Remote Sensing ISSN

Transcription

1 Remoe Ses ; do:0.3390/rs30874 Arcle OPEN ACCESS Remoe Sesg ISSN Comprehesve Ulo of Temporl d Spl Dom Ouler Deeco Mehods for Moble Terresrl LDAR D Mchel Leslr * J-guo Wg d Box Hu Deprme of Erh d Spce Scece Yor Uversy 4700 Keele Sree Toroo ON M3J P3 Cd; E-Mls: jgwg@yoru.c J.W.; box@yoru.c B.H. Idusrl d 3D Imgg Deprme Opech Icorpored 300 Ierchge Wy Vugh ON L4K 5Z8 Cd * Auhor o whom correspodece should be ddressed; E-Ml: mel@opech.c; Tel.: Receved: 5 Jue 0; revsed form: 9 July 0 / Acceped: 8 Augus 0 / Publshed: 6 Augus 0 Absrc: Terresrl LDAR provdes my dscples wh effecve d effce mes of producg relsc hree-dmesol models of rel world objecs. Wh he dve of moble erresrl LDAR hs bly hs bee expded o clude he rpd colleco of hree-dmesol models of lrge urb scees. For ll s usefuless does hve drwbcs. Oe of he mjor problems fced by he LDAR dusry ody s he uomc removl of oulyg d pos from LDAR po clouds. Ths pper dscusses he developme d combed mplemeo of wo mehods of performg ouler deeco georefereced po clouds. These mehods mde use of he rw d vlble from mos me-of-flgh moble erresrl LDAR scers boh he emporl d spl doms. The frs mehod volved movg fxed ervl smooher derved from he well-ow poso velocy ccelero Klm Fler. The secod mehod fed qudrc curved surfce o secos of LDAR d. The combed use of hese roues s dscussed hrough exmples wh rel LDAR d. Keywords: ouler deeco; moble erresrl LDAR; curved surfce fg; Klm Fler

2 Remoe Ses Iroduco LDAR Lgh Deeco d Rgg s ool whch llows for he fs d effce cpure of hree-dmesol spl formo from rel world rges. Ths bly hs llowed boh erresrl bsed d rbore LDAR o be used vrey of pplcos []. Ul recely erresrl bsed me of flgh LDAR hs bee releged o sory rpod mous wh comprvely low scg speeds 0000 pos per secod whe compred o rbore LDAR sysems pos per secod. Wh he dve of moble erresrl LDAR hs s o loger he cse. Terresrl bsed scees c ow be colleced fser h ever frsly becuse hey re beg colleced from movg plform d secodly becuse colleco speed hs grely cresed pos per secod. Ths crese he umber of erresrl bsed d pos colleced durg survey mes h greer d greer mous of d re beg produced fser. To complce mers due o he fc h he scers re ow mmersed he scee beg sced sed of flyg hgh bove he geomery coed hese mssve d fles s more complex h hose ecouered prevously. Ths mes flerg of he d hrder h prevously ecouered bu eve more ecessry. Specfclly deecg d elmg erroeously colleced pos or oulers becomes crcl. Smply sed ouler s po whch dffers from s eghbors or eghborhood sgfcly [3]. The deermo of wh he erm sgfcly mes s of course up o he dvdul user of he d. Oulers LDAR d occur due o vrey of resos. Some of hese resos such s boudres of occluso surfce reflecce d mul-ph refleco re descrbed [4]. To hs ls c be dded movg objecs whch pss hrough he sc re fser h hey c be cpured d prcule mer such s sow r dus ec. he r whch reflec he lser eergy. Severl sreges exs for delg wh hese oulers [4-9]. They c be clssfed s uvre sgle vrble mulvre mulple vrble prmerc ssc bsed d o-prmerc o-ssc bsed mehods [5]. The o-prmerc mehods c furher be broe dow o dsce-bsed deph-bsed desy-bsed d cluserg echques [578]. Despe hs lrge mou of reserch o ouler deeco correcly fdg oulers spl d rems vexg problem. Mos of he sreges lsed bove fl whe cofroed wh obscles such s surfce dscoues poor sscl dsrbuos d vryg locl deses wh he LDAR po cloud [4]. Improvg ouler deeco for LDAR requres he developme of lgorhms whch me use of s much of he d herely oupu LDAR po clouds s s prccl. Ths cludes usg he precse mgs vlble from me-of-flgh LDAR sysems rw polr coorde observos clculed Cres coordes d he esy d f possble. Oce developed hese lgorhms employg dffere deeco sreges c be combed o mprove overll deeco resuls. I hs sudy wo dffere lgorhms oe he emporl dom Movg Fxed Iervl Smooher d he oher he spl dom Curved Surfce Fg were developed d uled ovel wy for comprehesve ouler deeco rel moble erresrl LDAR d. The lgorhm he emporl dom deecs oulers by esg he dfferece bewee he compued coordes of po d predco of hese vlues bsed o he surroudg d. The predced vlues were obed hrough modfed verso of he movg fxed ervl smooher derved from he poso velocy d ccelero PVA verso of he Klm Fler [0]. Ulo of he precse mgs vlble from LDAR eher moble or sc me-of-flgh PVA Klm Fler for ouler

3 Remoe Ses deeco s ew cocep o lerure. The secod lgorhm uses bes-f qudrc curved-surfce o splly mesure ech po he cloud d compre o he pos s eghborhood. Ther performce ws umerclly suded boh dvdully d dem. Whle qudrc curved surfce fg s o ew lerure [-5] he sequel use of he spl dom lgorhm fer he emporl dom lgorhm s ew de d wll provde for overll beer resul.. Movg Fxed Iervl Smooher MFIS.. The MFIS Algorhm Gve dscree me seres K of couous me sgl wh her sdrd devos K d he ssoced precse mgs K secod order polyoml of c be used o model he me seres. By usg rdom vrble x o deoe he se of me s he secod order polyoml ws gve s follows: x & & x & x& & x = x x x = & x = & x 3 where he process ose s o cluded d he mesureme equo ws: = x Δ 4 where Δ ws he whe ose wh ero expeco d vrce of. The fler lgorhm bsed o Equo s clled he PVA fler poso rcg pplcos d lso clled he α-β-γ fler f s me vr [6]. The proposed movg fxed-ervl smooher ws developed o he bss of Equos 4 h esme he ses for me s usg he mesuremes over specfed wdow Fgure. Fgure. The Fxed Iervl Smooher. Wh he mesuremes K K he ubsed ler smooher ws derved bsed o he prcple of mml vrce. The smoohed soluo for he ses ws gve by [0].

4 Remoe Ses x = = ˆ 5 b x = = ˆ& 6 c x = = ˆ& & 7 wh her vrces = = x 8 = = x b & 9 = = x c & & 0 where { } 3 = λ λ λ { } 3 b = μ μ μ { } 3 c = η η η = = = = = = = = = = η μ λ η μ λ η μ λ 4 wh =. By rerrgg Equo 5 oe c predc he po : = = = 0 p 5 Usg he mesureme d predced vlue p he dfferece p = ws compued for he purpose of ouler deeco. The vrce of hs dfferece s s follows: = = = 0 6 Accordgly he sdrded dfferece ws ssumed o be ormlly dsrbued s: 0 ~ N 7

5 Remoe Ses uder he Null hypohess H 0 : = 0 gs he lerve hypohess H : 0. A me seres ws vesged where he poso of ech po exmple po cloud ws predced hrough he use of ppropre ervl d he ssc es ws performed. Oulers were defed hrough he use of Equo 7 s he predcor... Ouler Deeco Tme Dom I heory d from rog prsm moble erresrl LDAR c be regrded s se of dscree observos from sgle couous le of d. I prcce dscree observos provded by ll moble erresrl sysems clude rw gle-rge mesuremes whch were djused by he clbro model d used o compue he locl es orh up or x y coordes. Ths mes h we were provded wh choce of rw gle-rge djused gle-rge or coordes whe exrcg dscree observos from he oupu d. Mos mporly becuse of he ure of moble erresrl LDAR d ech dscree observo whchever s chose ws pred wh ccure mesmp dcg whe he observo ws mde. Ulg he vlble formo MFIS requres h movg wdow be creed o exrc smll smples of he po cloud for lyss. Ths wdow would cere roud ech dscree observo ur d use he d mmedely precedg he observo s well s he d mmedely succeedg he observo o clcule predced vlue. Comprg hs predced vlue wh he observed vlue llows oulyg d o be defed d removed from he LDAR d. Fgure shows sech of ypcl wdow of d h mgh be exrced from po cloud d how he dsce bewee he observed mesureme M d he predced mesureme P ws used o defy pos whch le ousde her eghborhood. Fgure. Tme seres of pos used o geere predcos P for mesured pos M. The movg fxed ervl predco recoges he fc h he po cloud c be reed s seres of les of po d. Formg wdows ou of hese les of d requres cre sce y sgfc gp he d hs he poel o produce erroeous predcos Fgure 3. As he gp show Fgure 3 ws llowed o crese he lelhood h he predced po P flls close o he rue poso decresed. Oce he predced mesureme hs sryed from he rue vlue y comprso bewee he mesured vlue d he predced vlue ws megless.

6 Remoe Ses Fgure 3. Tme seres of pos wh pprecble gp bewee wo eghborg pos. As he gp creses he lelhood h he predced mesureme P represes he rue vlue decreses. I prcce gps cused by occlusos reflecos d/or drop-ou redgs effecvely segmeed he couous le of d o smller secos. I ddo sce sgfc poro of y erresrl LDAR sc s lely o clude poros of he sy umerous LDAR pos were expeced o be mssg from he po cloud. These mssg shos effecvely segme he couous le beg followed by he scer s opcs o mulple smller le segmes. Treg hese smller le segmes s depede ees llowed us o pply he PVA fler o ech of hese subse les from he po cloud. Allowces hd o be mde for les shorer h he wdow se d he wdow se hd o be djused o ccommode pos he sr d ed of ech le. