RECOGNITION OF COMMON BUILDINGS IN CARTOGRAPHIC FILES

Transcription

1 RECOGITIO OF COMMO BUIIGS I CRTOGRPHIC FIES Ha-We Hsao, Kam W. Wog epatmet of Cvl Egeeg Uvesty of Illos at Ubaa-Champag 5. Mathews ve. Ubaa, Illos 68, US Emal: h-hsao@studets.uuc.edu, -wog@staff.uuc.edu Commsso III, Wog Goup 3 KEY WORS: Recogto, Foue Tasfom, Robust Estmato, Catogaphc BSTRCT To update a poto of a exstg catogaphc database, the commo pactce s to elate the ew data fle to the exstg fle by meas of suvey cotol pots that ae cluded both fles. I the absece of such suvey cotol pots, well-defed pots such as buldg coes ca be used. Ths pape pesets a algothm to pefom ecogto of commo buldgs epeseted as vecto data. The algothm stats wth a Foue-based tal matchg. sequece of valdty checs combed wth obust estmato povdes a complete ecogto of commo buldgs. The two maps may have dffeet scales, dffeet coodate systems, ad o detfyg catogaphc labels. Expemetal esults have demostated the obustess of the algothm. ITROUCTIO Ths pape pesets a algothm fo the automatc updatg of exstg dgtal catogaphc data fles by the ecogto of commo polygoal featues, such as buldgs, the two fles. Cosde, fo example, the two fles gaphcally epeseted Fgues ad. The fle Fgue has a ogal scale of :,5 ad may be cosdeed to be a pat of a achve database fo a ete cty. The fle Fgue has a ogal scale of :5, ad s a C fle that has bee geeated fo the edevelopmet of a eghbohood. Thee ae ecogzable buldgs that ae commo both fles, although small dffeeces may exst the detals of the coespodg buldgs the two fles. The C fle s moe cuet tme. It ca be see that ew buldgs have bee added, a old buldg has bee emoved, ad some old buldgs have bee expaded. Thee s o suvey cotol pots aywhee wth the aea. The pupose of the algothm to be peseted hee s to automatcally updatg the database epeseted by Fgue wth cotets of the C fle. The pocess cossts of two mao steps: ) ecogto of commo buldg coes the two fles, ad ) megg of the two data fles. Ths pape wll focus o the algothm developed fo the ecogto of commo buldgs. The algothm of megg wll be the subect of a futue pape. Fo the pupose of geealty, the algothm assumes that the two data fles cota oly stgs of coodates (x, y) epesetg each buldg, wth o detfyg fomato fo ay of the buldgs. The stg of coodates fo a buldg must fom a closed polygo, but the buldg coes ca be aaged ethe clocwse o coute-clocwse decto. The statg pot fo the sequece of coe pots epesetg a buldg ca be completely adom, ad be dffeet betwee the two fles. s s the case commoly ecouteed pactce, the same buldg each of the two C fles may also be cossted of dffeet umbe of coes due to catogaphc geealzato o tepetato. The two fles ca also have dffeet scales, ad dffeet coodate systems. THE GORITHM Shape aalyss s a mpotat phase of patte ecogto, ad may techques ca be foud the lteatue elatg to ths ssue: B-sples (Ja, 989), autoegessve models (Ja, 989; Kauppe et al., 995), Foue descptos (Zah ad Roses, 97; Rchad ad Hemam, 974; Pesoo ad Fu, 977; Wallace ad Wtz, 98; Pofftt, 98; Ja, 989; bte et al., 99; Ja ad xo, 995; Kauppe et al., 995; Rothe et al., 996;), etc. I geeal, the Foue-based methods usg dffeet models fo bouday epesetato povde supeo pefomace most cases (Kauppe et al., 995). The algothm to be peseted ths pape s also based o the use of Foue tasfom fo tal matchg. The ovato of the algothm les the developmet of multple levels of checg pocedues wthout dect omalzato of otato ad statg pot to solve the specfc poblems elatg to the ecogto of commo buldgs catogaphc data fles. The algothm cossts of the followg ma steps:. Reaagemet of all data pots wth each polygo to a couteclocwse sequece.. Compute the Foue tasfom of each polygo.. Matchg of polygos the two fles by cosscoelato. v. Pefom thee sepaate, but ceasgly goous, valdty checs of matched polygos: a. by sze-dstace atos; b. by cofomal tasfomato wth obust estmato; ad c. by geometc ovelay afte coodate tasfomato. These steps wll each be dscussed detals the followg paagaphs. 3 COUTERCOCKWISE SEQUECE The sequece of pots wth each polygo the two data fles s checed fst by calculatg the coss poduct c of each pot. c () V V VV +

