GIS remote sensing image 3D reconstruction with optimization of affine invariant

Transcription

1 GIS remote sesg mage D recostructo wth optmzato of affe varat Jg Lu Cvl Egeerg ad Archtecture Departmet of Archtecture, Xame Uversty of Techology, Xame 604, Fuja, Cha Zhuagwe Huag Cvl Egeerg ad Archtecture Departmet of Archtecture, Xame Uversty of Techology, Xame 604, Fuja, Cha Abstract Accordg to the low effect of preset D scee recostructo algorthm recostructo of GIS remote sesg mage D scee, ths paper proposes a GIS remote sesg mage D modelg algorthm based o cultural surface model ad the mproved RANSAC algorthm. Frst, use the Bezer curve to fttg curve of cultural, ad reduce the sum of the dstaces betwee pots to the correspodg pot o the curve. Ad the use the pot cloud characterstcs of pot pars, ad a pot cloud data set as referece, to solve the two pot cloud data sets betwee the parameters of geometrc trasformato matrx, ad elmate false matchg pots based o the RANSAC algorthm, to estmate the trasformato matrx. Fally by affe varat to costrat the sample extracted by RANSAC algorthm, to reduce the sample quatty, thereby creasg the speed of RANSAC regstrato algorthm. Smulato expermets show that the proposed GIS remote sesg mage D modelg algorthm based o the culture surface model ad mproved RANSAC algorthm has very good modelg effect, ad the mproved RANSAC algorthm effcecy has bee greatly mproved. Key words: CULTURAL SURFACE, RANSAC ALGORITHM, THE BLOCK BEZIER CURVE, POINT CLOUD DATA SETS, AFFINE INVARIANT Itroducto As quckeg the urbazato, may ctes are developg the real estate dustry. Real estate developers also have sprug up, the umber of ew buldg costructo ad developmet also has creased dramatcally. Prevous real estate marketg model has bee uable to meet the demad of real estate developers ad property buyers the formato age, such as: the producto of sad table model, floor door model fgure dsplay, meda propagada ad developers betwee the example that decorate, etc. []. At 80 Metallurgcal ad Mg Idustry, 05, No. 4

2 preset, the tradtoal real estate marketg mode wth the developmet of D vsualzato techology s gradually be replaced, combg applcato of D vsualzato techology ad desg cocept gradually become a ew marketg mode choce amog developers []. Based o the mprovemet of D vsualzato techology to make up for the adequacy of tradtoal real estate marketg mode, users the use of D vsualzato techology shows the scearo ca be free to browse, query, aalyss, ts mmersve dstct vsual effect, ca speed up the real estate sales []. D modelg s the research hotspot ad dffculty the feld of D GIS, may scholars at home ad abroad to do a lot of work ths feld. Requcha put forward that modelg algorthm based o etty s a kd of method ofte used the feld of the computer aded desg (CAD), t s a smlar to the actual machg process modelg methods, such as cuttg, drllg, etc. [4]. Hllyard ad Brad take the geometrc ettes as physcal framework, whe the frst frame Free State, wth loose coectos. Pots ad edges respectvely correspodg to the framework of odes ad coectg rod, ad sze formato s the frmware for restrag ad fxg framework [5]. Molear put forward D vector formal data structure model, the model s a smple exteso of D topologcal data model, four kds of basc geometrc elemets such as ts ode, segmet, border ad surface as the basc types of graphcs part, the relatoshp betwee geometrc elemets ad object type s determed by the fve prcples [6]. Robert study o buldg the world, ad extract the threedmesoal structure of polyhedro (such as the cube ad prsm, etc.) from the target dgtal mage wrtg computer programs, ad the shape of the object ad the mutual spatal relatos are descrbed, hs work started to uderstad the real world of D scee of mache vso for study [7]. KIM et al. to extract automatcally from the cty mage buldg has carred o the related research [8]. HUERTAS et al. combe the shadow ad perspectve geometry theory to do the relevat research [9]. Quadratc sple curve s studed for the recostructo of the terpolato algorthm by Mcallster [0]. Pecewse cubc curve terpolato s dscussed the applcato of curve recostructo by Frtsch. The recostructo of the surface, the Bezer surface s the typcal represetatve of ths aspect research whch s proposed by Bezer. The method beg equato s used to drect the target modelg, ca accurately express some space etty, eeds less memory ad computg speed, ad get the uque results []. Zhag Fa ad others study the sgle stato groud laser scag pot cloud modelg algorthm uder the stereographc projecto. Zheg Dehua ad others study ellpsod modelg algorthm uder dfferet space closed plae []. Accordg to the eed of D scee recostructo, ths paper puts forward a D modelg algorthm based o the culture surface model ad mproved RANSAC algorthm. Cloud feature extractos of costructo pots based o the culture surface The formato of each pot the D model s the coordate ad the color of D pots, cultural curve s composed of pot. For such as show a cultural curve of curve equato f( xyz,, ) = 0, for ts startg pot as pot, ed pot as pot, ts mathematcal model ca be expressed as a collecto of all the pots o the curve: C = { pot( coord, color) f ( coord. x, coord. y, coord. z) = 0 () pot. x pot( coord ). x pot. x} () Fgure. Cultural layer surface Feature extracto of cultural curve s the process of expressg cultural curve equato, amely for curve fttg of kow pots. I ths paper, use pecewse the Bezer curve to cultural curve fttg. For a seres of pots V0, V, V,... for fttg, f we wat to wth a Bezer curve Qt () to ft, eed to compute the dstace betwee fttg pot to the correspodg pot o the Bezer curve, f the dstace s wth a certa rage ε, the thk that fttg work s doe. For a gve pot V, the dstace betwee t ad the correspodg pot o the curve s dst = V Q( t). Therefore, the fttg purpose s Metallurgcal ad Mg Idustry, 05, No. 4 8

