Registration of Multiple Laser Scans Based on 3D Contour Features

Transcription

1 Regstato of Multple Lase Scas Based o 3D Cotou Featues st Shaoxg HU, d Hogb ZHA, 3 d Awu ZHANG st School of Mechacal Egeeg & Automato, Beg Uvesty of Aeoautcs ad Astoautcs, Beg 83, d Natoal Laboatoy o Mache Pecepto, Peg Uvesty Beg 87, 3 d Msty of Educato of Key Laboatoy o 3D Ifomato Acqusto ad Applcato, Captal Nomal Uvesty, Beg 37 husx@buaa.edu.c, zhagaw63@63.com Abstact Whe 3D lase scae captues age data of eal scees, oe of most mpotat poblems s how to alg all age data to a commo coodate system. I ths pape, we popose a algothm of egstato of multple age data fom eal scees usg 3D cotou featues. Fstly, 3D cotou featues ae extacted usg self-adaptve cuve fttg, ad a seachg stuctue of octee s bult fom the 3D cotou featues. Secodly, usg mahalaobs dstace, the leaf odes ae matched betwee two scas to compute ogal tasfom matx, ad the tasfom matx s efed step by step though ICP utl a best tasfom matx s obtaed. Lastly, a ew global egstato stategy s gve based o the eaby pcple. The expemets of multple age data egstato fom doo scees, outdoo scees ad acet buldgs ae doe, ad the esults show the poposed algothm s obust. Keywods---lase scae, cotou featue, mahalaobs dstace, matchg, egstato.. Itoducto The techque of lase scag also called "eal scee epoducto techology", t ca dectly captues age data fom eal scees, ad t s useful a vaety of felds such as uclea powe plat, cultual elc, achaeology, achtectue, aeospace, avato, shppg, maufactue, mltay, taffc, publc secuty ad so o. The basc pocessg of lase age data cludg age data segmetato, egstato of age data, modelg, ad egstato s the most ey wo. At peset, age data egstato maly depeds o 5 appoaches: poecto appoach, taget appoach, cougate appoach, exteal coopeato appoach, suface match appoach. Poecto appoach, fo example, Zhao et al. poposed z- mage method [,], egstato s completed usg z- mage. It educes the complexty of algothm, but t fals to eep the 3D featue, ad the pecso of egstato s low. Taget appoach [3], t places the tagets the ovelap ego of the eghbog scas, the usg lase eflecto chaactestcs to the tagets, the tagets ae ecogzed automatcally. Supposed thee ae thee o moe tagets ovelap ego, we ca obta the coodates tasfom betwee the eghbog scas. Howeve, sometmes t s dffcult to ecogze tagets f thee ae some egos wth the same eflectve featue as tagets o agle betwee lase beam ad the taget plae s lttle small. Cougate appoach [4], by the teactve way, the plae s fomed fom pots of coplaa (o close to the coplaa, the coodate tasfom s computed by moe tha thee upaallel cougate plaes. Ths method must loo fo moe tha thee upaallel cougate plaes the ovelap ego, othewse, egstato fals. The exteal coopeato appoach [5], t use GPS to help egstato. But GPS ca t accept the sgal whee the buldgs ae hgh ad the aveues ae aow. Suface match appoach [6], f the measued obect has suface wth the ups ad dows, the egstato ca be completed though matchg suface the ovelap ego, ad suface match ca ot be fully automated geeally. These poblems let us to develop automatc egstato method wthout ay addtoal devces. Ths pape poposes a fast egstato algothm fo 3D lage-scale scee usg cotou featues. Fstly, cotou featues ae extacted usg self-adaptve cuve fttg, ad a seachg stuctue of octee s bult fom the 3D cotou featues. Secodly, usg mahalaobs dstace, the ogal tasfom s computed by matchg leaf odes betwee two scas, ad the tasfom s efed step by step though ICP utl a best tasfom s obtaed. Lastly, a ew global egstato stategy s gve based o the eaby pcple.. Cotou featue extacto I the secto, the decto mages (X-mage, Y- mage, Z-mage ae defed based o the scag featues of lase scae ad the dexes of the lase pots, edges ae detected fom decto mages Poceedgs of the Ifomato Vsualzato (IV /6 $. 6 IEEE

