High Precision Edge Detection Algorithm for Mechanical Parts

Transcription

1 MEASUREMENT SCIENCE REVIEW, 18, (018), No., Journal homepage: Hgh Precson Edge Detecton Algorthm for Mechancal Parts Zhenyun Duan 1, Nng Wang 1, Jngshun Fu 1, Wenhu Zhao 1, Boqang Duan, Jungu Zhao 3 1 School of Mechancal Engneerng, Shenyang Unversty of Technology, Shenyang, , People s Republc of Chna College of Aerospace Engneerng, Nanjng Unversty of Aeronautcs and Astronautcs, Nanjng, 10016, People s Republc of Chna 3 Development Plannng Department, Chna Academy of Launch Vehcle Technology, Bejng, , People s Republc of Chna, fjs_sut@16.com Hgh precson and hgh effcency measurement s becomng an mperatve requrement for a lot of mechancal parts. So n ths study, a subpxel-level edge detecton algorthm based on the Gaussan ntegral model s proposed. For ths purpose, the step edge normal secton lne Gaussan ntegral model of the backlght mage s constructed, combned wth the pont spread functon and the sngle step model. Then gray value of dscrete ponts on the normal secton lne of pxel edge s calculated by surface nterpolaton, and the coordnate as well as gray nformaton affected by nose s ftted n accordance wth the Gaussan ntegral model. Therefore, a precse locaton of a subpxel edge was determned by searchng the mean pont. Fnally, a gear tooth was measured by M&M355 gear measurement center to verfy the proposed algorthm. The theoretcal analyss and expermental results show that the local edge fluctuaton s reduced effectvely by the proposed method n comparson wth the exstng subpxel edge detecton algorthms. The subpxel edge locaton accuracy and computaton speed are mproved. And the maxmum error of gear tooth profle total devaton s 1.9 μm compared wth measurement result wth gear measurement center. It ndcates that the method has hgh relablty to meet the requrement of hgh precson measurement. Keywords: Vson measurement, edge detecton, subpxel-level, Gaussan ntegral model, normal secton lne. 1. INTRODUCTION Mechancal parts are wdely used n most major equpment. The hgh precson and hgh effcency measurement for these components s becomng more and more urgent. Wth the rapd development of non-contact, hgh precson and automaton computer vson technology, the computer vson and ts applcatons become a research hotspot. Vson measurement can quckly and effcently detect the contours and plane shapes, angles and postons of varous complex parts, especally the mcroscopc detecton and qualty control of precson components, whch acheves the rapd measurement of object sze or relatve poston [1]-[4]. Recently, vson measurement has gradually attracted attenton and applcatons [5]-[6]. How to realze the edge detecton s one of key technologes n vson measurement because t decdes the measurng accuracy. In order to shft the measurng accuracy, one method s mprovng the accuracy of measurng equpment, whch wll ncrease the measurng expense. Another proper method s subpxel-level measurement. Accordng to current mathematcal models, subpxel detecton methods can manly be dvded nto three types, the moment method, fttng method, and nterpolaton method [7]-[11]. Among these methods, fttng method has hgher postonng accuracy owng to that t can flter off nose pxels. Thus, as a fttng method, the Facet surface model has been wdely used as an mage model. Ths model fts the gray surface wth the gray nformaton of dscrete dgtal mage to determne the subpxel edge locaton [1]- [14]. One problem of ths model s that t uses all pxels n a symmetrcal area wth the edge pxel ponts around, ncludng the mage background and foreground, and a few pxel ponts n transtonal zone. So, t may own a large error n the extracton of subpxel edge and low computng effcency. Therefore, ths study proposes an accurate and effcent subpxel edge detecton algorthm based on the Gaussan ntegral model to realze the hgh precson measurement of the mechancal parts, such as gauge block and standard nvolute gear.. EDGE CHARACTERISTICS Step edge and roof edge are two types of common mage edges. Edge of backlght mage belongs to step edge. So ths study focuses on step edge. The actual lens magng system s lmted by the modulaton transfer functon (MTF) cutoff frequency. Actual mage can be consdered as the convoluton of magng pont spread functon (PSF) and the deal mage DOI: /msr