3 desged to mmze the dstaces betwee fttg pots to the correspodg pot o the curve. We use a fucto S as a stadard for measurg, S s defed as equato (). [ ( )] () = S= d Qu I the equato, d s the coordate ( xy, ) of the fttg pots, u s parameter values assocated wth d. For the followg dervato process, we have the followg defto: ) P 0 ad P s the frst ad the last cotrol pot, the cocluso shows they are the frst ad the last oe pot of fttg pots; ) t ad t are respectvely the ut taget vector of pots P 0 ad P ; ) The other two cotrol pots P ad P respectvely: P = α t + P0 (4) P = α t+ P (5) For a fxed ed cotrol pots of the Bezer curve, ca chage the coordates of the secod ad thrd cotrol pots to chage the shape of the Bezer curve, ad thus the problem ca be coverted to fdg a α ad α to get the mmum S, thus has the followg two equatos: S = 0 (6) α S = 0 (7) α Equato () s take to equato (6) ad equato (7) ad calculated, fally we ca get equato (8) ad (9). ( A,) α + ( A, A, ) α = = = ( d ( PB 0 0 ( u) + PB 0 ( u) + PB ( u) + PB ( u))) A, = ( A, A, ) α + ( A,) α = = = ( d ( PB 0 0 ( u) + PB 0 ( u) + PB ( u) + PB ( u))) A, = I the equatos, A, j tb j j( u), j, (8) (9) = =. Make the equato (8) ad (9) sample, we get equato (0) ad (). c,α + c,α = X (0) c,α + c,α = X () The represet by matrx, amely c, c, α X c, c =, α X () c, c, Suppose that ς = = ( C C), c, c, X τ =, the accordg to the Cramer rule, the X soluto of the equato s as follows. det( τ C) α = () det( C C) det( C τ ) α = (4) det( C C) So we fd the α ad α wth elgble. Accordg to the above algorthm, carres o the smulato test, a remote sesg mage as a example, the extracto algorthm of costructo characterstcs pot cloud based o cultural surface for the costructo of a pot cloud, the results are as follows: Fgure. Pot cloud archtectural feature extracto results It s see from the result, the extracto result ca be very good expresso for the buldgs, s coducve to the structure of the D recostructo. Pot cloud matchg of RANSAC algorthm based o the affe varat optmzed Geometrc trasformato of pot cloud data Accordg to cultural curve feature extracto to get pot cloud data sets, make sure the feature pots of two pot cloud data sets wth regstrato, use these feature pots ad a pot cloud data sets for referece, to solve the parameters of geometrc trasformato matrx R betwee the two pot cloud data sets, aother pot cloud data sets s ormalzed to the stadard coordate system wth the referece pot cloud data sets. A gve projecto trasformato betwee two pot cloud data sets as follows: x r0 r r6 x y r r4 r 7 y = (5) r r5 r 8 8 Metallurgcal ad Mg Idustry, 05, No. 4