2 espectvely, ad the the edges ae tegated to cotou cuves... Decto mage We use Cyax-p5 to captue age data of the scee. See fom the scag pocess, the ow ad colum values of evey sca ae gve accodg to accuacy demad befoe scag. Lase samplg pots ae ogased o D gd. Evey gd pot (, coespods to 3D pot ( x(,, y(,, z(,, ust le fgue. Accodg to the dexes of lase samplg pots, (,, x(, foms X-mage, (,, y(, foms Y-mage, (,, z(, foms Z-mage. X-mage, Y-mage, ad Z- mage ae called decto mage. Xo Y o Z x(,(o y(, o z(, Fgue : The elatoshp betwee D gd pots ad 3D pots.. Self-adaptve local fttg Supposed each sca le ca be cosdeed as a pecewse smooth cuve ad the pots of decto mages ae samplg pots wth ose o these pecewse smooth cuves, the (, L(, ( s fxed We choose a teval D(,, ad local quadatc cuve fttg s doe. fˆ (, a a a ( Whee, f ca be X, Y, Z a,a,a s coeffcet. Geeal speag, the least squae method ca calculate coeffcets a, a, a but the least squae method s ot sestve to ose ad outles, so f the fttg teval cludes outles, we caot obta the best fttg esults. Howeve, befoe fttg we caot ecogze ad emove outles, ad the sze of the teval s fxed oce the teval s selected. So we employ the method of self-adaptve cuve fttg wth weght [] to compute the coeffcets of the fttg cuve because t oly fts the pots o the same smooth cuve ad does ot ft those dscotuous pots ad outles. We defe the cuve fttg eo fucto as follow, E, f (, fˆ(, w(, ( ( whee (, D(,, ad t s mmzed fo computg the coeffceta, a, a w(, s weght fucto, whch descbe elablty of each pot the fttg teval D(,. The weght of the elable pot s cosdeed as, ad the weght of the uelable pot s assg to vey small value. We choose teatve appoach to mpove the weght of evey pot cotuously to elmate the effects of outles. Supposed the coeffcets the tme ae a, a, a, how the coeffcets of the tme a, a, a s computed? Fst we calculate fttg esdual eo ad weght of the tme. ˆ e (, f (, f (, (3 E (, bs w (, b (4 s E (, b s E (, wheew (, Usg (3 ad (4 costatly mpove the weght of evey pot utl fttg esdual eo meet demad. Meawhle, these pots coespodg vey small weght ae cosdeed as outles ad emoved..3. Edge detecto Evey pot ad the pots ts coespodg fttg teval fom a cuve, ad the fo the eghbog pots ( l,, f ( l, ad (,, f (,, two cuves exst, they ae ecoded as ˆ fl (, al a l al, (, L( l, (5 ˆ f (, a a a, (, L(, (6 If al a thesh, the eghbog pots ae depth dscotuous pots; If al a thesh, but al a thesh, the thee s a omal dscotuous pot betwee the eghbog pots. We calculate the pot of tesecto ( c,, f fomed by fˆ l (,. If ( ˆ l,, fl ( l, ( c,, f (7,, fˆ (, ( c,, f, the the left pot s omal dscotuous, o the ght pot s omal dscotuous..4. Edge tegato Usg the method descbed secto. ad secto.3 to pocess X-mage, Y-mge ad Z-mage, we obta the edge maps. They descbe the dscotuty of thee dectos of 3D scee espectvely. We fuse the edge maps to descbe cotou featues of 3D scee. Poceedgs of the Ifomato Vsualzato (IV /6 $. 6 IEEE

