THE THEORY AND APPLICATION OF STRUCTURED LIGHT PHOTOGRAMMETRY WITH KNOWN ANGLE

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1 THE THEOR AD APPICATIO OF TRUCTURED IGHT PHOTOGRAMMETR WITH KOW AGE i in * Hou Wengung hng Holing hool o Remote ensing nd Inormtion Engineering Wuhn Universit 9 uou Rod Wuhn Chin - li6@gmil.om -houwengung99@6.om The Hong Kong Poltehni Universit Industril Center Hung Hom Kowloon Hong Kng - shngholing@6.om Commission V WG V/ KE WORD: trutured light Angle Industril Photogrmmetr Computer Vision Reonstrution on-metri Digitl Cmer Mthemtis Model Ojet without Teture ABTRACT: In omputer vision ield strutured-light is deined s the light with ertin eture. Hene ll o the light point light line nd light plne whih re projeted lser equipment nd projetor n e lled strutured light. In mn ses the diretion o those light rom strutured light resoure re unknown in spe. I the diretion o the strutured light n e otined the equipment rom whih it is trnsmitted the surveing steps nd the ollowing dt proessing will e ilitted. Aording to wht ws mentioned ove two kinds o snning mthemtil models o strutured light with known ngle sed on lser theodolite re introdued. When the horizontl irle is ied nd ollimtion is rottes round the horizontl is plum line plne is ormed with the snning o trnsmitted lser em. When the vertil irle is ied nd the lidde rottes round the vertil is irulr one sure is ormed with the snning o trnsmitted lser em. I one mer is used to shoot the strutured light projeted on the ojet -D oordinte o point n e otined ter etrting strutured light inormtion on the imge nd lulting point o intersetion o photogrph line nd strutured light snning sure. There the detiled mthemtil equtions o lulting -D oordintes o strutured light is dedued sed on lser theodolite in strutured light photogrmmetr. Through the solution o the equtions omposed o ollinerit ondition equtions nd strutured light snning eqution the epressions o D oordintes n e inerred simpl nd lerl. In order to testi the ur o the ove theor preision testing eperiment nd -D reonstrution o ojet eperiment re onduted. In preision testing eperiment lose rnge indoor - D ontrol ield with high preision is regrded s the surveed ojet whose preision is less thn.mm. The known oordintes o ontrol point is thought s true vlue nd the lulted -D oordintes s mesured vlue to lulte the preision o strutured light photogrmmetr. Under the se o plum line sure snning mode twent ontrol points re hosen to lulte the preision. The men squre error o oordintes re m ±.44mm m ±.45mm m ±.85mm seprtel. Under the se o irulr one sure snning mode ort seven ontrol points re hosen to lulte the preision. The men squre error o oordintes re m ±.4mm m ±.mm m ±.7mm seprtel. In -D reonstrution o ojet eperiment mnnequin is onsidered s the reonstrution ojet nd the eperimentl instruments re pled s wht is done in the ove eperiments. The - D model is reonstruted respetivel ording to plum line sure snning mode nd irulr one sure snning mode. The ove eperiments prove the ur o Photogrmmetr theor o strutured light sed on lser theodolite.. ITRODUCTIO In omputer vision ield strutured-light is deined s the light with ertin eture Peng Ronghu et. 4. Hene ll o the light point light line nd light plne whih re projeted lser equipment nd projetor n e lled strutured light. In mn ses the diretion o those light rom strutured light resoure re unknown in spe. Onl through the sstem lirtion -D oordintes n e determined. When the inoulr vision equipment is emploed the strutured light is reputed s tetures rom the ngle o photogrmmetr in order to simpli the lter step o imge proessing nd imge mthing. I the diretion o the strutured light n e otined the equipment rom whih it is trnsmitted the surveing steps nd the ollowing dt proessing will e ilitted. o in this pper the theories o strutured light snning nd the determintion o orresponding ojet points -D oordintes re introdued. owds in the surveing ield the strutured light produing pprtus with the lrgest volume re lser theodolite nd totl sttion instrument with lser. I the instrument is lttened horizontl ngle nd vertil ngle n e red through horizontl irle nd vertil irle. Then the spe diretion o lser em whih n orm strutured light n e determined. When the strutured light is projeted on the surveed ojet lser point trget ome into eing. Then i the mer whose interior orienttion elements nd eterior orienttion elements re known is used to shoot the lser point trget its -D oordintes n e otined. The lser em o theodolite with two rottion reedoms orresponds with the ollimtion is nd it n rotte round the horizontl is nd vertil is. The lser spot n e djusted theodolite telesope. A lser theodolite is shown in Figure.