4 I the equato, ( x, y ) s the pots of referece pot cloud data sets, ( x, y ) s the pots correspodg to ( x, y ) o target pot cloud data sets. Here called the trasformato matrx as R, R has eght degrees of freedom, the theory of choce at least 4 dagoal pots ca estmate the R [7].By equato (5) we ca get equato (6). rx 0 + ry + r6 x = rx + ry 5 + r8 (6) rx + r4y + r7 y = rx + ry 5 + r8 Get 4 eght depedet lear equatos from dagoal pots, ad get the R through soluto of equatos, so we put the pots o the target pot cloud data sets oeto-oe correspodece to ormalze to the referece pot cloud data sets the coordate system. Made a prelmary ormalzed crosscorrelato matchg, there are a lot of false matchg pots, at ths tme use RANSAC algorthm to elmate false matchg pots, estmate the trasformato matrx. RANSAC make full use of all the tal matchg pots, accordg to a permssble error ca make all match be dvded to sde ad outsde, takg advatage of the accurate characterstcs of teror pot data for parameter estmato, thus the accurate matchg pots are exclud. The specfc steps of homography matrx estmated by RANSAC are as follows: Frst of all, the curret best estmate teror pot umber T s set to 0. ) Repeated N tmes of radom samplg. Matrx R matchg pot estmate eed 4 pars, to determe a proper samplg umber N, to esure that the sample of 4 pars matchg pots are wth a hgh eough probablty. P s represet to the probablty, commoly takes 95%. Set P as the probablty to ay a par of matchg pots s teror pot, ω = P s the probablty of ay matchg pots for outsde. So the samplg to 4 N N tmes are: ( P ) = P, the log( P) N =. 4 log( ( ω) ) ) Accordg to 4 pars matchg pots to calculate the trasformato matrx R ; ) Calculate each match pot after matrx trasformato to the correspodg matchg pot Eucldea dstace l( x, Rx) ; 4) Set a threshold value G, the matchg pot meet l < G as the teror pot; 5) Comparg the curret teror pots umber wth T, f t s greater, the R ad the curret pot set as the curret best estmate, update T ; f t s equal, the select the lower regstrato as the curret best estmate. The remag requred umber of teratos of dyamc estmate s N at the same tme, f the curret umber of teratos to R, the retaed the curret teror pot set ad stop the terato; 6) All of the matchg pot the curret pot set reestmate R by the DLT algorthm. The speed optmzato of RANSAC algorthm Affe varat s used to restra the sample whch extracted by RANSAC algorthm, ca effectvely reduce the amout of sample, so that ca accelerate the rate of RANSAC regstrato algorthm. Assume that, the proporto of the overlap betwee the source data set S ad target data set T s ω data set. I order to coveet, overlap rato estmato s drectly gve. I Eucldea dstace, compute the legth l max betwee two pots data whch are the furthest data pots, whch ca draw coplae four-pot costrats of the legth of the dstace betwee the pot: dω = l max ω (7) Radomly select a pots S the source data set S, ad radomly look for aother S, to get equato (9): dω σ S S d ω + σ (9) Ad meet equato (0) at same tme. m(, ) (0) Ths meas that makes the dstace legth meet the costrat codtos at the same tme, ad should as far as possble betwee the vertcal. Through the former three pots, we compute the vector: + = ( S S) + ( S S) () From ths we ca get pot S : S = S + + () Metallurgcal ad Mg Idustry, 05, No. 4 8

