二维几何特征的机器视觉高精度自动测量

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Joumal of Southeast University(English Edition) Vo1.28，No.4，PP.428-433 Dec.2012 ISSN 1003-79851r1r · A A Hlg11-precision autom atic m easurem entn J 1 l J - l 1 l OI tw 0-I llm ensional ge0m etn c Ieatures base1 on m aclnne VIS10nHe Boxia He Yong Xue Rong Yang Hongfeng(School of Mechanical Engineering，Nanjing University of Science and Technology，Nanjing 210094，China)Abstract：To realize high-precision automatic measurement oftwo dimensional geometric features on parts. a cooperativemeasurement system based on machine vision is constructed。

Its hardware structure， functional composition and workingprinciple are introduced. The mapping relationship betweenthe feature image coordinates and the measuring spacecoordinates is established. The method of measuring pathplanning of small field of view (F0V)images is proposed。

with the cooperation of the panoramic image of the object tobe measured，the smal FOV images with high object planeresolution are acquired automatically. Th en， the auxiliarymeasuring characteristics are constructed and the parameters ofthe features to be measured are automaticaly extracted。

Experimental results show that the absolute value of relativeerror is less than 0.03% when applying the cooperativemeasurement system to gauge the hole distance of 100 1/lnlnominal size.When the object plane resolving power of thesmal F0V images is 16 times that of the 1arge FOV image。

the measurement accuracy of small FOV images is improvedby 14 times compared wim the large FOV image.It is suitablefor high.precision automatic measurement of two.dimensionalcomplex geometric features distributed on large scale parts。

Kev words： machiRe vision； two-dimensional geometricfeatures；high-precision measurement；automatic measurementdoi：10.3969/j.issn.1003-7985.2012.04.010T n some manufacturing industries such as precision ma-.I-chinery and household appliances.the measurement oftwo dimensional geometric features， especially complexfeatures such as curves and hole distance， is inefficientand unstable， which has greatly restricted the productionlevels on the spot of large batch assembly line produc-tion.In recent years.with the rapid development Of ad。

vanced man ufacturing technology，the test an d metrologi-Received 20l2 7-21。

Biographies：He Boxia(1972～)，male，doctor，lecturer，heboxia###163.com；He Yong(1964-)，male，doctor，professor，yhe1964###mail.njust.edu.cn。

Foundafion iterns：The National Natura1 Science Foundation of China(No.5 1 175267)， the Natural Science Foundation of Jiangsu Province(No.BK2010481)，the Ph.D.Programs Foundafion of Ministry of Ed。

ucafion of China(No.20l1321912OOO4)， China Postdoctoral ScienceFoundafion(No.20100481148)，the Postdoctoral Science Foundation ofJiangsu Province f No.1001 004B1。

Citation：He Boxia，He Yong，Xue Rong，et a1.High-precision automatic measurement of two-.dimensional geometric features based on ma-chine vision[J.Journal of Southeast University(English Edition)，2012，28(4)：428-433.[doi：10.3969/j.isn.1003-7985.2012.o4.0101cal technology is required to change from traditional non-spot to manufacturing spot and from traditional afterwardsmeasurement to in-process measurement iI. It has been animportant developing direction to realize high-precision，large ran ge. automatic an d digital measurement at theman ufacturing spot .Because of the advantages of non-contact，rich information，easy-to。get automatization andintellectualization，machine vision measurement f MVM )has become an innovative approach for measurement andinspection in the manufacturing process” 。

In the existing MVM technologies of two-dimensionalgeometric features，the study and the application of mi-croscopic feature measurement and control with high.pre。

cision and automatization are relatively successful 。

This is owing to the fact that the target can be observedwith high resolution in a single image while the measuringscope is small 71. W hen the feature size is uD tO 50 to 500mm or even larger.in order to obtain higher measurementaccuracy，the image with a high object plane resolution isrequired.In this aspect，two MVM methods that are re-spectively based on image mosaic technology and se-quential partial images have made some useful explora-tion.However.when the amount of high resolution ima-ges that need mosaic technology is numerous，the M VM using mosaic technology can hardly meet the demands offast in.situ measurements.Moreover.this method needsto artificially add the characteristics of the points or lineson the parts to be measured，which is inconvenient to becarried out on the spot of automatic measurement .Asfor the M VM technology based on sequential partial ima-ges， it only applies to the measurement of straight edgeparts and linear geometric features。. Furtherm ore， itdoes not have the function of automatic measurement.Inindustrial practice， the measurement system integratingM VM technology with CMM has achieved goodeffects 121.However，this scheme still cannot realize au。

tomatic measurement due to the lack of the whole informarion of the parts to be measured.In addition，its meas。

urement accuracy depends on the precision of mechanicalcoordinates. The high-precision mechan ical coordinateswill bring about a complex measurement system， highman ufacturing cost， high requirements for the control o-ver the measurement environments such as temperatureand the subsequent high use cost。

To realize high-precision automatic measurement of thetwo-dimensional complex geometric features on largerparts. an MVM system with the cooperation of multipleF0V is constructed。

High-precision automatic measurement of two-·dimensional geometric features based on machine vision 4291 Cooperative M easurem ent System Based onM achine Vision1.1 Hardware and functional compositionThe cooperative measurement system based on machinevision is constructed as shown in Fig.1.It is mainlY com-posed of the mechanical subsystem， the optical imagingsubsystem ，the motion control subsystem ，the image ac-quisition subsystem，the image processing subsystem andthe database subsystem. The mechanical subsystem isused to construct the physica1 space for automatic meas-urement.It consists of XYZ three-directional moving co-ordinates and the rotating mechanism of a small FOVcamera.The optical imaging subsystem is composed of alight source.a large FOV lens an d a small FOV telecen-tric lens.The motion control subsystem controls the dis-placement of the three coordinates and the rotation of thesmal FOV camera.The image acquisition subsystem an-tomatically collects the panoramic image of large F0Van d sequential images of smal1 F0V.The image process-ing subsystem mainly completes the tasks of identifyingthe features to be measured in the 1arge F0V image。

plan ning the measuring path of small FOV images and ex-tracting the dimensional characteristics in sequential smalFOV images.The database subsystem stores the directionand position data of the features identifed in the largeF0V image.The parameters of the measured features arealso stored in the database。

Fig.1 Composition of the cooperative measurement systemI.2 Working principleThe working principle and steps of the cooperativemeasurement system are as folows：1)Calibrating measuring space and identifying featuresto be measuredA three-dimensional measuring space OMXYZ is con-structed as shown in Fig.2.Suppose that the area of theobjects to be measured is Fo.First，the measuring planeis calibrated at O an d the panoramic image of the targetarea S is taken at O，.It should be ensured that the ima-百ng FOV Fl1 is a little bigger than F0.Then，the map-ping relationship between the image coordinate and themeasuring space coordinate is established.After that.thefeatures to be measured are identified in the large FOVimage and the direction and position coordinates of thesefeatures in the measuring space are calculated。

Ql、s11(Fl1)Fig.2 Ilustration of the measuring space2)Planning measuring path of smal FOV images andacquirng small FOV imagesAccording to the size of the smal FOV and the direc。

tion and position of the features to be measured，an opti。

mized acquisition path of the smal FOV images is ob-tained through the specifc algorithm.Then，the sequen-tial small FOV images are automaticaly collected accord。

ing to the path.As shown in Fig.2，O2 is the plane of thecam era position while acquirng the sequential smal FOVimages S2f(i：l，2 .，n).It should be noted that the im-age plane S2 (1≤k≤n)is rotated relative to the largeFOV image S ，3)Extracting parameters of features to be measuredAccording to the position of the smal FOV images inthe measuring space and the distribution of the geomet-rical features in the images，the auxiliary measuring char-acteristics are constructed in the overlapping areas of thesequentia1 small F0V images and the homonymous char-acteristics are matched. After that. in each small F0Vimage，the partial parameters of the features to be meas-ured are extracted through the coordinates of the featuresand the auxiliary measuring characteristics.Then the localmeasuring errors are estimated and compensated for.Fi-nally，in accordance with the direction and position of thesmall FOV sequential images in the measuring space.thelocal parameters are added up and the whole parameters ofthe features to be measured are derived。

2 Relationship Between Image Coordinates andM easuring Space CoordinatesAs shown in Fig.3.a measuring space COOrdinate sys。

tem O XYZ is established，which is the physical spacewhere all the measuring activities are carried out. Sup-pose that the target to be measured is located in the planeXoMY.oMXY is addressed as a measuring plane coordi-nate system .Th e cam era optic axis oo is always parallel toax is Z.The fields of view with diferent sizes can be ob-tained through adjusting the Z coordinate valHe of the point 、、 、tⅣ" ，.、、、、 -、、、、、、，、 、、 430 He Boxia，He Yong，Xue Rong，and Yang Hongfengo in OMXyZ. Different regions of the measuring planecan be imaged by altering the X coordinate value and/orthe y coordinate value of the point o .oxy is the obiectplane coordinate system，which is used to determine thedirection and position of the imaging FoV in the measur-ing space.oxy and OMXy are in the same plan e.The ori-gin o is the intersection of the camera optical axis and themeasuring plane.o gv is the image coordinate system.Theaxis u represents the horizontal ordinate of the image，which is parallel to the x axis of the object plane coordi-nates.Th e v ax is is the vertical coordinate of the image。

which is paratlel to the Y ax is.The unit of the image coor-dinates can be pixels or floating.point numbers 。

Fig.3 Measuring space coordinate system，object plane coot-dinate system and image coordinate systemSuppose that P is a point in a two-dimensional target。

Its coordinate in oxy is(x，Y)and in OMXY is(X，y)。

The relationship between the object plane coordinates andthe measuring plane coordinates can be expressed as湘x R ：cI]where 0 is the rotating angle of the object plane over themeasuring plane；R is the rotating matrix；T is the two-dimensional translation vector with T[X ，whichis the coordinate vector of o in OMX and C is the coor-dinate transform ation matrix。

After the measurement system is calibrated， supposethat the pixel equivalent of the object plane coordinatescale in the image co0rdinate system is and 6v an d theprojection of point p(x，y)in the image coordinate systemis Pi(， ).111e relationship between the image coordi-nates and the object plane coordinates can be derived as- 。6 ]1 1- Q Jwhere(u。， 。)is the image coordinate of o。，which isthe projection of o，i.e.，the center point of the image。

Substituting Ix，Y，1] into Eq.(1)，the mapping rela-tionship between the image coordinates an d the measuringplan e coordinates is obtained asX [ ][誊虽--U 。o6xJ1t c U c3where CQ is a 3 x 3 invertible matrix.Thus，the follow-ing equation can also be derived asu v I Q c x Y 1 W (4)wherer 1/8 0 u。]- iL。0 ， j厂 cosO sin0c-l：I-sin cos L 0 0-。

AIIt is clear that the mapping relationship between the im-age coordinates and the measuring space coordinates is es-tablished by Eqs.(3)and(4).The specific values can befigured out as long as R，T， and are known。

3 Measuring Path Planning of Smal FOV IlllagesAfter the features to be measured are identified in thelarge FOV image，the measuring path of small FOV ima-ges can be plan ned according to the size of the small FOVand the shape， the direction an d the position of the features in the large FOV image. Two problems must besolved when the measuring path is planned.One is howto determine the numbers of the smal1 F0V images；theother is how to obtain the measuring space COOrdinates ofevery image.The measuring path must satisfy four basicconditions： 1 1 The features to be measured or partialcharacteristics in small F0V images should be easy to beidentified and the identification accuracy should be ashigh as possible；2)In a segment of the measuring path，the angle of the image plane should be kept consistent toavoid the difficulties of feature matching caused by therelative rotation between images：3)Th e auxiliary meas-uring characteristies should be parallel to the row or co1。

umn direction of the image，which can ensure the accura-cy of matching the homonymous characteristics；4)Un-der the condition that the auxiliary measuring characteris-tics can be matched reliably，the number of small FOVimages should be minimal to minimize cumulative errors。

For the specific features to be measured， which are con。

strained by the above four conditions，an optimized meas-uring path can be figured out。

As shown in Fig.4. the measurement of the hole dis-tance between 01 an d 0，is taken as an example to explainO 0 0 0 -............L 1tIIJ y 1 -.。 L High-precision automatic measurement of two-dimensional geometric features based on machine vision 43 1the method of the measuring path planning of small FOVimages.According to the conditions 2)and 3)，the ac-quisition of the small FOV sequential images should be a-long the center line O1 O2.According to the condition 1)，the round hole should be imaged Near the image center asshown in Fig.4 f a1.This can eliminate the influence ofdistortions an d obtain higher accuracy of the feature hole。

According to the condition 4 1.in order to minimize thenumbers of smal F0V images. the two round holesshould be imaged Near the image edge as shown in Fig.4(b).Thus.there are two schemes for choice as indicatedin Fig.4(a)and Fig.4(b).111e test shows that the meas-uring accuracy of the hole distance mainly depends on thecoordinate accuracy of the hole centers an d the matchingaccuracy of the sequential images.Therefore.the schemeshown in Fig.4(a)is more conducive to improving themeasurement accuracy. In this scheme， the center of thefirst small F0V image is coincident with the center of thefirst hole.The coordinates of its colecting position in themeasuring space can be obtained by substituting the imagecoordinate of the hole center in the large F0V image intoEq.(3).111e acquisition parameters of the remaining smallFoV images cal be calculated by the following equations：(b，Fig.4 Ilustration of measuring path planning.(a)Round holenear the image center；(b)Round hole near the image edgennl2 (5)，z ：ceil( D- H) (6)丢(H )， ： 。

D --H (8)z where n is the total number of smal1 F0V images thatneed to be colected between two holes；n is the numberof small FOV images except the first an d the n.th image；m.is the moving distance from the position of collectingthe first image to that of collecting the second image.Thedisplacement of the n.th image relative to the f n-1 1.thimage is also m..m，is the displacement of collecting thek-th(k3，4 .，/，-1)image relative to the(k-1)-thimage； D represents the distance between two holes。

which Cal be substituted with the measured value in thelarge FOV image；H represents the transverse size of thesmal FOV：6 is the pixel equivalent value of small FOVimages：e is the displacement error factor of the measur。

ing device，and it generally takes the value of three timesthe locating eror；ceil(-)is the rounding function，i。

e.，to tak e the smallest integer greater than or equal tothe value of the expression。

4 Experiment and ResultsTh e part to be measured is an instrument base.The di-am eter of the circular base is击150 mm. Six round holes0l to O6 with西10 mm nominal diameter are evenly dis-tributed along the circumference of击1O0 mm in the base。

They are used to locate six spindles.The positions of thesix holes need to be precisely controlled. Their relativelocations can be refered to in Fig.5. The application ofthe cooperative measurement system is illustrated throughthe experiment of measuring the distances of O1 O4，D2O5，and O3O6。

In the experiment.two Basler CCD cameras with reso-lutions of 1 390×1 038 pixels and 2 448×2 050 pixelsare adopted。which are labeled as No.1 an d No.2，re-spectively.The No.1 camera is used to collect the largeFOV image in the measuring space while the No.2 to col-lect the sequential images of smal FOV.The No.1 cam-era is matched with a fixed focal lens. The FOV is208.08 mm ×155.39 mm when imaging clearly.In thesesettings，it can take a ful image ofthe object to be meas-ured. The No.2 camera is alocated with a telecentriclens.Th e FOV is set to be 22.89 mm ×19.17 mm.It isused to observe the holes with high accuracy.The meas-urement system is calibrated with a national second classstandard line scale.The calibrating data of the system aregiven in Tab.1。

Tab.1 Calibration dataAfter calibrating the system，the large FOV image ofthe part to be measured is colected by the No.1 camera，which is shown in Fig.5.In this experiment，the imagingparameters of the large FOV are as follows：： 69 5.5]6 6 6l0.149 7According to Eq.(3)，the point(X，Y)in the meas-uring plane coresponding to the pixel point(/，t，v)in thelarge FOV image is obtained byr X1 r0. 4卯.。47"83；1[；0 0 149 7 c90 432 He Boxia，He Yong，Xue Rong，and Yang HongfengFig.5 Features and pixel coordinatesidentifedinlargeFOVimageAfter identifying the features in the large FOV image，the pixel coordinates of the center of circular holes(X ，y ) and their diameters can be obtained through fittingthe boundary points of the identified features.The resultsare shown in Fig.5.The values of the holes distances andthe measuring space COOrdinates of O.to Oare calculatedaccording to Eq.(9).which are listed in Tab.2。