3 3. Local egstato algothm Accodg to the pcple of octee, we establsh a seachg stuctue of the cotou featues. Usg mahalaobs dstace, a ogal tasfom s obtaed though matchg the leaf odes betwee two scas, ad the tasfom s efed step by step though ICP utl the best tasfom s obtaed. 3.. Mahalaobs dstace betwee pot sets Mahalaobs dstace s avalable to defe the dstace fom ay pot to a pot set. Compaed wth Eucldea dstace, Mahalaobs dstace descbes ot oly the elatve dstbuto of pot sets, but the ow dstbuto of pot sets [8, 9]. Mahalaobs dstace betwee pot p ad the th pot set g s defed as m( p ( p m C g ( p m (8 T Whee p ( x, y, z ; m s the mea vecto of the N th pot set g, m ; g s pot vecto of N th pot set g ; C g s covaace matx of th pot set g. T C g E[( m ( m ] (9 Mahalaobs dstace betwee two pot sets ae defed as m( m, m ( m m Cg ( m m ( I ode to eep the geealty we emove the coelato of locato ad sze of pot set, matx A fomed by pot set s omalzed. x x x A y y y ( z z z Afte omalzato x x A y y z z x y z x x y y z z Whee x y z x x y y z z ( ( x x ( y y ( z z ( x, y, z s the cete of pot set, s aveage dstace fom pot ( x, y, z 3.. Octee seachg stuctue to the cete the pot set.. The pocess of establshg octee seachg stuctue s the pocess of ecusve subdvso of cotou featues. Befoe establshg octee seachg stuctue, we eed to desgate the theshold codto to cotol subdvso. The theshold codtos ae gve by the followg ways: Deteme whethe each ode cotas pots ae collea, f they ae collea, stop subdvdg. Judge each ode cotas pots ae less tha the Max pot umbe, f less tha, stop subdvdg. We gve the algothm of octee of the cotou featues as follows: Vst all data, deve the smallest cube cotag all pots ad ecod fomato of the cube, establsh oot ode, the push t to the stac ad set t as the cuet ode. Judge the cuet ode meets theshold codtos o ot, f meetg, the cuet ode s pushed out the stac. If the stac s ot ull, the top ode of the stac s set as the cuet ode, ad etu ; f the stac s ull, stop. If the cuet ode does t meet theshold codtos, etu 3. 3 Let the cuet ode dvde equally to 8 subcubes the thee coodates axs decto, push the subcubes stac, add the fomato elated to seveal subodes to cuet ode. Set top ode of the stac s the cuet ode, to Leaf ode matchg Leaf odes of octee cota some cotou featue pots. Accodg smlates betwee a ode of sca A ad evey ode of octee of sca B by Mahalaobs dstace, the coespodg leaf odes ae seached fom top to bottom. The smlates of the two odes s defed as S( m, m (3 m( m, m Whee m( m, m s Mahalaobs dstace betwee two odes. scaa, s leaf ode, f S( m A, m Bl max S( m, m LeapThesh, the leaf ode s A B smla wth leaf ode l of sca B. A leaf ode of sca A may coespod to two o moe tha two leaf odes of sca B, we choose oe pa of leaf odes wth the lagest smlates Optmal egstato Accodg to the metoed appoach, pas of leaf odes ae matched betwee two scas. A ogal tasfom ca be calculated by the cetes of thee pas of leaf odes. If pas of leaf odes ae composed 3 3 accodg to C, we wll get C ogal tasfoms. Accodg to the degee of matchg, we do optmal egstato by the followg two steps. Hee, the degee of matchg s computed accodg to the umbe of matchg pots. The fst step of optmal egstato, cotou featues of two scas ae tasfeed to the same Poceedgs of the Ifomato Vsualzato (IV /6 $. 6 IEEE

4 coodate system by the ogal tasfom, the the degee of matchg s calculated ad the ogal tasfom whch matchg degee s moe tha theshold MacthThesh s ecoded. O the bass of them, usg of ICP algothms, the tasfoms ae mpoved. The secod step of optmal egstato, accodg to the mpoved tasfoms of the fst step, all pots of two scas ae alged to the commo coodate system, the the degee of match s calculates. The mpoved tasfom of the fst step whch matchg degee s moe tha theshold MacthThesh s ecoded. O the bass of the fst step, ICP algothm s executed fo all the pots. Fally, the tasfom whch matchg degee s lagest s selected as the fal tasfom. If matchg degee of the tasfoms ae equal, the aveage dstace of coespodg pots s calculate, the tasfom whch the aveage dstace s the most shot s employed. Dug Optmal egstato pocessg, the value of theshold s 7% of matchg pots of the best tasfom. 4. Global egstato stategy I a typcal scag sesso, tes ad hudeds of age scas must be egsteed. What method do we employ to egste all age scas? We developed a global egstato based o the eaby pcple. Ths method ca solve the dawbacs of sequetal ad smultaeous stateges. Afte all ovelappg age scas ae put to ou system, we fst execute the local egstato, ad the use the eaby pcple to buld a topologcal gaph of global egstato. Oe of scas s chose to be the acho sca S a fom the topologcal gaph, ad all othe scas S ae egsteed wth espect to the acho S a based o the topologcal gaph. The steps of ceatg the topologcal gaph ae showed as follow: Regste all pas of ovelappg scas, compute tasfomato T [ R, t ] ad degee of egstato g( T (t s the umbe of pots that ae matched. Regad the age sca S as a ode, ad egad as coectg weght betwee two odes, the a g( T weghted udected gaph s ceated G V, E. Whee V s ode, E s edge wth weght, ad e E. g( T 3 Based o e E usg MST, ceate g( T MST compute a topologcal gaph GLR. GLR cludes all age scas ad descbes the best egstato path of all age scas. Fgue shows the ceatg pocessg of a topologcal gaph. G LR step step step step3 step4 step5 Fgue :The topologcal gaph of global egstato 5. Results We tested ou methods o scas fom doo scees, outdoo scees ad acet buldgs ad so o. A age sca of outdoo scees clude may omeasued obects ad outles, t s the best way to test the egstato algothm. Fg.3a s the mage of Shaoyua of Peg Uvesty. Fg.3b shows cotou featues, Fg.3c shows the egstato esult of a pa of ovelappg age scas. Fg.3d s the global egstato esult of 5 age scas. We ca see fom the fgues that the egstato algothm poposed by us ca ot oly detect ch cotou featues but also mae may age scas bette togethe to the commo coodate system. The most of doo scees ae moe composed of obects wth smple stuctue, ad less ose ad outles, they ae easly egsteed togethe the shot tme. Fg.4a ad 4b ae the egstato esults of two age scas of the compute house of scetfc fomato cete of Peg Uvesty. Fg.5a ad 5b ae espectvely the egstato esults of two ad thee age scas of the fst oc cave of Yugag gotto. Fg.6 employs the global egstato method poposed ths pape to alg age scas of Ql the fot of offce buldg of Peg Uvesty. Fom these egstato esults, they show: we ca obta pefect egstato esults fom age scas of acet achtectues, ad they test that the egstato method poposed by us s obust ad t ca be used the complex achtectues. 4. Cocluso We have descbed a fully automated method fo the egstato of lage-scale scees. Ou algothm s based o cotou featues that educes complexty of egstato ad solve pactcal poblem of egstato of lage-scale scees, the ma cotbutos of ths pape ae as follows: Use self-adaptve cuve fttg techques to extact cotou featues fom age scas so that egstato algothm s ot oly adapted to the scee composed of smple stuctues, but also adapted to the scees composed of complex stuctues. Poceedgs of the Ifomato Vsualzato (IV /6 $. 6 IEEE

5 (a (b (c (d Fgue3: The egstato esults of Shaoyua of Peg Uvesty (a (b Fgue4: The egstato esults of doo scees (a (b Fgue 5: The egstato esults of Yugag gotto Poceedgs of the Ifomato Vsualzato (IV /6 $. 6 IEEE

6 (a Fgue 6: The egstato esults of Ql the fot of offce buldg of Peg Uvesty. (b Itoduce mahalaobs dstace to descbe the dstbuto law of pots the pot set. 3 Establsh octee seachg stuctue to ot oly povde matchg ut but also speed up matchg. 4 Employ egstato mode fom bottom to up: cotou featues of scees leaf odes all pots of scees, step by step, ad avod fallg to local mma. Refeeces [] Hug Zhao, Ryosue Shbas. A obust method fo egsteg goud based lase age mages of uba outdoo obects. I Photogammetc Egeeg & Remote Sesg,, 67 (: [] Hug Zhao, Ryosue Shbasa. Recostuctg Uba 3D Model usg Vehcle-boe Lase Rage Scaes. I Poc. of 3D Dgtal Imagg ad Modelg,, 49~356. [3] Cya Techologes: [4] Multple Rage Data Set Regstato: edu/~b/poects/multple/ [5] 3D Imagg Seso LMS-Z4: [6] Yamay.S.M, Faag.A.A. Suface sgatues: a oetato depedet fee-fom suface epessetato scheme fo the pupose of obects egstato ad matchg, I Patte Aalyss ad Mache Itellgece, IEEE Tasactos o, 4(8: 5 ~. Acowledgemets The pape s suppoted by Pogam fo Iovatve Reseach Team Uvesty ad Natoal Key Techologes R&D Pogam (4BA8B. [7] T. Padla ad L. Va Gool. Matchg of 3-D cuves usg sem-dffeetal vaats. I 5th Iteatoal Cofeece o Compute Vso, IEEE Compute Socety Pess, Cambdge, MA,995, 39~395. [8] Xua Guoog. The Optmal Chaactestcs of Mahalaobs dstace a featue selecto. I Poc of th teatoal Cofeece Compute ad applcato, Beg: CCF ad Compute Socety of IEEE, 987(6: [9] Zhag Jume, J Shmg ad L Ha. Applcato of vaat Theoy to Geomety-pat Recogto. I Mechacal & electcal egeeg magaze, 999(5: 6~64. [] R.Begev, M.Soucy, H.Gago, ad D. Lauedeau. Towads a geeal mult-vew egstato techque. IEEE Tas. PAMI. 996, 8(5:54~547. [] D. Hube ad M. Hebet. Fully Automatc Regstato of Multple 3D Data Sets, IEEE Compute Socety Woshop o Compute Vso Beyod the Vsble Spectum (CVBVS, Decembe, Poceedgs of the Ifomato Vsualzato (IV /6 $. 6 IEEE