Summary of DLT method for stereo camera calibration, 3D reconstruction and robot-camera integration

Transcription

1 tes n T Smma f T meth f stee camea calbatn, ecnstctn an bt-camea ntegatn. amea calbatn Statng pnt: pespecte eqatns f a camea These eqatns map the cnates f a genec pnt n space,, nt the cespnng cnates n the plane f the camea,. These eqatns ae nn lnea wth espect t bth the tansfmatn f cnates an nknwn paametes: amea pstn:,, ] amea entatn: j ] Pncpal stance: Ttal: The tck f the T ect nea Tansfm s t epess eq. nn lnea n nepenent paametes nt an eqatn lnea n the fllwng paamete that, n the the han, ae nt nepenent : GOSYS ntenal ept, septembe,. P. Mass an V. Mhan, IST.

2 tes n T GOSYS ntenal ept, septembe,. P. Mass an V. Mhan, IST. amea calbatn cnssts then f pesentng t the camea a nmbe f cntl pnts,.e. tagets f whch we knw, b esgn, bth the atesan cnates,, an the cespnng camea cnates,. Snce each pnt geneates eqatns an the nknwns ae the mnmm nmbe f pnts s bt the me, the bette. The calbatn becmes then a pblem f least sqae estmatn SE, wth : U

3 tes n T T T ] U. Etensn f the mel f nclng ptcal stns Eq. can be etene n e t ncle tpcal ptcal sch as bael an pn-cshn sttn: wth hang ntce, th, an th e sttn tems,, an e-centeng sttn tems,. The nknwn paametes f each camea ae nw nstea f an eq. becmes R R R R R R R R R R wth R gan we can wte an algebac eqatn f the fm U whch fmall allws a SE f the th mensnal ect wth an eqatn smla t. Hwee, eq. s nt lnea-n-the paametes anme, e t the pesence f the R tem. Ths, the sltn can be fn nl n an teate manne:. chse an abta ale f R e.g.. cmpte the weght ect b sng eq.. pate the estmate f R. teate f the tw estmates f R ffe sgnfcantl.. albatn f mltple cameas Wth mltple cameas e.g. n the basc stee sstem the pcee abe s apple n paallel t all f them wth the same set f cntl pnts, estmatng a ect paamate f each camea:,,... The cmplcatn f cectng the ptcal sttns b means f the teate pcee s wth the efft f, f the chsen setp, the ecnstctn f cnates s nt sffcentl accate. GOSYS ntenal ept, septembe,. P. Mass an V. Mhan, IST.

4 tes n T GOSYS ntenal ept, septembe,. P. Mass an V. Mhan, IST.. Recnstctn f the cnates f makes mage salent pnts. fte hang calbate all the cameas, the ecnstctn algthm f the cnates f a taget pnt we gne ptcal sttns f the mment can be etemne b eaangng eq. n sch a wa t make eplct the epenence n the nknwns,,: B wtng these eqatns f all the cameas e.g. n the stana stee cnfgatn we en p wth the fllwng lnea algebac eqatn X Y ] T X,, whch allws the ect SE sltn ] Y X T T If we ntce als ptcal sttns eq, s tansfme nt the fllwng ne ] ] ] ] ] ] fm whch t s pssble, n pncple, t btan an SE f the pnt cnates fmall smla t the pes ne.. Rbt-camea ntegatn Sppse that W s the wkspace f the bt,.e. the set f pnts eachable b the bt eneffect entfe f eample b a small E hl b the gppe. Hw we ca t an ntegatn f the atesan sal cnates an the bt cnates bth angla an egcentc atesan f the en-effect? The fst step s t geneate wth the bt a set f cntl pnts f the camea calbatn. Hw t chse them? We nt nee a e ense samplng f W bt we nee at least t hae a sffcent nmbes f pnts n the bna f W becase T peates as a kn f nteplat an s knwn t hae apal eceasng pefmance when we pefm estmates f taget

5 tes n T pnts tse the cne hll f the cntl pnts. The pcee cnssts f hang the bt hlng a small E an can be smmae as fllws: albatn. Theetcal entfcatn f the cntl pnts, n egcentc atesan cnates f the ef bt : {,, ]... }. Pefm nese knematcs f calclatng the jnt efeence cmmans { q } ef... an geneate f the cespnng bt cmmans. Reat the actal jnt angles { q } eal... eal {,... }. Etact the camea cnates f the E mages {,,, ] }. Pefm ect knematcs f calclatng the eal E cnates, ]. alclate the camea paametes..., sng eqatns. Vefcatn. Pt an E n a pnt f the wkspace. Etact the camea cnates. Ealate the atesan cnates b means f eqatn.. Pefm nese knematcs f cmptng the jnt angles. mman the bt wth the jnt angles. Estmate the e between the E an the en-effect In the pesl escbe pcee we btan a well calbate camea-bt sstem wth espect f the wkspace W f the en-effect. Hwee, f we cnse that n the GOSYS epemental setp the actal wkspace wll ncle a stck tl hl b the gppe, we shl pefm the calbatn wth an etene W, efne b the tl f mamm se. GOSYS ntenal ept, septembe,. P. Mass an V. Mhan, IST.