Tab.2 Coordinates and size of the features in large FOVBy substituting the distance Dj. i3listed in Tab.2 intoEqs.(6)to(8)，the acquired direction and position ofthe small FOV sequential images are obtained.The meas-uring path is shown in Fig.6After colecting the smal FOV images，the auxiliarymeasuring characteristics are constructed and matched.Asshown in Fig.7，dimensional characteristics (i1，2，， 3； ：1，2，，6)are constructed in sequential ima-ges S .In order to simplify the calculation of the searcharea for the matched characteristic f ， ，the characteris-tic to be matched should be located in the central sectionsof the overlapping areas.The matched characteristic f issearched in the sequential image Sl 3.After eliminatingthe gross errors of the matched points，the mearl value ofthe abscissa of the matched points is taken，an d the nB-merical coordinate dcx(f)of is derived。

Fig.6 Illustration of the measuring path of smal FOV imagesIn Fig.7，G，is the distance between the center of O，and the auxiliary measuring characteristic .The coordi-nates of the circle centre are derived by fiting the pixelpoints located in the circumfe；rence of the holes.G is thedistan ce between the center of O.. and the auxiliarymeasuring characteristic .L is the distance between thedimensional characteristic line and the matched line， .D . 3 is the hole distance between O and O 3.Thesedimensional characteristics can be calculated using themeasuring method based on sequential partial images 。

g -( ) (/ ) 厶 ) (fl；)gaL ：GFig.7 Schematic diagram of measurement of small FOV ima gesThe measured values of the distan ces between six holesare given in Tab.3.From Tab.3.it can be seen that theabsolute value of relative errors is less than 0.03% whenusing small F0V images to gauge the holes distances。

The measurement accuracy of the small FOV images isimproved by more than 12 times compared with that ofthe large FOV image.This proves that it is reasonable touse the large FOV image to guide and smal FOV imagesto measure in the cooperative measurement system 。

Tab.3 Results of the cooperative measurement-. High-precision automatic measurement of two-dimensional geometric features based on machine vision 4335 ConclusionAiming at the requirements of high-precision， largerange，automatic and digital measuring an d detecting tech-nology Ol the advanced manufacturing spot，a cooperativemeasurement system based on machine vision is set up.Itscomposition and principle are introduced.The mapping re-lationship between the image coordinates an d the measur-ing space coordinates is established.The method of plan-ning the measuring path is developed.Experimental resultsverify that the cooperative measuring method can realizethe high·-precision automatic measurement of two-dimen-·sional geometric features on large size parts.Th e coopera-tive measurement system well regulates the commonly ex-isting contradiction between the resolution an d the measur-ing range in the MVM .M ean while，it fully exploits thepotentials of physical features of the imaging device.It hasthe advan tages of simple structure，low use cost an d highdigital degree. Its measuring accuracy is not affected bythe precision of the mechanical coordinates.It is suitablefor high-precision automatic measurement of two-dimen-rsional geometric features in the field of industry。

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二维几何特征的机器视觉高精度 自动测量何博侠 何 勇 薛 蓉 杨洪锋(南京理工大学机械工程学院，南京 210094)摘要：为了对零件上二维几何特征进行高精度 自动测量，建立了机器视觉协同测量系统.介绍了系统的硬件组成、功能结构及工作原理，建立了特征图像坐标与测量空间坐标之间的映射关系，提出了小视场图像测量路径的规划方法.在被测目标全景图像信息的协同下，自动采集具有高物面分辨率的小视场序列图像，自动构造辅助测量特征并提取被测特征的参数.应用该系统测量 100 mm的孔距，结果表明：相对误差的绝对值不超过 0.03%：当小视场图像的物面分辨力是大视场图像的 16倍时，小视场图像的测量精度比大视场图像平均提高14倍.故该系统适用于对大尺寸零件上分布的二维复杂几何特征进行高精度 自动测量。

关键词：机器视觉；二维几何特征；高精度测量；自动测量中图分类号 ：TP216；TH741