3D Object Localization using Superquadric Models with a Kinect Sensor

Transcription

1 D Objet Lolton ung Superqur Moel th Knet Senor Il Afnev Nolo' B Lu Bglvo Mrolno De Ceo Mehtron Deprtment Deprtment of Mehnl n Struturl Engneerng DIMS Unvert of rento rento Itl {l.fnev mrolno.eeo}@untn.t Unvert of Pov Pov Itl

2 Abtrt h pper preent metho for D objet reognton n poe etmton b ung D enor lke Mrooft Knet. he poe etmte b robut let qure fttng of D pont th SuperQur SQ moel of the erhe objet. he oluton verfe b evlutng the mthng ore beteen the SQ objet moel n D rel t pture b D enor. h metho n be ue for D objet reognton lolton n reontruton. Keor: Superqur D enor Knet RANSAC fttng D objet lolton.. INRODUCION he tk of D objet reognton n poe etmton from untruture D rel t th ung uperqur moel n be olve fferent. Some uthor propoe to ue metho of probblt poe etmton th herrhl RANSAC erh []. o etet the l-lfe objet the ue the votng of orte qult-of-ft rter be on rnkng proeure n rnke votng proe hen the moel hpothee re elete. here nother metho of reoverng n objet b uperqur moel th the reover-n-elet prgm [6]. or th purpoe the uthor fll rnge mge th et of ee mll SQ moel n then nree thee ee ung groth terton pproh th follong eleton of the utble moel. In ton the metho erbe n the pper [6] nlue lo the to tge votng heme eletng relevnt uperqur moel ung let men error n etmton rter. A fr lot of the l-lfe objet hve nvrble truture hh n be moele pror e propoe to ue RANSACbe moel-fttng tehnque th ompote uperqur moel to reogne omple objet retl urng one tge of RANSAC-moel-fttng proeure. h pproh e for pplng n ft for moel fttng lulton. he log of D objet lolton lgorthm repreente b the blok-heme n gure. pont reltve to the groun re entfe th RANSAC plnefttng tehnque n then remove from t et. he net tep ont n fttng uperqur moel of the objet of nteret th D t. SQ moel permt to erbe omple-geometr objet th fe prmeter n generte mple mnmton funton to etmte n objet poe. o ope th meurement noe n outler the objet poe etmte b RANSACbe moel-fttng tehnque.. D OBJEC LOCALIZAION ALGORIHM. About D Senor Objet n D t he propoe metho of D objet reognton n poe etmton n ork th fferent D enor: RGB-D Re Green Blue - Depth mer nnng rngefner me-offlght O mer et. In our e e pple lo-ot RGB-D mer Mrooft Knet [7] th Nol Burru oftre RGBDemo-.. []. he lbrton ettng of the oftre llo to orret the rnge mge torton n to qure D rt of n objet n metrl oornte tem th the orgn t Knet D epth enor. Although the etrte D t of n objet o lle lou of pont h the nformton bout poton n RGB olor of ever vble pont e re nterete onl n ther -oornte. A orkblt of the metho ll be emontrte b the reognton of omple objet Cube-Clner gure. he lou of pont of th objet hon n gure left. gure : Imge of the objet Cube-Clner pture b Knet RGB mer left n Knet D epth enor fter mutul proeng th the mge of RGB mer rght. gure : Blok-heme of D objet lolton lgorthm. he objet poe etmton trt th preproeng of lou of pont pture b D enor. In th preproeng tge the gure : Clou of pont of the objet Cube-Clner pture b Knet D epth enor before groun removng left n fter rght.

