3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS

Transcription

1 3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS George Voelma ad Sader Dijkma Departmet of Geodey Delft Uiverity of Techology The Netherlad KEY WORDS: Buildig recotructio, laer altimetry, Hough traform. ABSTRACT Airbore laer altimetry ha become a very popular techique for the acquiitio of digital elevatio model. The high poit deity that ca be achieved with thi techique eable applicatio of laer data for may other purpoe. Thi paper deal with the cotructio of 3D model of the urba eviromet. A three-dimeioal verio of the well-kow Hough traform i ued for the etractio of plaar face from the irregularly ditributed poit cloud. To upport the 3D recotructio uage i made of available groud pla of the buildig. Two differet trategie are eplored to recotruct buildig model from the detected plaar face ad egmeted groud pla. Wherea the firt trategy trie to detect iterectio lie ad height jump edge, the ecod oe aume that all detected plaar face hould model ome part of the buildig. Eperimet how that the ecod trategy i able to recotruct more buildig ad more detail of thi buildig, but that it ometime lead to additioal part of the model that do ot eit. Whe retricted to buildig with rectagular egmet of the groud pla, the ecod trategy wa able to recotruct 83 buildig out of a dataet with 94 buildig. INTRODUCTION 3D city model become icreaigly popular amog urba plaer ad the telecommuicatio idutry. Aalyi of propagatio of oie ad air pollutio through citie ad etimatio of real etate tae are ome other potetial applicatio of 3D city model. Curretly 3D city model are produced by covetioal aerial photogrammetry or by emi-automated procedure for meauremet i aerial imagery. The high poit deitie of airbore laer caer triggered reearch ito the automated recotructio of 3D buildig model. Thi paper report o our progre i thi area. With the icreaig poit deitie that ca be achieved by moder laer caer, the detectio of plaar roof face i the geerated poit cloud ha become eaier. May laer caer mouted i aeroplae ca owaday achieve poit deitie of up to oe poit per quare meter. Survey with ytem mouted i helicopter have bee coducted with poit deitie of five to te poit per quare meter [Baltavia, 999]. Thee high poit deitie uually reult i a large umber of poit o a igle roof face. By aalyi of the poit cloud thee roof face ca be detected automatically. Due to the overwhelmig evidece provided by the large umber of poit, the detectio of plaar roof face i quite reliable. For the detectio of plaar poit cloud we eteded the well-kow Hough traform to a three dimeioal traformatio [Voelma, 999]. While the orietatio ad height of a roof face ca be etimated accurately, the outlie of a roof face i more difficult to determie. To improve thi part of the 3D buildig model recotructio we make ue of buildig groud pla that are available for may citie. The outlie of the buildig a give i uch groud pla give the precie locatio of the buildig wall. By iterectig the wall with the detected roof plae, ome of the boud of the roof face ca be recotructed. Other boud are to be foud by the iterectio of pair of adjacet roof face ad by the detectio of height jump edge i the poit cloud. The groud pla ot oly upport the accurate locatio of the outer roof face edge. Ofte a groud pla reveal iformatio o the tructure of a buildig [Haala ad Ader, 997, Haala ad Breer, 997]. Whe modellig buildig by cotructive olid geometry, buildig ca be regarded a compoitio of a few compoet with imple roof hape (like flat roof, gable roof ad hip roof). The corer i the buildig outlie of the groud pla ofte give a idicatio o the poitio of thee buildig compoet withi the groud pla. Thu, the groud pla i alo ueful for the accurate locatio of ome of the roof face edge i the iterior of the buildig. The paper preet reult o the etractio of the roof face ad the geeratio of 3D buildig model by combiig the etracted roof face with the groud pla. Sectio two decribe the etractio of the plaar face from the laer data ad the uage of the groud pla for thi purpoe. I the et two ectio two differet trategie for the recotructio of the buildig model are preeted. The firt trategy refie a iitial groud pla egmetatio util every egmet correpod to oly oe plaar face. The ecod trategy tart with a coure 3D model ad refie thi model baed o the aalye of poit cloud that do ot fit well to the coure model. Reult ad a compario of the two trategie are preeted ad dicued i the lat ectio.

