some previous operat ors,such as Sobel,Lapla cian operator and so on.T he ex periment result s are shown in Fig.2.(a)is the original image of bacilli,(b)is the edge det ect ion result through Sobel operat or,(c)is the result of LoG operat or,(d)is the result of Robert s operat or,(e)is the result of Prewitt method,and(f)is the result based on our met hod.T hrough the experiment result s in Fig.2,we can see the effect of our new met hod is prett y good.For edge de t ect ion,it almost has the same ef fect as LoG operator, and has bet ter ef fect t han Sobel operat or,Robert s opera t or,and Prewitt met hod.Because we t ransact t he result f rom the zero cross point s of second derivat ive,delete those pixels might pro duced by noise,the new met hod in this paper has bet t er abilit y t o resist noise t han LoG operat or and ot her met hodsFig.2 Compariso n amo ng the Effects o f DifferentEdg e Detectio n M ethodsment ioned above,and can get distinct boundary of Image edge.4 ConclusionsIn this paper,a new method f or image edge det ect ion which is based on t he first derivat ive and zero crossings of second derivat ive knowledge is present ed.T hrough t he experiment result s,we can see t he effect of our new met hod is prett y good.Because we t ransact the result from the zero cross points of second derivat ive,delet e those pixels might produced by noise,t his approach has bet t er abilit y to resist noise.It has not only good effect for edge det ect ion,but also has bett er Robustness than other met hods mentioned in t his paper.A lso,this good met hod can be applied t o many fields of signal processing.References[1] M AR R D,HIL DR ET H E,T heor y of edge detection[J].Pr oc.Ro yal So c.Lo ndon,B,1980,(207):187217.[2] ZH AO ZH Q.A new appro ach to edge detectio n of SA Rimages[J].Jounal of Electro nics A nd Infor mat ion T echnolog y(in Chinese),2001,23(7):625630.824仪 器 仪 表 学 报第27卷[3] YA N G S B.Introduct ion of image edg e detection technolo gy.[J]J.W uhan Inst.Chem.T ech,2003,25(1):7376(in Chinese).[4] N IE XIA N GF.Imag e edg e detectio n based o n w avelettr ansfo rmation[J].China Cable T elev isio n,2004.作者简介赵志刚 男 1973年出生 博士 副教授 主要研究方向为小波分析 神经网络 图像与信号处理。