2 MEASUREMENT SCIENCE REVIEW, 18, (018), No., functon. The actual edge as shown n Fg.1.a), and the frst dervatve dstrbuton of actual edge s consstent wth Gaussan dstrbuton as shown n Fg.1.b) [15]. It s the same wth the pont spread functon of the magng system. The most nose sgnals of mage are accordng to Gaussan dstrbuton. So the Gaussan flter could be an effectve method to suppress nose. One dmensonal Gaussan functon G(x) was chosen to establsh the flter. Basng on the convoluton processng of orgnal mage f(,j), the gray value of smooth mage I(,j) can be expressed as I(,j)=[ GGj () ()]* f(,j ) (1) a) Actual edge b) Frst dervatve Fg.1. Gray dstrbuton of step edge. In ths study, charge-coupled devce (CCD) was used to capture mage. Accordng to the square aperture samplng prncple, the gray value s equal to the ntegraton of CCD lght ntensty wth the fxed area n a fxed tme perod. The output results are the pxel gray value of mage, whch can be expressed as a dscrete matrx [16]. 3. DETECTION METHOD OF PIXEL EDGE A. Image smoothng In the collectng and transferrng process of mage, some nose s usually produced. It nfluences the subsequent processng results serously. So t s mportant to preprocess the orgnal mage to reduce nose after mage capture. Image smoothng s a practcal dgtal mage processng technology to reduce the nose. A better smoothng method usually elmnates mage nose and also guarantees clear mage edge contour. Fg.. shows the orgnal and Gaussan flter processed mage. It can be seen that Gaussan flter removes the nose ponts n the margnal zone. It ncreases the gray contrast. B. Edge detecton process In dgtal mage, each target pxel has eght neghborhood pxels except for the boundary one. It s very complex for tradtonal detecton algorthm to calculate frst or second order dervatve, so as to determne the mage edge by means of pxel gray tendency. If the neghborhood pxels are only consdered and are not calculated repeatedly, the processng tme wll be reduced effectvely. Therefore, here an eght-neghborhood edge trackng algorthm s proposed to realze edge detecton. The process to detect pxel edge s as follows: 1) The gray value of each pxel s frst scanned by column. If the gray value of a pont f(, j) T, then ths pont (, ) x y s consdered as the edge of the startng pont, ts coordnate s noted as tag to avod repeatng track. As shown n Fg.3., ths pont s marked as startng pont P0. a) Orgnal mage b) Gaussan flter processed mage Fg.. Comparson between orgnal and Gaussan flter processed mage. Fg.3. Schematc dagram of edge trackng. ) After P0 s consdered as the startng pont of the edge, the maxmum gray value pont s searched around the eght neghborhoods of the pont P0. The maxmum gray value pont s consdered as the next edge pont of the mage, named as P1. After that the pont P1 s marked as the next edge pont. Accordng to the two exstng edge ponts P0, P1 and characterstcs of sngle pxel edge, the next maxmum gray value pont after P1 cannot be P and P8. So the gray value of these two ponts s cleared. When searchng the maxmum gray value pont around the eght neghborhoods of the pont P1, the maxmum pont s only one of the P9 to P13. So, these ponts can only be calculated, whch greatly reduces the computng complexty. 66

3 MEASUREMENT SCIENCE REVIEW, 18, (018), No., ) When the searchng pont s located at the boundary or startng pont of the mage, the edge extracton s fnshed, else repeat the process. 4. SUBPIXEL EDGE DETECTION Subpxel edge pont s located n the normal drecton of the edge secton lne. In order to determne accurate poston, Gaussan ntegral model s establshed to obtan the locaton of subpxel edge by searchng the mean pont. A. Establshng the Gaussan ntegral model Accordng to the above analyss, the PSF [17] can be expressed by p( t) = 1 π σ ( t u ) σ e where t denotes the mpacted pont coordnate, u s the spread pont coordnate, and σ s the standard devaton. The deal step edge can be defned as () g t µ Et () = g + k t > µ (3) Then, the partal dervatve of C to μ and σ s set equal to zero. N C = ( ) = 0 t µ aσ µ = N C = = σ N ( at aµ a σ) 0 = N Ths can be further solved to obtan t a ta µ = t σ a a a t = a ta σ a a a Where t, a, ta, and a denote the arthmetc mean value oft, a, ta, a, respectvely. μ denotes the dstance between subpxel edge ponts n normal secton lne and pxel edge ponts, t denotes the