2 Fgue. chve fle Fgue. ew fle coute s ceased by oe f c s postve, ad vce vesa. These pots ae the eaaged ufomly to a couteclocwse decto f the coute s egatve. The sg of the coss poduct c of each pot, defed as ξ, s saved fo use as a attbute late computato. l b V V V V + + V V fo > ad l (3) 4 FOURIER TRSFORM OF POYGOS The ext step s to compute the Foue tasfom to extact useful attbutes fo each polygo. Two dffeet pocedues fo computg the Foue tasfom of polygos ae commoly used: cumulatve agula fucto (Zah ad Roses, 97), ad complex coodate fucto (Rchad ad Hemam, 974; Pesoo ad Fu, 977; Wallace ad Wtz, 98; Pofftt, 98; Ja, 989). The latte was selected ths study fo ts smplcty. Equato s the fomula fo computg the Foue tasfom of a polygo (Pesoo ad Fu, 977). The (b - - b ) tem s actually the vecto of cuvatue of a coe, ad wll also be saved as a attbute fo pot. The tem, ow as the cetod of a polygo, ca ot be computed usg the above equato, ad s obtaed depedetly by computg the cete of mass of the polygo. whee ( π) ( b b ) exp( πl ) () et be the aea of tagle,,+ fomed by vetces V, V, V + ; ad let C be the cete of tagle,,+. The cete of mass (Psley et al., 989),.e. the tem, would be C (4) lthough the tem wll be set to zeo the ext step, t s cosdeed as a attbute of a polygo ad s saved fo use late steps. Sce two coespodg buldgs may dffe posto, oetato, sze, statg pot, ad a ceta degee of dssmlaty caused by dffeet map scales, the computed Foue descptos have to be omalzed po to coss coelato. Ule the omalzato algothms poposed the lteatue (Zah ad Roses, 97; Rchad ad Hemam, 974; Wallace ad Wtz, 98; Pofftt, 98; bte et al., 99; Ja ad xo, 995; Rothe et al., 996), oly the emovals of tasla-

3 to ad scale factos ae cosdeed. The fact fo ths study s that maps ae usually two-dmesoal coodate system wth aspect ato close to oe ad wthout shea effect oe decto. The cofomal tasfomato s thus easoable fo the mappg fucto betwee two maps. Theefoe, thee s o eed to fd vaats ude the affe tasfomato wth the shea o mo effect. The dffeeces oetato, statg pot, ad umbe of pots would ot be omalzed ths step. Istead, the ecogto poblem wll be solved late fom a dffeet aspect usg the chaactestc of the cofomal tasfomato. ssgg zeo to the tem omalzes the taslato facto. To omalze the sze facto of a buldg, the coodates of the sequece of pots ae dvded by the stadad devato of the bouday wth espect to ts cetod. lteatvely, to omalze the sze fequecy doma s to dvde the Foue descptos by the squae oot of the summato of the powe spectum (Pofftt, 98). Theefoe, the ew Foue descptos fo a buldg ae obtaed as * whee σ σ fo (5) M S pq max c (8) g If thee wee m buldgs the achve fle, ad buldgs the ew fle, thee would be m possble combatos of matches. The smlaty measues fo the m possble matches ae computed to costuct the smlaty table fo all possble combatos of matchg buldgs. pa of buldgs s cosdeed a match f ts smlaty measue, S pq, s the maxmum both alog the ow ad alog the colum the smlaty table. et I epeset the collecto of t matched pas, the fo a matched pa P pq the set: P pq I, whee 4 f m max g ( S ) max( S ) q p (9) p m ad q ew Fle fte omalzato of taslato ad sze, the cete of buldg les o the og ad the om of the ew Foue descptos s equal to oe. 5 chve Fle * (6) The paamete σ epesets