2 The Interntionl Arhives o the Photogrmmetr Remote ensing nd ptil Inormtion ienes. Vol. VII. Prt B5. Beijing 8 peil Cse When H 9 snning plne eqution is.. The nning Mthemtil Model o Cirulr Cone ure Figure. Theodolite with two rottion reedoms. CAIG MATHEMATICA MODE OF TRUCTURED IGHT WITH KOW AGE There re two snning modes sed on lser theodolite. The re snning mode o plum line plne nd snning mode o irulr one sure Feng wenho i in The nning Mthemtil Model o Plum ine Plne As shown in Figure in the ojet spe oordinte sstem D- lser theodolite is sttioned t the point whose oordinte re. Eh oordinte is o the deined lser theodolite oordinte sstem - prllels tht o the ojet spe oordinte sstem D-. When the horizontl ngle H is ied nd ollimtion is rottes round the horizontl is plum line plne pssing point is ormed. uppose is the point in the plum line plne. Its oordintes in the oordinte sstem D- re ut in -. In the ojet spe oordinte sstem D- lser theodolite is set t the point whose oordintes re. Eh oordinte is o the deined lser theodolite oordinte sstem - prllels tht o the ojet spe oordinte sstem D-. When zenith distne V is put nd ollimtion is is rotted round vertil is ter the rottion o lidde the irulr one sure pssing is ormed. uppose is the point in the irulr one sure. Its oordintes in the oordinte sstem D- re ut in -. In oordinte sstem - the eqution o the irulr one sure is: tg V The pek o the irulr one sure is the intersetion point o the vertil is nd horizontl ones. In the ojet spe oordinte sstem D- the eqution is: C V tg V 4 Figure. The sketh o snning mode o plum line plne Oviousl in oordinte sstem -the eqution o the plum line plne is: H In oordinte sstem D-the eqution o the plum line sure is: H peil Cse When H snning plne eqution is. Figure. The sketh o snning mode o irulr one sure peil Cse When V or V 8 the irulr one sure is redued to the plum line pssing point its eqution is: peil Cse When V 9 or V 7 the irulr one sure is redued to the horizontl plne its eqution is:

3 . THE DETERMIATIO OF -D COORDIATE OF TRUCTURED IGHT Beuse the lotion o the strutured light snning sure is known in spe onl one mer whose elements o interior orienttion nd elements o eterior orienttion re known is enough to e emploed to shoot the strutured light snning sure nd then the -D oordintes o the intersetion point etween photogrph line nd strutured light snning sure re lulted i in 6. uppose the lser point whih is ormed ter strutured light is projeted onto the surveed ojet is P the oservtion vlue o its orresponding imge point p is ollinerit ondition equtions ter the orretion o sstem error is Wng hizhuo 99: Δ Δ Δ Δ Δ Δ Δ Δ 5 where prinipl distne oordintes o imge prinipl point liner elements o eterior orienttion i i i diretion osine o orienttion mtri ΔΔ distortion error uppose Δ Δ nd the eqution 6 etween imge spe oordinte sstem nd imge spe uilir oordinte sstem is introdued. 6 Then eqution 5 n e hnged into: 7 Where re the oordintes o the imge point in imge spe uilir oordinte sstem. I the elements o interior orienttion nd elements o eterior orienttion nd distortion oeiient o digitl mer re omputed through spe resetion n e lulted through eqution 6.. Clultion o -D Coordintes o trutured ight in Plum ine Plne nning Mode In the plum line plne snning mode the lultion o the - D oordintes o trget points is equl to lulting the intersetion points o photogrph line determined the mer nd the plum line plne. In the right-hnd oordinte sstem D- shown in Figure suppose the liner elements o eterior orienttion o the mer re. The liner equtions onsisting o eqution nd eqution 7 re: 8 Then the -D oordintes n e epressed s ollowing: 9. Clultion o -D Coordintes o trutured ight in Cirulr Cone ure nning Mode In the irulr one sure snning mode the lultion o the -D oordintes o trget points is equl to lulting the intersetion points o photogrph line determined the mer nd the irulr one sure. In the right-hnd oordinte sstem D- shown in Figure suppose the liner elements o eterior orienttion o the mer re nd in oordinte sstem - the liner elements o eterior orienttion re supposed s. o we hve: In the right-hnd oordinte sstem - the equtions onsisting o eqution nd eqution 7 re: V tg Thus eqution n e hnged into single qudrti eqution or : The Interntionl Arhives o the Photogrmmetr Remote ensing nd ptil Inormtion ienes. Vol. VII. Prt B5. Beijing 8