3 . RANSAC lgorthm. We ue RANSAC "RANom SAmple Conenu" lgorthm both for Preproeng n Moel ttng tge of D objet lolton lgorthm. o remn the b onept of RANSAC lgorthm the peuooe of RANSAC lgorthm preente n gure. he number of terton performe b RANSAC the prmeter k n be etermne from the follong formul [8]: log p k nler log n here p the probblt ere for hoong t let one mple free from outler n mot of pplton: p.99 number of pont requre to ft the moel. Algorthm RANSAC fttngfn tfn t rl % - tet n of n obervton. % fttngfn - funton tht ft moel to t from. % tfn - funton to hek tne from moel to. % - mn number of t requre to ft the moel M. % t - tne threhol beteen tpont n moel. % rl - number of terton performe b lgorthm. ter : % ount of terton betm : % the bet moel nler : % umultor for nler ore : % mount of nler p :.99 % probblt to tke mple thout outler hle k > ter % rnoml elete j vlue from t n j : rnom n % moel prmeter hh ftte to j M : fttngfn j for ll from n f tfnm n < t nl k : en f en for % mount of nler m : lengthnl m % the tet to hek ho goo the moel f m > ore ore : m % mount of nler nler : nl % nler betm : M % the bet moel log p k en f nrement ter f ter > rl brek en f en hle return betm nler nler log n gure : Peuooe of RANSAC lgorthm [8]. he ue of RANSAC uge epen on orret hoong the moel. he ttempt of reognton or ner eprtel n the lou of pont of thee to objet ee gure rght ll be fle beue of bg mount of outler. ht h e propoe to ue ompote objet moel for RANSAC fttng.. Preproeng: groun removng. he preproeng elmnte the groun plne from D t orng to the metho erbe b Peter Kove []. he RANSAC-be oftre robutl ft plne to D t pont. h RANSAC t Plne lgorthm erbe b the peuooe gure preente pell to ompre th the peuooe of RANSAC Moel ttng lgorthm ee gure 8. Algorthm RANSACIPLANE t % - tet n of n obervton. % t - tne threhol beteen tpont n plne. % mnmum No of pont neee to ft plne. % fttngfn - funton to efne plne b pont from. funton fttngfn P % t pont from t n % tfn - funton to hek tne from moel to. funton tfn P n n : length n % mount of obervton : eron % rr of tne vlue % P efne three pont of plne P [ P P P ] % Unt norml vetor N P P P P N P P P gure : Peuooe of RANSACIPLANE lgorthm [].. Superqur objet moel. for ll from n for k : % k orrepon to oornte P N en for en for return k k k rl % number of terton funton RANSAC fttngfn tfn t rl return P nler he eplt equton of uperqur hh uull ue for SQ repreentton n vulton []: gnumoη oη gnumoω oω gnumoη oη gnumnω nω gnumnη nη

4 here - uperqur tem oornte prmeter of objet lng prmeter of objet hpe η ω pherl oornte. π / η π / π ω π. he objet uner nvetgton ont of to uperqur Cube n Clner lng n hpe prmeter of hh re: - for Cube:. m.. - for Clner:..7 m.. he objet repreente n metrl uperqur oornte tem gure 6. he tne beteen enter of to. Superqur ner SQ moellng llo lo repreentng ome geometrl hrtert of the objet lke urfe norml n urvture n loe form. h nformton n be eplote to entf moel frmeork n poton of ege n further nvetgton.. RANSAC moel fttng. he log of RANSAC moel fttng lgorthm eplne b peuoooe ee gure 8. We re fttng moel erbe b the uperqur mplt equton to D Knet t of knon objet trtng th RANSAC-be objet erh to fn poe hpothe.e. 6 vrble: ngle of rotton n trnlton oornte of SQ entre n the orl oornte tem. Eh RANSAC mple lulton trte b pkng et of rnom pont 6 pont fttng the SQ moel to th rnom tet b mnmng n ne-oute funton of tne to SQ urfe pplng the rut-regon lgorthm or Levenberg-Mrqurt lgorthm n nonlner let-qure mnmton metho n evlutng nler b omprng the tne beteen D pont n SQ moel th gne threhol. o pee up the fttng proe the poton of ntl trtng pont of mnmton erhng n orl oornte n be hoen n the enter of grvt of ll t pont. he uge of uperqur llo to reover n objet n untruture lou of pont of D t thout prelmnr t egmentton. he vntge of reoverng the D objet b RANSAC-moel-fttng lgorthm th uperqur n ung the lmte number of D t pont nepenentl f the belong to ege n orner of the objet or not. he mnmton proe th rut-regon or Levenberg-Mrqurt lgorthm tble thout reunnt omplet n tme onumng. he gure 7 ho the reult of fttng b the lgorthm. gure 6: he objet Cube-Clner multe b Superqur. he objet poe moelng n be epree th the follong rotton n trnlton equene:. rnlton of enter of SQ long oornte.. Rotton mong loke.. Rotton mong loke.. Rotton mong loke.. rnlton of enter of SQ ner on tne long. he rotton mtr for the R CUBE : o n o n o n n o R n o n o he trnformton mtr for the n the ner re: R gure 7: he reult of fttng the KINEC rt of the objet Cube-Clner b multe Superqur.

