A Traffic Camera Calibration Method Based on Multi-rectangle

Transcription

1 Traffc Camera Calbrato Method ased o Mult-rectagle Lyg Lu Xaobo Lu Sapg J Che Tog To cte ths verso: Lyg Lu Xaobo Lu Sapg J Che Tog. Traffc Camera Calbrato Method ased o Multrectagle. Zhogzh Sh; Zhaohu Wu; Davd Leae; Ul Sattler. 8th Iteratoal Coferece o Itellget Iformato Processg (IIP) Oct 04 Hagzhou Cha. Sprger IFIP dvaces Iformato ad Commucato Techology ICT-4 pp Itellget Iformato Processg VII. <0.007/ _6>. <hal-087> HL Id: hal Submtted o 8 Oct 06 HL s a mult-dscplary ope access archve for the depost ad dssemato of scetfc research documets whether they are publshed or ot. The documets may come from teachg ad research sttutos Frace or abroad or from publc or prvate research ceters. L archve ouverte plurdscplare HL est destée au dépôt et à la dffuso de documets scetfques de veau recherche publés ou o émaat des établssemets d esegemet et de recherche fraças ou étragers des laboratores publcs ou prvés. Dstrbuted uder a Creatve Commos ttrbuto 4.0 Iteratoal Lcese

2 Traffc Camera Calbrato Method ased O Mult-Rectagle Calbratg a camera usg mult-rectagle costructed by mar les traffc road Lyg Lu Xaobo Lu* Sapg J Che Tog Key Laboratory of Measuremet ad Cotrol of CSE Mstry of Educato School of utomato Southeast Uversty Najg 0096 Cha *E-mal: xblu0@6.com STRCT: s dstace detecto s frequetly eeded moder traffc maagemet camera calbrato has a sgfcat fluece o the accuracy of dstace detecto. The tradtoal calbrato methods usually eed a calbrato target ad the exact dstace of calbrato pots has to be measured. I ths paper accordg to the camera magg model we put forward a calbrato method based o mult-rectagle whch costructs several rectagles wth the mar les of the traffc road. Wthout measurg the teral or exteral parameters of the camera or the exact dstace of calbrato pot we oly eed the sde legths of rectagles ad the mage coordates of the rectagular vertexes to establsh the vdeo mage dstace coverso model. For mprovg the accuracy of coverso we use multple rectagles to determe the coordates of the vashg pots ad modfy the coordates of the rectagular vertexes. Expermetal results show that our method s more accurate whe compared wth the mastream methods. KEYW ORDS: dstace detecto; camera calbrato; mult-rectagle; parameter modfcato

3 Traffc Camera Calbrato Method ased O Mult-Rectagle. Itroducto I moder traffc maagemet traffc vdeo mage processg s frequetly used the feld of dstace detecto speed detecto ad vsblty detecto. s a mportat part of traffc mage processg camera calbrato has a sgfcat fluece o the accuracy of detectos whch related to dstace. Camera calbrato meas establshg the coverso model betwee the posto of mage pxel pot ad the posto of actual pot. ccordg to the camera model we get the camera parameters usg some feature pots of a real scee ad these pots coordates the mage. Fally we buld the coverso model betwee the mage coordates ad the actual dstace usg the camera parameters (Zheg 998; Hartley 00). Tradtoal camera calbrato methods usually eed some stadard calbrato targets whose actual sze has bee accurately measured before calbratg. These methods use the correspodg relatoshp of mage pots ad actual pots to establsh the costrat codtos of camera parameters the calculate the parameters of camera by some olear optmzato algorthm(zhag 000; Zhag 004; Ye). It s bee prove that the calbrato method based o vashg pot s effectve ad relable the posto of vashg pot could b e determed by oe-dmesoal target of calbrato targets(gullou 000; Ya 0). We Geg ad Yag Lu put forward a ew algorthm based o sgle rectagle whch uses the mar les traffc road to calbrate the parameters of camera the establsh mutual coverso model betwee mage coordate system ad the actual dstace(geg 0). The method uses the actual legths of rectagular patters ad the correspodg formato of coordates to establsh detecto model wthout tag maual measuremet to get camera teral ad exteral parameters ad the absolute dstace of stadard fxed pots. ut uder actual stuato as the mar les may have bee wor ad the feature pots are maual mared that method may brg serous error. To solve ths problem a calbrato algorthm based o mult-rectagle s troduced ths paper whch costructs several rectagles wth mar les of the traffc road the modf es the Y-axs drecto vashg pot by fttg a straght le wth multple pots. I the X-axs drecto straght les wll geerate tersecto pots we choose the pot wth hghest accuracy as the X-axs drecto vashg pot. To get more accurate calbrato parameters we use the posto formato of vashg pots ad the accuracy of each rectagular vertex to modfy the posto of every rectagular vertex the establsh dstace coverso model wth these modfed parameters. Through a lot of expermet ths method s more accurate tha the sgle-rectagle algorthm.

4 Itellget Iformato Processg VIII. Calbrato Method ased O Mult-Rectagle s the whte mar les ad the gray road surface mae the cotrast rato of the mage ot strog eough ad the mar les may have bee wor t s dffcult to localze the posto of feature pots accurately ad the calbrato method based o sgle-rectagle s cled to brg error. We study a parameter modfcato method ths paper to reduce the error. s show Fgure we ca costruct multple rectagles a road surface mage Fgure. Costruct multple rectagles a road surface mage.. Modfyg the coordate of the vashg pot Y-axs drecto The projecto le of mar les mage plae wll tersect at pot Q whch s the vashg pot Y-axs drecto. ssume that we costruct sgle rectagle wth pot straght le ad ca be vewed as the projecto les of mar les but error wll be brought whe ay pot s localzed accurately. To reduce the error we ft straght le L wth pot usg the least squares method hece L ca be vewed as the projecto le mage plae of the left mar le. The we ft the projecto le mage plae of the rght mar le L the same way. Fd the tersecto pot Q of straght le L ad L so Q s the vashg pot Y-axs drecto... Modfyg the coordate of the vashg pot X-axs drecto Straght le road surface plae all parallel to X-axs so straght le mage plae should tersect at vashg pot Q but there may be multple tersecto pots actual mage geerally straght les wll geerate C tersecto pots. ssume that straght le ad j j tersect at pot P j the closer P j ear to other straght les the closer P j to the actual posto of vashg pot Q. Defe D j as the accuracy of P j :

5 Traffc Camera Calbrato Method ased O Mult-Rectagle D j dj j () 0 j.. Modfyg the coordates of the rectagular vertex Some feature pots may have bee accurately localzed as we use mar les to costruct calbrato target so these coordates must be modfed. To characterze the accuracy of pot ad we sum all D( ) value from pot P to pot P o straght le the calculate the ormalzed summato. Defe the accuracy of ay rectagular vertex the Q drecto: E sq Dt t max( D ) t I the formula s could be a or b t so s represets a rectagular vertex t t max( Dt ) s the largest value of accuraces o straght le q meas the curret value s the accuracy Q drecto. ut E aq equals E bq Q drecto whch meas t s uable to dstgush the accuracy of ad. So we have to fd other straght les other drecto mae ad belogs to dfferet straght les thus to separate the accuracy of ad. () Y Q Q X L L Q ( a) Fgure. Feature pot coordate modfcato s Fgure (a) shows every dagoal the same drecto parallels to each other as a example we choose a group of straght les ( ) these straght les wll tersect at a vashg pot Q. The coordate of Q could be calculated the same way as how we calculate the coordate of Q the the ( b)

6 4 Itellget Iformato Processg VIII accuracy of ad Q drecto E ca be calculated. s a excepto sq ether or belogs to a straght le Q drecto so ther E value s 0. sq Smlarly a group of straght les ( ) wll tersect at vashg pot Q we get calculate the coordate of 4 Q ad the 4 E sq4 value of every feature pot. Defe the accuracy of a feature pot as: Esq Esq Esq4 Es () efc( E ) efc( E ) sq sq4 I the formu la rages from to efc( E sq )=0 whe s a or s b ; efc( E sq4)=0 whe s a or s b otherwse efc( E sq)= sq4 efc( E )=. fter gettg the accuracy of every feature pot we ca modfy the coordate of feature pots. We tae pot ad as a example the exact feature pot should be the tersecto pot of the straght les whch pass through Q ad straght le L or L we mar them as square pots Fgure (b). The roud dots Fgure (b) represets the maual mared feature pots. s the accuracy of ad s ow we choose the pot whch has a smaller accuracy value as referece pot the coect t ad Q to costruct the modfed straght le so the tersecto pot of ad L s the modfed pot the tersecto pot of ad L s the modfed pot..4. Dstace coverso model Co mpared to the sgle-rectagle method the mu lt-rectagle method mae Q Q ad every rectagular vertexes modfed so we ca get more accurate calbrato parameters. Z O 0 plae O0QQx O Q y Y P L X Q x P P P Q road surface plae P L Fgure. Calculatg calbrato parameters

7 Traffc Camera Calbrato Method ased O Mult-Rectagle 5 ccordg to camera magg model we ca calculate scale factor ad X-axs drecto. s Fgure shows P s the tersect pot of mar le L L ad plae O0QQ y P s the tersecto pot of mar le L L ad plae O0QQ. y s QQ parallels to X-axs ts projecto le mage plae passes through y Q so QQ s the projecto le of QQ y P s the projecto pot of L P ad t s the L tersecto pot of QQ ad tersecto pot of QQ ad l represets the X-axs coordate of xb P L dstace coverso model: P ad t s the L l represets the X-axs coordate of P L L P s the projecto pot of L L let xa accordg to the oe-dmesoal lxa p (4) lxb p where p s the recprocal of the p xel-value dfferecg betwee pot P ad L Q p s the recprocal of the pxel-value d fferecg betwee P ad L Q. Let s represets the dstace betwee L ad L s lxb lxa ( p p ) accordg to hghway costructo specfcatos [6] s.75 m so: s.75 = p p p p ccordg to the relatoshp betwee ad we ca get : s cos (6) f The we calculate scale factor ad Y-axs drecto. s rectagular vertexes have bee modfed every straght le passes through Q so straght le parallels to X-axs assume the tersecto pot of ad plae O0QQ x s P ( ) the actual dstace betwee every two pots s easly calculated accordg to hghway costructo specfcatos. P s the projecto pot of P ad t s also the tersecto pot of straght le ad QQ. ccordg to the oe-dmesoal dstace coverso model Y-axs drecto for pot P : ly p where l y s the Y-axs coordate of P p s the recprocal of the pxel-value dfferecg betwee pot P ad Q whch could be easly calculated mage. Smlarly for P : ly d p where d represets the dstace betwee P ad P p represets the recprocal of the pxel-value dfferecg betwee pot P ad Q. s rages from to we ca get equatos the we ca establsh a coordate system wth d (5)

8 6 Itellget Iformato Processg VIII ( ly d) -axs as vertcal axs ad p -axs as horzotal axs ft a straght le usg the pots we got the equatos the slope of the straght le s. ccordg to the relatoshp betwee ad : s cos / f d. I cocluso we ca establsh the two-dmesoal dstace coverso model as: lx p s cos / fd / p / (( u ux) ( v vx) ) (7) ly p s cos / fd / p / (( u uy) ( v vy) ). Results d alyss Of Expermet.. ccuracy testg expermet To evaluate the accuracy of the proposed method we compare the effect of mult-rectagle method ad the sgle-rectagle method through expermet. We mar sx pots mage that are correspodg to.00m to 4.m actual road plae the calculate the dstace of these pots usg the vdeo mage dstace coverso model ad compare the results wth the actual dstace. s Table shows compared to the sgle-rectagle method the proposed method has a mproved measurg accuracy o each dstace ad as the dstace creases the error of sgle-rectagle method creases fast but the error of the proposed method remas the rage of 5%. I the study we foud that the accuracy of vashg pot Q ad Q have a major mpact o the model parameters for the proposed method we use multple rectagles to determe the posto of vashg pot so we could get more accurate vashg pot coordate tha the sgle-rectagle method. ctual dstace (m) Sgle-rectagle method Test value (m) relatve error Mult-rectagle method Test value (m) relatve error % 0.5.0% % % % % % 00.8.% % % % % Table. Results for dstace detecto expermet

9 Traffc Camera Calbrato Method ased O Mult-Rectagle 7.. Stablty testg expermet To evaluate the stablty of the proposed method we measure the maxmum error of the sgle-rectagle method ad the mult-rectagle method 0 dfferet traffc mages the dstace of each test pot s less tha 00 meters. seral umber Maxmum error (sglerectagle method) 9.6% 4.0%.7% 4.7% 9.88% 5.4% 4 6.4% 6.9% % 4.% 6 0.0% 5.6% 7.7% 7.44% % 5.9% 9.4% 5.7% 0 9.8% 4.58% Maxmum error (multrectagle method) Table. Results of stablty testg expermet s Table shows the maxmum error of the mult-rectagle method floats aroud 5% whle the maxmum error of the sgle-rectagle method floats aroud 0%. I addto the 4th ad 7th mage the maxmu m error of the sglerectagle method rse to 6.4% ad.7% due to the mar le has bee wor whle the maxmum error of the mult-rectagle s oly 6.9% ad 7.44%. Through ths expermet we ca see the proposed method s more stable tha the sglerectagle method. 4. Cocluso Ths paper put forward a camera calbrato algorthm based o mult-rectagle whch costructs multple rectagles wth mar les actual traffc road the modfes the calbrato parameters ad establsh vdeo mage dstace coverso model. We modfy the coordate of vashg pot Y-axs drecto by fttg a straght le wth multple rectagular vertexes modfy the coordate of vashg pot X-axs drecto by choosg the pot wth hghest accuracy amog all tersecto pots the we modfy the posto of every rectagular vertex ad establsh the dstace coverso model usg the modfed parameters. Compared to sgle-rectagle method the proposed method provdes more accurate calbrato parameters ad the dstace coverso model we got has a mprove accuracy. Expermet result shows that as dstace creases the detectg error creases too but the effect of the proposed method s stll better tha the sgle-rectagle method.

10 8 Itellget Iformato Processg VIII However ths method stll belog to the category of maual calbrato the tal feature pots stll eeds to be maual mared that would brg some uow error ad reduce the calbrato accuracy. How to automatcally localze the feature pots that s what we eed to mprove further study. cowledgmets Ths wor was supported by the Natoal Natural Scece Foudato of Cha (No.67494) ad Cha Postdoctoral Scece Foudato Fuded Project (No.0M540405). 5. Refereces Cha Mstry of Trasportato Road traffc sgs ad margs set orms JTG D Geg W Detecto lgorthm of Vdeo Image Dstace ased o Rectagular Patter 0 5th Iteratoal Cogress o Image ad Sgal Processg Gozales Dgtal Image Processg. ejg: Publshg House of Electrocs Idustry 007. Gullou Usg vashg pots for camera calbrato ad coarse D recostructo from a sgle mage The Vsual Computer Vol pp Hartley et al Multple vew geometry computer vso Cambrdge Uversty Press 00. Hautère et al Daytme Vsblty Rage Motorg through use of a Roadsde Camera IEEE Itellget Vehcles Symposum 008 pp Ya H Camera Self-Calbrato I Hghway Dyamc Evromet Computer ded Desg ad Computer Graphcs Vol. 5 No 7 0 pp Ye Y Study o the Camera Calbrato pproach ad lgorthm of Edge Detecto ad Cotour Tracg Dala :Dala Uversty of Techology. Y W Camera calbrato based o OpeCV Computer Egeerg ad Desg Vol.8 No. 007 pp Zheg N Computer Vso ad Patter Recogto Defese Idustry Press ejg 998. Zhag Z flexble ew techque for camera calbrato IEEE trasactos o patter aalyss ad mache tellgece Vol. 000 pp.0-4. Zhag Z Camera calbrato wth oe-dmesoal objects IEEE trasactos o patter aalyss ad mache tellgece Vol pp