4 The Interntionl Arhives o the Photogrmmetr Remote ensing nd ptil Inormtion ienes. Vol. VII. Prt B5. Beijing 8 [ tg V ] [ tg V tg V ] [ tg V ] Then the -D oordintes in the oordinte sstem - n e epressed s ollowing: Where W W W tg V W tg V tg V tg V tg V 4. Preision Cheking Eperiment Preision testing eperiment is held under two ses the plum line plne snning mode nd the irulr one sure snning mode. During the test ser theodolite ims t the ontrol points in the ontrol ield with high preision nd using the digitl mer to shoot lser points in the drk environment ilittes the strtion o oordintes o lser points lter. 4. Preision test under the se o plum line plne snning mode In the preision test under the se o plum line sure snning mode the equipment used or trnsmitting the strutured light is BOIF DJD-GJA eletroni lser theodolite. The ur o ngulr mesurement is ±. When the lser em emits rom the theodolite it is oil with ollimtion is. The digitl mer used or shooting is FUJI-FinePi Pro single lens rele mer whih is equipped with IGMA lens with 8mm ol length the CCD hip o whih is.mm 5.6mm in size the imge resolution o whih is 4piel 6piel the size o eh piel is 7.7μm. or Where W W W In the test the lser theodolite is pled on the ored entering plte o the let oservtion post. Thus the horizontl projetion o the entre o the lser theodolite n e onsidered s the oordinte origin nd its elevtion n e lulted oserving the vertil ngles o some ontrol points in the ontrol ield. The ontrol ield n e shot ter the digitl mer is put in the proper ple the verge photogrphi distne is 5.m. The interior orienttion elements nd eterior orienttion elements o the mer n e otined using spe resetion. tg V W tg V tg V tg V tg V Ater hnged into the oordinte sstem D- the -D oordintes n e epressed s ollowing: Twent ontrol points re hosen in the ontrol ield. And the horizontl ngle o these ontrol points n e otined respetivel ter lser theodolite ims t them respetivel. Their -D oordintes n e lulted ording to eqution 9. The dierene etween the oordintes o those omputed ontrol points nd true vlue o ontrol points surveed the theodolite is displed in Tle. or W 4 W W W 4 W W o. d d d o. d d d TET ABOUT TRUCTURED IGHT WITH KOW AGE The test on how to otin the -D oordintes o the trget point with strutured light on known ngle inludes two eperiments: the re preision heking eperiment nd -D reonstrution o ojet eperiment oth o whih re onduted in the indoor -D ontrol ield with high preision in hool o Remote ensing nd Inormtion Engineering o Wuhn Universit. Tle. Coordintes Dierene under Plum ine Plne nning Mode The men squre error o oordintes shown in Tle re m ±.44mmm ±.45mmm ±.85mm seprtel. 4

5 The Interntionl Arhives o the Photogrmmetr Remote ensing nd ptil Inormtion ienes. Vol. VII. Prt B5. Beijing 8 5. PRECIIO TET UDER THE CAE OF CIRCUAR COE URFACE CAIG MODE In the preision test under the se o irulr one sure snning mode the equipment used or trnsmitting the strutured light is OKKIΛ ETR totl sttion. The ur o ngulr mesurement is ±. When the lser em emits rom the totl sttion it is oil with ollimtion is. The digitl mer used or shooting is Kodk DC Pro R/n whih is equipped with ikon lens with 8mm ol length the CMO hip o whih is 6mm 4mm in size the imge resolution o whih is 45piel pielthe size o eh piel is 8μm. Following the proedure o the eperiment in setion 4.. the onerned oeiients o totl sttion nd digitl mer n e determined. Wht is dierent is the emploment o irulr one sure snning mode. Fort seven ontrol points re hosen in the ontrol ield. The dierene etween the oordintes o those omputed 47 ontrol points nd true vlue o ontrol points surveed the theodolite is displed in Tle. o. d d d o. d d d Tle. Coordintes Dierene under Cirulr Cone ure nning Mode Figure 4. Reonstruted ojet: mnnequin 5.. Reonstrution o Ojet under the Cse o Plum ine Plne nning Mode The equipment whih is the sme to the equipment in setion 4.. is used. The distne etween the digitl mer nd the mnnequin is out.4m. ong time eposure mode is emploed to get the liner strutured light. Onl one snning line is reorded on eh imge. The digitl mer sts motionless during the whole test. In order to reonstrut the mnnequin the rottion