the stadad devato of the bouday of a polygo wth espect to ts cetod, ad wll be used late fo pefomg valdty chec. σ d ew Fle σ 5 MTCHIG BY CROSS CORRETIO The method of coss coelato s used to detfy the most lely matches of coespodg buldgs the two fles. et p epesets the Foue descptos of a buldg the achve fle, ad q epesets the Foue descptos of a buldg the ew fle; whee M-; -; ad M >. The coss coelato s computed as c g M u ( πg M) p q exp (7) M exp ( πg M) whee g, M-. The coss coelato s equvalet to pefom the dscete Foue tasfom of u, whch s the multplcato of p ad the complex cougate of q (Rchad, 974), ad u u M- ae padded zeo (Pofftt, 98). The smlaty measue, S pq, of the match betwee two buldgs s the computed as σ d chve Fle σ Fgue 3. Matched buldg pas 6 SIZE-ISTCE RTIO CHECK The collecto I of matched pas may cota msmatched pas, because oly the shape facto s tae to accout dectly by the above coss coelato of spatal fequeces. Two coespodg buldgs mght ot be matched f the effect of map geealzato s sgfcat. O the othe had, two etely dffeet buldgs mght be matched as a pa whe the omalzed Foue descptos ae vey smla. These cases happeed fequetly whe two maps have vey dffeet map scales. The valdty of the matched pas obtaed fom coss coelato s fst checed by compag the elatve sze ad sepaato dstaces betwee two matched pas. Cosde, fo example, the two matched pas Fgue 3. s a esult of coss coelato, buldgs os. ad 5 the achve fle ae matched to buldgs os. 4 ad espec-

4 tvely the ew fle. If the two pas ae coectly matched, the the elatve sze of the two pas should dffe by o moe tha %. Smlaly, the sepaato dstaces betwee the cetods of the two buldgs should also ot dffe by moe tha %. s show Fgue 3, let σ ad σ deote the sze attbute, epeseted as the adus of a ccle, of buldgs the achve ad ew fles espectvely. Futhemoe, let d ad d epeset the dstaces betwee the cetods of buldgs ad the achve ad ew fles espectvely. The, the two pas ae cosdeed coect matches f ad oly f the followg ctea s satsfed: t m max whee σ σ σ σ, σ d <. σ ad d d d () The σ value s saved dug the omalzato of shape (see Secto 4 above), whle the cetod to calculate the dstace betwee buldgs s ept dug the Foue tasfom of polygo. The cetod computed usg the cete of mass of a polygo s moe sestve to the effect of map geealzato tha the oe obtaed by tegato of the bouday of a polygo o by aveagg coodates of pots. ccodgly, the computed value fom the above equato fo a coect pa should be vey close to zeo. efg the theshold s cucal to flte out msmatched pas. It s ot expected that the dffeece of dstaces betwee two buldgs o two maps would exceed % of the actual dstace. The obustess of the szedstace ato chec les ts ease to dstgush the coect pas fom the msmatched oes. It should be oted that ths pocedue eques that thee be at least two coectly matched pas the set I. the two fles. y coectly matched pa s detfed by the lage esduals the coespodg cetod coodates the least squaes soluto. The followg weghtg fucto (Che ad ee, 99) fo the coodates has bee foud to be effectve flteg out the coectly matched pas: v w exp.5 σˆ v exp.5 σˆ whe v whe v aftewads < σˆ fo teatos,, 3 > σˆ fo teato 4 ad () lthough the sze-dstace chec ca usually flte out most msmatched pas, ths step s ot edudat at all. I addto to povdg a addtoal chec o the match esults, ths step also povdes pelmay values fo the coodate tasfomato paametes fo the ew fle. 8 GEOMETRIC OVERY FTER COORITE TRSFORMTIO fte coodates of the ew fle have bee tasfomed to the same system as the achve fle, valdty of the matched polygos ca be checed by meas of geometc ovelay. Eve assumg some small eos the computed tasfomato paametes, two commo buldgs fom the two fles should be ovelappg each othe the commo coodate system. t the ed of ths step, the tas of ecogzg the commo buldgs fom the two fles s complete. 9 MERGIG OF IFORMTIO FROM TWO FIE The pocess of megg fomato fom the ew fle to the achve fle volves the followg steps: chve ew Fgue 4. ocato of matched buldg cetods 7 COFORM TRSFORMTIO WITH ROBUST ESTIMTIO secod valdty chec of the emag matched pas s coducted by pefomg a cofomal tasfomato of the ew fle to the achve fle. Icoect matches ae detfed the pocess by obust estmato. Fgue 4 shows the cetod locatos of the emag matched pas the two fles. The cofomal tasfomato paametes (scale facto, otato, ad two taslatos) betwee the two coodate systems s computed usg the cetods of the coespodg buldgs. Idetfy commo coe pots of the matched buldgs fom the achve ad ew fles.. Compute moe accuate values fo the cofomal tasfomato paametes by usg the coodates of the coe pots.. Tasfom the pot coodates of the ew fle to the coodate system of the achve fle. Estmated stadad eos of the tasfomed coodates ae also computed by meas of eo popagato. v. Pots fom both fles ae combed ad meged to fom closed polygos. v. Fally, catogaphc edeg s pefomed to squae the buldg coes. It s beyod the scope of ths pape to deal to the detals of the above steps. Show Fgue 5 s the fle esulted fom megg the two fles epeseted Fgues ad. Sce the ew map s of lage scale ad moe ecet, t s expected that the meged map s gaphcally detcal to the ew map. COCUSIOS

5 algothm has bee successfully developed fo the automatc ecogto of commo polygoal featues fom two catogaphc data fles, ad to mege the fomato cotets of the two fles. The algothm has bee foud to be obust, ad computatoally effcet. The ete pocess of ecogzg commo buldgs ad megg the two fles Fgues ad above was accomplshed automatcally less tha mutes of tme usg a 66-MHz destop pesoal compute. lthough the algothm s teded fo the automatc updatg of exstg catogaphc databases, the algothm fo ecogto of polygoal featues should also have potetal applcatos the matchg of commo featues steeo pas of photogaphs. [bte, 99] bte, K., W.E. Syde, H. Buhadt, G. Hzge, 99. pplcato of ffe-ivaat Foue escptos to Recogto of 3- Obects. IEEE Tasactos o Patte alyss ad Mache Itellgece, (7), pp [Che, 99] Che,.C.,.H. ee, 99. Pogessve Geeato of Cotol Famewos fo Image Regstato. Photogammetc Egeeg ad Remote Sesg, 58(9), pp [Ja, 989] Ja,.K., 989. Fudametals of gtal Image Pocessg. Petce-Hall, pp [Ja, 995] Ja, X., M.S. xo, 995. Extedg the Featue Vecto fo utomatc Face Recogto. IEEE Tasactos o Patte alyss ad Mache Itellgece, 7(), pp [Kauppe, 995] Kauppe, H., T. Seppäe, M. Petäe, 995. Expemetal Compaso of utoegessve ad Foue-Based escptos Shape Classfcato. IEEE Tasactos o Patte alyss ad Mache Itellgece, 7(), pp. -7. [Pesoo, 977] Pesoo, E., K.S. Fu, 977. Shape scmato Usg Foue escptos. IEEE Tasactos o Systems, Ma, ad Cybeetcs, 7(3), pp [Psley, 989] Psley, S.P., T.G. Gegoe, J.. Smth, 989. The Mea ad Vaace of ea Estmates Computed a c-ode Geogaphc Ifomato System. Photogammetc Egeeg ad Remote Sesg, 55(), pp [Pofftt, 98] Pofftt,., 98. omalzato of scete Plaa Obects. Patte Recogto, 5(3), pp [Rchad, 974] Rchad, C.W., H. Hemam, 974. Idetfcato of Thee-mesoal Obects Usg Foue escptos of the Bouday Cuve. IEEE Tasactos o Systems, Ma, ad Cybeetcs, 4(4), pp [Rothe, 996] Rothe, I., H. Süsse, K. Voss, 996. The Method of omalzato to eteme Ivaats. IEEE Tasactos o Patte alyss ad Mache Itellgece, 8(4), pp [Wallace, 98] Wallace, T.P., P..Wtz, 98. Effcet Thee-mesoal caft Recogto lgothm Usg omalzed Foue escptos. Compute Gaphcs ad Image Pocessg, 3, pp [Zah, 97] Zah, C.T., R.Z.Roses, 97. Foue escptos fo Plae Closed Cuves. IEEE Tasactos o Computes, (3), pp Fgue 5. Megg esult REFERECES