dstance between dscrete ponts on the normal secton lne and pxel edge ponts. As shown n Fg.4., the coordnates of subpxel edge ponts can be easly obtaned. (7) (8) where μ denotes edge, and k s the gray values dfference between the background and prospect. The theoretcal gray value of an mage can be expressed as follows: Pt () = pt () Et () µ = pt () Et () + pt () Et () = g+ + k πσ + µ ( t u) µ σ e dt It s dffcult to solve the ntegral expresson drectly. In order to obtan the mean pont of the Gaussan ntegral model, the (t-u)/σ was replaced by v. Therefore, v t µ k σ Pt () = g+ e dv π t µ = g+ kφ( v) = g+ kφ( ) σ Accordng to the standard normal dstrbuton table, the upper lmt of the ntegral n (5) can be defned as a t µ σ =. Accordng to the mnmum mean square error prncple of least-squares fttng, we can obtan N ( t µ aσ) = C = N (4) (5) (6) Fg.4. Gaussan ntegral model on normal secton lne. B. Soluton method for the proposed model The subpxel edge nformaton could be obtaned by solvng the above Gaussan ntegral model. The solvng process to locate the subpxel edge nvolves: 1) The pxel edge of mage was frst thrce ftted wth the least-squares method. Then the pxel edge ponts were obtaned by dscretzng the fttng curve. The normal secton lne of each pxel edge pont was also determned based on the fttng curve. ) The normal offset curve could be obtaned on each sde of the pxel edge-fttng curve by choosng a seres of equdstant lnes n arthmetc progresson. Then the Gaussan ntegral model fttng ponts can be determned by fndng the ntersectons of the normal secton lne and the normal offset curve. 3) The gray value of fttng ponts was gven to the Gaussan ntegral model by usng Bezer surface nterpolaton. Then, the ntal gray value of fttng pont was fltered along the tangental drecton of the normal offset 67

4 MEASUREMENT SCIENCE REVIEW, 18, (018), No., ts normal drecton angle s.94. The dscrete ponts nformaton correspondng to ths pont s provded n Table 1., and the Gaussan ntegral fttng curve s shown n Fg.8. curve wth the Gaussan flter method. Lastly, the fnal gray value of the fttng ponts was obtaned. 4) The gray values of dscrete ponts n normal secton lne of pxel edge were ftted based on Gaussan ntegral model. Then the coordnates of subpxel edge were obtaned accordng to the mean pont μ of the Gaussan ntegral model usng (8). 5. EXPERIMENT The vson measurement system was desgned as shown n Fg.5. It manly conssts of a CCD camera, double telecentrc lens, LED blue lght, dgtal controller, gude ral slder and holder. It can be used for the measurement of mechancal parts. a) Poston 1 b) Poston c) Poston 3 d) Poston 4 e) Poston 5 f) Poston 6 Fg.6. Gauge block mage. Fg.7. Edge mage for vson measurement. Fg.5. Vson measurement system. Table 1. Informaton of dscrete ponts on normal secton lne of pxel edge. A. Error analyss of subpxel locaton Accordng to the JJG standard verfcaton system for length measurng nstruments, the accuracy of the frstgrade gauge block wth the sze of 1 mm to 10 mm s below 0.05 μm. Due to ts hgh accuracy and smple edge, the frstgrade gauge block wth the sze of 5 mm n dfferent postons was used for verfcaton of the above algorthm. Fg.6. shows the mages of the gauge block mage wth the sze of 5 mm n dfferent postons. In order to analyze the accuracy of the algorthm, the proposed algorthm and Facet surface fttng method were compared to detect the subpxel edge of the gauge block. Owng to the hgh qualty of the gauge block edge, the result of each mage processng shows the same character. It llustrates that the poston of mage has no effect on the mage processng. Therefore, the lower edge of the gauge block was taken, for example, to verfy the proposed algorthm as shown n Fg.7. Frst, seven normal offset curves on each sde of the pxel edge fttng curve were obtaned symmetrcally, each nterval between equdstant lnes can be expressed by arthmetc progresson, of whch the frst term s 0.3 and the common dfference s 0.1. Thus, ffteen dscrete ponts on the pxel edge normal secton lne were chosen for fttng. For example, certan pont coordnate on the fttng pxel edge s ( , ), No. t/pxel Gray value Image coordnates/pxel (190.04, ) ( , ) ( ,151.14) ( , ) ( ,15.51) (190.09,153.01) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) (189.88, ) ( , ) The mean value of the Gaussan ntegral fttng curve s pxels. Accordng to the coordnates of pxel edge and normal drecton angle, the correspondng coordnate of the subpxel edge s ( , ). 68

5 MEASUREMENT SCIENCE REVIEW, 18, (018), No., Fg.9. shows the subpxel detecton results obtaned by the proposed algorthm and Facet surface fttng algorthm. It concludes that the extracted subpxel n the proposed algorthm s consstent wth the Facet surface fttng algorthm, whch verfes the proposed algorthm. Fg.10. gves the comparson of the ftted subpxel of the two-edge detecton algorthm. As can be seen from the fgure, straghtness error of local fluctuaton n the subpxel edge extracted by the Facet surface fttng algorthm s 6 μm. The straghtness of local fluctuaton n the subpxel edge s smoother when usng the proposed algorthm, wth error of 1 μm. The 5 mm gauge block n a dfferent poston was measured to verfy the measurng accuracy of ths algorthm. Then the subpxel edge of the gauge block was extracted usng the two algorthms proposed n ths paper and the Facet surface fttng algorthm. One-gauge block edge was frst ftted usng the least-squares method and then the dstance between the ponts on the other edge and the fttng lne was calculated. In that case the measurng sze of gauge block can be expressed by the average dstance. Then, the measurng error was obtaned by comparng the theoretcal sze wth the measured sze. The executon tme for the proposed algorthm and that of the Facet surface fttng algorthm are 9 ms and 47 ms, respectvely. The measurng errors of two algorthms are provded n Table. The calculated results ndcate that the subpxel edge extracton method of the proposed algorthm s relable. It generates a smaller measurng error than that of the Facet surface fttng algorthm. Table. Measurng error of two algorthms (μm). Fg.8. Gaussan ntegral fttng curve on normal secton lne. Measurng mage Proposed Algorthm Algorthm for Facet surface fttng Poston Poston Poston Poston Poston Poston Average B. Verfcaton usng hgh precson gear The bult-n vson measurement system was calbrated by our prevous work [18]. Thus, t can be used to measure tooth profle total devaton of gear. The measured gears are standard nvolute spur gear. The basc parameters are shown n Table 3. Table 3. Basc parameters of the measured gear. Fg.9. Subpxel edge obtaned by the two algorthms. Order Tooth Grade Modulus number level Gear # Gear # 60 5 On the bass of obtanng pxel edge of gear profle, each profle was ftted wth nvolute lne. Then accurately locatng subpxel profle was acheved by the secton 4 algorthm. Accordng to the coordnate of gear center [19], the ntal phase angle φ correspondng to each pont of nvolute tooth profle can be obtaned. The gear radus of base crcle r b has been known. So, the tooth profle total devaton of gear can be ndcated by usng the nvolute ntal phase angle, Fg.10. Dstance of pxel edge ponts to the fttng lne. ε = max( ϕ ) mn( ϕ ) (9) r b j j 69

6 MEASUREMENT SCIENCE REVIEW, 18, (018), No., In order to analyze the accuracy of the measurement method n ths paper, the M&M355 gear measurement center was adopted as shown n Fg.11. The tooth profle total devaton of the gear wth the proposed method was compared wth the measurement result of gear measurement center. Fg.11. Gear measurement center. The measured tooth profle total devaton obtaned by two methods s shown n Table 4. M1 s the measurement result of the proposed method. M s the measurement result obtaned by the gear measurement center. The M s the dfference between them. The bggest error of the two methods s smaller than 1.9 μm. And the trend of measurement results s bascally the same. It shows that the method n ths paper has certan relablty to hgh accuracy of measurement. Table 4. Measurement result of two methods (μm). Measured Gear #1 Gear # tooth M1 M M M1 M M Tooth Left Rght Tooth Left Rght Tooth Left Rght Tooth Left Rght Accordng to the relevant provsons of GB/T 10095, the tooth profle total devaton allowable value of two ffth level spur gear s 7 μm and 6 μm. The measured results show that the tooth profle total devaton obtaned by two methods s less than the maxmum. We can conclude that the gears meet the accuracy requrement of ffth level gear. 6. CONCLUSIONS A subpxel edge detecton algorthm based on the Gaussan ntegral model was proposed. The algorthm constructed the step edge normal secton Gaussan ntegral model. Based on the obtaned normal of the pxel edgefttng curve, a Gaussan flter along the tangental of the edge was appled. The gray value of dscrete ponts on the normal secton lne of the pxel edge was calculated wth surface nterpolaton. Ths mantans the smoothness of the edge tangental and the steepness of the edge normal. Coordnate and gray nformaton was ftted n accordance wth the Gaussan ntegral model for accurate subpxel locaton. Ths approach solved the problem of senstvty to gray value change by usng a gradent to determne the subpxel edge; thus, t has good nose resstance, and t mproves the precson of edge detecton. In addton, the algorthm adopts curve fttng, reduces the amount of calculaton, and mproves the calculaton speed compared to the Facet surface fttng. The bult-n vson measurement system was calbrated, then, the algorthm was appled to measure the gauge block and standard nvolute spur gear. The measurement error of frst grade gauge block s μm, and the tooth profle total devaton measured by ths method s compared wth the measurement result of the gear measurement center, ts maxmum error s 1.9 μm, whch ndcates that the method has hgh relablty and can meet the requrement of hgh precson measurement. ACKNOWLEDGMENT Ths work was supported by Funder: Key Projects n the Natonal Scence & Technology Pllar Program No.014BAF08B01. REFERENCES [1] Kumar, B.M, Ratnam, M.M. (015). Machne vson method for non-contact measurement of surface roughness of a rotatng workpece. Sensor Revew, 35 (1), [] Gadelmawla, E.S. (011). Computer vson algorthms for measurement and nspecton of spur gears. Measurement, 44 (9), [3] Kosarevsky, S., Latypov, V. (013). Detecton of screw threads n computed tomography 3D densty felds. Measurement Scence Revew, 17 (), [4] Robnson, M.J., Oakley, J.P., Cunnngham, M.J. (1995). The accuracy of mage analyss methods n spur gear metrology. Measurement Scence and Technology, 6, [5] Chen, F., Brown, G.M. (000). Overvew of threedmensonal shape measurement usng optcal methods. Optcal Engneerng, 39 (1), [6] Lu, N.-G., Deng, W.-Y., Wang, Y.-Q. (005). Profle measurement of mcrowave antenna usng close range photogrammetry. In Thrd Internatonal Conference on Expermental Mechancs and Thrd Conference of the Asan Commttee on Expermental Mechancs, Proc. SPIE 585,

7 MEASUREMENT SCIENCE REVIEW, 18, (018), No., [7] Sdor, K., Szlachta, A. (017). The mpact of the mplementaton of edge detecton methods on the accuracy of automatc voltage readng. Measurement Scence Revew, 13 (6), [8] Shang, Y.-C., Chen, J., Tan, J.-W. (010). The study of sub-pxel edge detecton algorthm based on the functon curve fttng. In nd Internatonal Conference on Informaton Engneerng and Computer Scence. IEEE, 1-4. [9] We, B.-Z., Zhao, Z.-M. (013). A sub-pxel edge detecton algorthm based on Zernke moments. The Imagng Scence Journal, 61, [10] Lu, G., Lu, B., Chen, F., Hu, T. (009). Study on the method of the accuracy evaluaton of sub-pxel locaton operators. Acta Optca Snca, 9, [11] L, S., Lu, R., Sh, Y. et al. (011). Sub-pxel edge detecton algorthm based on Gaussan Surface Fttng. Tool Engneer, 45, [1] Ma, R., Zeng, L., Lu, Y. (009). Improved sub-pxel edge detecton based on Facet model. Journal of Basc Scence and Engneerng, 17, [13] Wang, K., Zhang, D., Huang, H. et al., (005). A study of sub voxel edge detecton method based on 3-D Facet model. Mechancal Scence and Technology, 4, [14] Xu, L.-Y., Cao, Z.-Q., Zhao, P., Zhou, C. (017). A new monocular vson measurement method to estmate 3D postons of objects on floor. Internatonal Journal of Automaton and Computng, 14, [15] Yu, Q.-F., Shang, Y. (009). Vdeometrcs: Prncples and Research. Bejng, Chna: Scence Press. [16] He, Z., Wang, B. (003). Sub-pxel extracton algorthm usng curve fttng method. Journal of Scentfc Instrument, 4, [17] Chang, S.-T., Sun, Z.-Y., Zhang, Y.-Y., Zhu, W. (014). Radaton measurement of small targets based on PSF. Optcs and Precson Engneerng, (11), [18] Duan, Z.-Y., Wang, N., Zhao, W.-H. et al. (016). Study on calbraton method based on lattce calbraton plate n vson measurement system. Acta Optca Snca, 36 (5), [19] Fe, Z.-G, Xu, X.-J., Anthmos, G. (016). Short-arc measurement and fttng based on the bdrectonal predcton of observed data. Measurement Scence and Technology, 7 (), Receved August 11, 017. Accepted March 0,