o the mnnequin is omplished mnull euse it should e the theodolite nd the digitl mer in dierent sides. Common tie points re used to relize the onnetion o trget points in dierent sides. iner strutured light snning imge is shown in Figure 6. Figure5. Imges o plum line plne snning mode In the test 9 imges o strutured light re shot nd 8746 trget points re lulted. The trget points o mnnequin in dierent sides in the orm o snning line re shown in igure 6. From the result o the -D reonstrution the loss o model evidene o medil leg is rought out on ount o snning ded ngle. As whole the reonstruted model is lose to the rel ojet. The men squre error o oordintes shown in Tle re m ±.4mmm ±.mmm ±.7mm seprtel. 5. Test o -D Reonstrution o Ojet In the test o -D reonstrution o ojet plum line plne snning mode nd irulr one sure snning mode re pplied into snning the mnnequin mde o toughened glss the size o whih is height 95m width 4m thikness m. Thirteen ommon tie points mde up o steel nil re distriuted in the hed shoulder wist nd the plnk in the lower prt o the mnnequin s od s shown in igure 5. The mnnequin is set eore the ontrol ield when the strutured light is used to sn nd mer is used to shoot. Figure 6. The trget points o mnnequin in dierent sides in the orm o snning line 5

6 The Interntionl Arhives o the Photogrmmetr Remote ensing nd ptil Inormtion ienes. Vol. VII. Prt B5. Beijing 8 Ater points resmpled TI o mnnequin is reonstruted. The ontrsts etween the -D reonstrution models nd the rel imges in dierent sides re shown in Figure 7. Figure. -D reonstrution model in dierent sides From the onsequene o the test the loss o model evidene o medil leg is rought out still euse o the snning ded ngle. evertheless s whole the reonstruted model is lose to the rel ojet. The model o pleur relets the proile o mnnequin vividl under the se o this mode s it does under the se o plum line sure snning mode. 6. COCUIO Figure 7. Contrsts etween the -D reonstrution model nd the rel imge in dierent sides 5.. Reonstrution o Ojet under the Cse o Cirulr Cone ure nning Mode The equipment whih is the sme to the equipment in setion 4.. is used in this test. The whole test proedure is lso the sme. Wht is dierent is the usge o irulr one sure snning mode. In the test 49 imges o strutured light re shot nd 5 trget points re lulted. The imges o liner strutured light re shown in Figure 8. The trget points o mnnequin in dierent sides in the orm o snning line re shown in Figure 9. In the pper two kinds o snning mthemtil models o strutured light with known ngle sed on lser theodolite re introdued how to otin imges o strutured light on the sis o singulr digitl mer nd how to determine the eqution o -D oordintes o strutured light points re given. The orretness o vrious equtions is demonstrted in tests. When the theor o strutured light photogrmmetr with known ngle is pplied the quisition o -D oordintes o strutured light points onl depends on lulting the intersetion point o photogrph em nd the snning sure o strutured light. Tht voids imge mthing nd suits the surveing o ojets without tetile. Additionll it is it or surveing the ojets in the dim or without verge light round. The snning mthemtil models o strutured light mentioned in the pper n e used s the design prototpe o some lser snning sstem. I some dvned hrdwre is equipped the utomtion o snning surveing n e relized. REFERECE Figure8. Imges o irulr one sure snning mode Feng Wenho i in 998. The theor nd pplition o the struture light engineering surveing sed on lser theodolite with three reedoms o rottion Chinese. Journl o Wuhn Tehnil Universit o urveing nd Mpping 4 pp i in 6. The studies o ke tehnologies o three dimensionl oordintes surveing sed on digitl mer Chinese. Dotorl disserttion Wuhn Universit Wuhn Chin. Peng Ronghu hong uein hng Wuming 4. Reserh o humn-od -D non-onnet mesurement sstem Chinese. Mesurement Tehnique pp Figure 9. The trget points o mnnequin in dierent sides in the orm o snning line Wng hizhuo 99. Priniples o Photogrmmetr with Remote ensing. Press o Wuhn Tehnil Universit o urveing nd Mpping Pulishing House o urveing nd Mpping Beijing pp. 5. Ater points resmpled TI o mnnequin is reonstruted. The rendered -D mnnequin reonstrution models in dierent sides re shown in Figure. 6