2 EXTRACTION OF ROOF PLANES Several algorithm have bee propoed for the egmetatio of rage data [Hoover et al., 996, Geibel ad Stilla, ]. May of thoe algorithm require the computatio of urface ormal vector. Sice thee vector ted to be very oiy i the cae of laer dataet with high poit deitie, we prefer algorithm that do ot require ormal vector. Oe uch algorithm i the Hough traform eteded to 3D [Voelma, 999]. Geibel ad Stilla [] preeted a plit ad merge algorithm that alo how to be uitable for laer data egmetatio. To prevet thi, we plit the dataet ito maller part (figure ) ad apply the Hough traform to the poit of each part eparately (figure 3). By plittig the dataet the chace that a part will cotai may face i dimiihed. For a ueful egmetatio of the dataet we make ue of a egmeted groud pla of the buildig. By etedig the edge of the buildig outlie at the cocave corer a egmetatio i obtaied (figure ). Thi egmetatio ofte ha edge that correpod to the locatio of roof face boud. Thu thee edge are likely to eparate the poit of differet roof face. Thi further reduce the likelihood of fidig may roof face withi a igle egmet.. 3D Hough traform I the claical Hough traform [Hough, 96] a give poit (,y) i a image defie a lie y a + b i the parameter pace with ae for the parameter a ad b. If a image cotai everal poit o a traight lie, the lie of thee poit i the parameter pace will iterect ad the poitio of the iterectio yield the parameter of the lie i the image. Thi priciple ca eaily be eteded to three dimeio. Each poit (,y,) i a laer dataet defie a plae + y y + d i the 3D parameter pace paed by the ae of the parameter, y, ad d, where ad y are the lope i - ad y-directio ad d deote the vertical ditace of the plae to the origi. If a laer dataet cotai poit i a plaar face, the plae of thee poit i the parameter pace will iterect at the poitio that correpod to the lope ad ditace of the plaar face. For the detectio of thi iterectio poit the tadard procedure of amplig the parameter pace ad earchig for the bi with the highet umber of plae ca be ued [Ballard ad Brow, 98]. Figure : Partitioed buildig outlie a overlay o grey value coded height. The Hough traform doe ot check whether the poit that are foud to be i the ame plae ideed make up a cotiuou face. It may a well fid ome cattered poit that are i oe plae by coicidece. To check thi, the TIN of all laer poit i ued. Oly thoe poit of the detected plae are ued that form a coected piece of the TIN of a miimum ie. Poit that are ow aiged to a plaar face are removed from the parameter pace before lookig for the et bet plae.. Uage of partitioed groud pla I the cae of buildig with may roof face the Hough traform may fid puriou plae. Each bi of the parameter pace correpod to a more or le plaar area i the object pace. It may happe that ome arbitrary plaar area cotai more poit tha the area aroud oe of the roof plae. Thi i how i figure. I uch cae wrog plae are detected. Figure : Plaar regio with mot poit doe ot coicide with a roof face. Figure 3: Boud of plaar face detected by the 3D Hough traform withi the partitio. For may buildig the roof face are parallel to oe of the edge of the egmeted groud pla [Haala ad Breer, 997]. Oe ca make ue of thi heuritic to reduce the parameter pace. After projectig all poit iide a egmet oto a vertical plae through a egmet edge, the Hough traform ca agai be doe i D. Figure 4 how a poit cloud of a gable roof buildig with a dorm that i projected oto two perpedicular vertical plae. After performig the Hough traform o both D dataet it will become obviou that the lie foud i the firt projectio correpod to the deired roof face.

3 Figure 4: Poit of a gable roof projected oto two wall plae..3 Growig plaar face A how i figure 3, everal plaar face will be foud i multiple egmet of the groud pla. I ome egmet o plaar face ca be foud, becaue the egmet oly cotai a few poit. To fid better decriptio the plaar face eed to be merged over the boud of the egmet ad, if poible, to be eteded to a few poit that are uclaified util ow. The reult of thi procedure i how i figure 5. For each roof plae oe plaar poit cloud ha bee idetified. The fial determiatio of the plae parameter follow from a leat quare adjutmet uig all poit that are aiged to a plae. A a alterative to growig the plaar face, oe could alo perform a leat quare adjutmet withi each egmet ad merge the plaar face over the egmet uig tatitical tet o the imilarity of the etimated plae parameter. Thi trategy i fater, but ha the diadvatage that uclaified poit are ot coidered for memberhip of a plaar face that wa foud i aother egmet. Figure 5: Boud of plaar face after mergig ad epadig the face detected iide the egmet..4 Leat quare etimatio of plae To etimate accurate plae parameter all poit aiged to a plaar face are ued i a leat quare adjutmet. For the etimatio i D uig the projectio a i figure 4a, the mot imple model would be y I Q d with E σ () with lope ad ditace d a lie parameter ad σ a tadard deviatio of the height meauremet. Thi model, however, igore that the plaimetric coordiate of the laer poit are tochatic too. They uually eve have a higher tadard deviatio. To take thi ito accout the model i liearied to d E with () y I I Q σ σ

4 where the upper ide deote a approimate value. The lope value etimated with () differed up to.3 from the value etimated with (). Aumig σ 5 cm ad σ 9 cm (baed o [Voelma ad Maa, ]), the etimated parameter tadard deviatio are about /5 higher uig the liearied equatio () for lope aroud 35. the gable roof. Sice the locatio of thi edge i very ear to a edge of the groud pla egmet, the height jump edge i aumed to be lightly dilocated ad i ot take ito accout i the further proceig. 3 REFINEMENT OF GROUND PLAN PARTITIONING Ule the umber of poit i a egmet i very mall, oe or more plae will have bee foud by the above procedure. Segmet with oly oe plaar face ca be fully aiged to that plae. By combiig the plaimetric boud of the groud pla egmet with the detected plae, a 3D model for that egmet ca be cotructed. For thoe egmet that cotai poit of multiple plaar face further plittig of the egmet i attempted util oly oe plaar face i left per egmet. A egmet i plit if evidece i foud for the preece of a iterectio lie of two adjacet plaar face or a height jump edge betwee two uch face. 3. Detectio of iterectio lie To detect the iterectio lie, all (o-parallel) pair of plaar face are iterected. A iterectio lie i coidered to be foud if the followig requiremet are met: The iterectio lie i iide the groud pla egmet. The cotour of both plaar face are ear the iterectio lie over ome rage. Thee rage overlap over ome miimum ditace. The eample buildig i the figure ha three gable roof. The detected ridge lie are how i figure 6. They are a little horter tha the actual ridge ice the poit cloud uually do ot eted util the very ed of a roof face. The accuracy of thee recotructed ridge lie i very high, ice it reult from the iterectio of two plae that have bee determied uig may poit (typically > ) [Voelma, 999]. Figure 6: Detected iterectio lie ad height jump edge. 3.3 Splittig ad mergig of egmet The fial tep of cotructig the 3D model of a buildig coit of plittig ad mergig the groud pla egmet util there i a oe-to-oe relatiohip betwee the egmet ad the roof face. Oce a iterectio lie or height jump edge ha bee detected iide a egmet, thi egmet i plit ito two part. For both reultig egmet it i agai evaluated whether there are poibilitie to further plit the egmet. For the eample buildig the groud pla egmetatio reultig after the plittig i how i figure Detectio of height jump lie The detectio of height jump edge i the mot difficult part of the recotructio. The accurate locatio of a height jump edge require a high poit deity. To implify the detectio it i aumed that the height jump edge i parallel to oe of the edge of the groud pla egmet. For each plaar face withi a egmet, hypothee for locatio of height jump edge are geerated baed o the orietatio of the egmet edge ad the etet of the plaar face. If other plaar face eit withi the egmet ad their cotour are ear a hypotheied height jump edge, thi hypothei i accepted. The rage over which the cotour poit are foud ear the height jump edge determie the rage of thi edge. I the middle of the eample buildig there i a clear height jump edge. I two egmet of the groud pla thi edge i detected (figure 6). A little to the right a hort height jump edge i foud. Thi edge i caued by a few poit of the gable roof o the right had ide of thi edge that were preet iide the egmet left of Figure 7: Refied egmetatio after plittig egmet at poitio of iterectio lie ad height jump edge. If o further plittig i poible, all egmet are aiged to a detected plaar face. I ome egmet there till may be poit belogig to differet plaar face. I that cae the face with the larget umber of poit i elected. All adjacet egmet of the groud pla that are aiged to the ame plaar face are merged. Thi reult i the fial partitioig of the groud pla where

5 each egmet correpod to a roof face (figure 8). By combiig thi partitioig with the parameter of the detected plae, the 3D buildig model ca be cotructed (figure 9). perpedicular orietatio, ad two gable roof with perpedicular orietatio. Figure how a buildig with four groud pla egmet. The buildig ha a cropped hip roof with a dormer ad a perpedicular part with aother hip roof. Chooig from the four model, gable roof are foud to be the bet fit for each of the egmet. By aalyig the etimated parameter of the gable roof, it i cocluded that three gable roof have colliear ridge ad eave. The correpodig egmet are merged ad the parameter of the gable roof are re-etimated uig all poit of the three egmet. The iitial model for thi buildig coit of two adjacet gable roof with perpedicular orietatio. Figure 8: Fial partitioig after mergig egmet aiged to the ame plaar face. Figure 9: Recotructed 3D buildig model. 4 REFINEMENT OF AN INITIAL MODEL The trategy decribed above relie o the detectio of iterectio lie ad height jump edge. For thi detectio the preece of poit of two differet plaar face ear the hypotheied lie or edge i required. I particular for mall face thee hypothee ca ofte ot be cofirmed. The reultig uder-egmetatio of the groud pla the lead to a geeraliatio of the buildig model. I order to preerve more detail i the model, aother recotructio trategy ha bee eplored. I thi trategy we tart with a relatively coare 3D buildig model that i derived by fittig hape primitive to the origial egmet of the groud pla. By aalyig the cloud of poit that do ot correpod to thi model, refiemet are etimated. 4. Creatio of a iitial model Baed o the Hough traform a decribed i ectio two, plaar face are detected withi each egmet. Aumig rectagular egmet, hypothee for five differet roof model for the egmet are geerated: flat roof, lated roof with two Figure : Buildig with two hip roof ad a dormer. 4. Aalyi of remaiig poit cloud Thi buildig model i the refied by modellig the poit cloud that do ot fit to the iitial model [Maa, 999]. If oe of the five model fit to a poit cloud a local correctio i made to the iitial model. Mot ofte thi mea a mall object (like a bo modellig a dormer) i put o top of the iitial model. Sometime, a mall part eed to be ubtracted from the iitial model. Thi i the cae, e.g., if a gable roof i corrected to a hip roof. The etet of the additioal model i determied by the boudig bo of the eamied poit cloud. The orietatio of uch a boudig bo i take to be parallel to the boud of the egmet of the groud pla. For the merged top three egmet i figure a gable roof wa aumed a the iitial model. Figure how that four cluter of poit that do ot fit thi model ca be dicered. The left ad right cluter fit bet to the lated roof model ad are ituated below the gable roof model. Coequetly, the gable roof i adapted to a (cropped) hip roof. The top cluter i alo modelled bet by a lated roof. The poit cloud i higher tha the iitial gable roof ad therefore lead to a model for the dormer with a rectagular groud pla. Fially the lower cluter i bet modelled by a gable roof. It i foud that the parameter of thi roof correpod to the gable roof that wa already foud i

6 aother egmet of the groud pla. The parameter of thi gable roof are therefore re-etimated uig the poit of from both egmet. The reultig model i how i figure. therefore fail to further refie the iitial groud pla egmetatio. I ome cae the ecod trategy lead to mall detail that are icorrect. Figure 3 how a icorrect eteio of the gable roof ito the rectagle with a flat roof. Thi eteio wa caued by a few poit of the gable roof that were ituated iide the groud pla egmet of the flat roof due to a mall mialigmet betwee the groud pla ad the laer data. Figure : Cluter of poit that do ot fit the iitial model. Figure 3: Buildig model with recotructed dormer ad chimey ad a icorrect eteio of the gable roof. A dataet of 6 buildig ha bee proceed with the ecod trategy. Twelve buildig did ot meet the aumptio of the method. I mot of thoe cae the groud pla egmetatio did ot yield rectagular egmet which i a retrictio i the curret implemetatio. 83 out of the remaiig 94 buildig were recotructed uccefully (figure 4). The error were motly caued by a iufficiet umber of poit withi a groud pla egmet. Thi i due to the ometime very mall ie of a egmet or bad reflectio propertie of the roof urface [Voelma ad Suveg, ]. To improve thee reult a more global reaoig trategy that icorporate kowledge o the commo hape of buildig eed to be developed. Figure : Recotructed model ad a photograph of the buildig from the ame perpective. 5 RESULTS AND CONCLUSIONS I the paper two trategie for the recotructio of buildig model were decribed. The firt trategy relied o the detectio of iterectio lie ad height jump edge betwee plaar face. The ecod trategy adopted coare iitial model that were refied o the bae of fittig model to poit cloud that did ot correpod to the iitial model. Overall, the latter trategy how a larger umber of recotructed detail. I dataet with a high poit deity (5-6 pt/m ) eve chimey were ofte recotructed. I particular i dataet with a lower poit deity, the ecod trategy lead to better reult, ice a few poit provide eough evidece for the correcte of a model. I uch cae the firt trategy would ofte ot fid ufficiet evidece for the preece of iterectio lie or height jump edge ad Figure 4: Part of the recotructed buildig. The arrow idicate two apparet error i thi area. The poit deity of the dataet wa reduced from 5-6 poit per m to.5-.5 poit per m to tudy the poibility to recotruct the ame buildig from dataet that ca owaday be acquired by laer caer i aeroplae. Obviouly, the amout of detail that ca be recotructed i lower (figure 5). It wa further foud

7 that i more buildig could ot be recotructed. The other 77 buildig were recotructed correctly, be it with le detail. Haala, N. ad C. Breer, 997: Geeratio of 3D city model from airbore laer caig data. Proceedig EARSEL workhop o LIDAR remote eig o lad ad ea, pp. 5-, Talli, Etoia. Hoover, A., Jea-Baptite, G., Jiag, X., Fly, P.J., Buke, H., Goldgof, D.B., Bowyer, K., Eggert, D.W., Fitgibbo, A. ad Fiher, R.B., 996: A eperimetal compario of rage image egmetatio algorithm. IEEE Traactio o Patter Aalyi ad Machie Itelligece 8 (7) : Hough, P.V.C., 96: Method ad Mea for Recogiig Comple Patter. U.S. Patet Maa, H.-G., 999: Cloed Solutio for the Determiatio of Parametric Buildig Model from Ivariat Momet of Airbore Laercaer Data. Iteratioal Archive of Photogrammetry ad Remote Seig, vol. 3, part 3-W5, pp Figure 5: Effect of reducig the poit deity from 5-6 poit per m (top) to poit per m (bottom) o the amout of recotructed detail. ACKNOWLEDGEMENT The FLI-MAP laer data were provided by the Survey Departmet of the Miitry of Traport, Public Work ad Water Maagemet of the Netherlad. The large cale map data (GBKN) wa provided by the Dutch Cadatre. The author thak both orgaiatio for makig thee data available. REFERENCES Ballard, D.H. ad C.M. Brow, 98: Computer Viio. Pretice-Hall, Eglewood Cliff, NJ. Maa, H.-G. ad G. Voelma, 999: Two algorithm for Etractig Buildig Model from Raw Laer Altimetry Data. ISPRS Joural of Photogrammetry ad Remote Seig 54 (-3): Voelma, G., 999: Buildig Recotructio uig Plaar Face i Very High Deity Height Data. Iteratioal Archive of Photogrammetry ad Remote Seig, vol. 3, part 3-W5, pp Voelma, G. ad H.-G. Maa, : Adjutmet ad filterig of raw laer altimetry data. OEEPE workhop o Airbore Laercaig ad Iterferometric SAR for Detailed Digital Elevatio Model, Stockholm, -3 March, p. Voelma, G. ad I. Suveg, : Map baed buildig recotructio from laer data ad image. I: Automatic Etractio of Ma-Made Object from Aerial ad Space Image (III), Swet & Zeitliger Publiher, to appear. Baltavia, E., 999: Airbore laer caig: eitig ytem ad firm ad other reource. ISPRS Joural of Photogrammetry ad Remote Seig, 54 (-3): Dijkma, S.T., : Automatic buildig recotructio from laercaer data ad GBKN data (i Dutch). M.Sc.-thei Delft Uiverity of Techology, 66 p. Geibel, R. ad U. Stilla,. Segmetatio of Laer Altimeter Data for Buildig Recotructio: Differet Procedure ad Compario. Iteratioal Archive of Photogrammetry ad Remote Seig, vol. 33, part B3, pp Haala, N. ad K.-H. Ader, 997: Acquiitio of 3D urba model by aalyi of aerial image, digital urface model ad eitig D buildig iformatio. SPIE Coferece o Itegratig Photogrammetric Techique with Scee Aalyi ad Machie Viio III, SPIE Proceedig vol. 37, pp. -.