5 Ad fd the pot S 4 close to S source data set S, ad meet the equato (). ( 4 ) m ( ) () Ths codto makes the pots S4 s the same plae wth { S, S, S, S 4} as much as possble. Through the above way, ca choose four coplaar{ S, S, S, S 4}, so affe varats s formed betwee them as follows: es r = (4) es4 r = (5) 4 To do so s to costra the shape of quadrlateral as square as possble, ad to avod quadrlateral ueve legth, whch ca lead to elarge error ad affect the match result. Although we wat to costra quadrlateral for the square, but the actual cases ca t completely appears as a square, so pot e s t mdpot, varats r ad r ot completely equal, for cosstet coplaar wo't mpact for four sets. I addto, ths method eeds oly two pots o repeat radom, to fd the rght pots S ad S to meet the codtos, ad therefore the complexty of the selecto s O ( ). Kow accordg to the prevous aalyss, ca make use of teratve selecto cosstet coplae four-pot, do estmate for Eucldea trasform H c, ad choose the estmate trasformato H wth the best degree of cosstecy betwee the source set S ad target set T ad uder the estmated trasformato. Uder the estmated trasformato H c, the degree of cosstecy betwee source data S ad target data set T, usg meet uder the certa error threshold δ, cosstet pot umber s for measurg. Besdes, also costrat correspodg pots the drecto of the surface, make them wth a certa rage of devato. Assume that the source oe pot as S S, the correspodg pots the target s T T, a costraed by the followg equato: T H S δ (6) c T Hc S T Hc S cos (7) θ δ I the equato, s the ormal vector of the pot, ad θ δ s the error threshold of the pot of vew. The smulato of algorthm To verfy the effectveess of the proposed mproved algorthm, smulato expermets o t. Takg a resdetal area as a example, based o the GIS mages, the proposed D modelg algorthm based o the culture surface model ad the mproved RANSAC algorthm for the costructo of D recostructo. The result s show as follows Fgure. GIS remote sesg mages of resdetal area Fgure 4. D modelg dagram of resdetal area The, the mproved RANSAC algorthm of speed the smulato, the results are as follows: 84 Metallurgcal ad Mg Idustry, 05, No. 4

6 Fgure 5. Computato speed smulato of mproved RANSAC algorthm Cocluso See from the smulato results, that the proposed D modelg algorthm based o the culture surface model ad the mproved RANSAC algorthm has better performace of D modelg, ad the computg speed of the mproved RANSAC algorthm s better tha the orgal algorthm. Refereces. Lg Yag (04) Buldgs Recostructo Based o Geeralzed Pot Photogrammetry. Scece of Surveyg ad Mappg, 9, p.p Hachao Ra (04) Itellget evacuato gudace system modelg ad expermet buldg fres. Fre Scece ad Techology,, p.p Qgwe Zhu (04) Applcato ad Research of Buldg Modelg Based o D Laser Scaer. Geography ad Geo- Iformato Scece, 0, p.p Ruju Lu (04) GIS-based Threedmesoal Buldg Modelg Method wth Closed Ehacemet. Joural of System Smulato, 6(9), p.p Zhke Qa (04) Modelg ad Smulato Aalyss of Idoor Buldg Polluto Dffuso Degree ad Area. Bullet of Scece ad Techology, 0, p.p Xafeg Zhag (04) D Modelg of Urba Buldgs ad Trees ad Its Applcato Buldg-scale Solar Eergy Potetal Mappg. Joural of Basc Scece ad Egeerg,, p.p Huxa Zhag (04) Study o buldg modelg based o -D laser scag techology. Laser Techology, 8, p.p Wel Dg (04) Automatc modelg of archtecture ad frared smulato based o Ope Flght API. Laser & Ifrared, 44, p.p Fagja Wag (04) Aalyss o Dgtzato ad D-recostructo of Large Buldg based o Terrestral Laser Scag Data. Remote Sesg Techology ad Applcato, 9, p.p Feg Xue (0) Rapd Ahu Styled Archtecture Modelg Based o Sub- Topology Geerato. Joural of Graphcs, 4, p.p Mgmg Su (0) A Method of Establshg D Model of Buldgs Based o Sgle Image Measuremet across Multple Plaes. Geography ad Geo-Iformato Scece, 9, p.p Ru WANG (0) Realzato Method of the BIM-based MgQg Acet Archtecture Model System. Joural of Doghua Uversty, 9, p.p Metallurgcal ad Mg Idustry, 05, No. 4 85