5 gure 8: Peuooe of RANSAC-Moel-ttng lgorthm.. RESULS he gure 7 ho the orkblt of the RANSAC-be moel-fttng tehnque th ompote uperqur moel gure 6 of omple objet preente n lou of pont gure rght. or the preente emple the mount of nler bout 6% from 67 pont of D rt. he lgorthm of RANSAC moel fttng rell ft: for the objet Cube- Clner t neee bout terton to fn oluton for the omple objet poe etmton. he lgorthm h been evelope n MALAB. he RGB-D nformton obtne th Mrooft Knet eve n then proee offlne.. CONCLUSION he propoe RANSAC-be metho of uperqur moel fttng to the omple objet preente n D lou of pont t gve robut mple n ft erh of n objet. he poe etmton tehnque erbe h been tete th the multple objet of mple geometr ner gvng enourgng reult.. REERENCES [] Begelbuer G. n Vne M. Effent D Objet Deteton b ttng Superqur to Rnge Imge Dt for Robot' Objet Mnpulton. IEEE Conf. Pro.. ICRA-7. P [] Burru Nol. Knet oftre RGBDemo [] Jkl A. Leonr A. Soln. Segmentton n Reover of Superqur. Computtonl mgng n von Kluer Dorreht. [] Kove Peter. RANSAC oftre n MALAB. -8..e.u.eu.u/~pk/reerh/mtlbfn/. [] Leonr A. Jkl A. Soln. Superqur for Segmentng n Moelng Rnge Dt. IEEE Conf. Pro.. PAMI- 9. P DOI:.9/ [6] o L. Ctelln U. uello A. n Murno V. D out mge egmentton b RANSAC-be pproh. CteSeerX. P DOI: [7] Wkpe. Knet. [8] Wkpe.RANSAC. Algorthm RANSACMODELIING t % - tet n of n obervton hh re vetor of % oornte n orl oornte tem. % t - tne threhol beteen tpont n SQ. 6 % mnmum No of pont neee to ft SQ. t - % threhol for n objet ft to mm t t % threhol for objet n ner. % fttngfn - funton to efne SQ b pont from. funton fttngfn et. % ntl vlue of vrble et prmeter - of SQ n ner. ner for ll from n o n n o o n n o o n n o R R [ ] mn n en for lulte ung for n mn return % tfn - funton to hek tne from SQ to. funton tfn for ll from n % rr of tne vlue en for return rl % number of terton funton RANSAC fttngfn tfn t rl return nler

6 6. AKNOLEDGMENS h ork of Il Afnev upporte b the grnt of EU\P7-Mre Cure-COUND - rentno poto progrm -. he uthor re ver grteful to ollegue from Mehtron ep. nmel Alberto orner n Mtt vernn for ther help n upport of D t quton About the uthor Il Afnev pot-o t Unvert of rento Deprtment of Mehnl n Struturl Engneerng DIMS Mehtron Deprtment. H ontt eml l.fnev@untn.t. Nolo' B Ph.D. tuent t Unvert of Pov. H ontt eml nolob@lbero.t. Lu Bglvo PhD/reerher t Unvert of rento Dep. of Mehnl n Struturl Engneerng DIMS Mehtron Deprtment. H ontt eml lu.bglvo@ng.untn.t. Mrolno De Ceo n ote profeor t Unvert of rento Dep. of Mehnl n Struturl Engneerng DIMS. Mehtron Dep. H eml mrolno.eeo@untn.t.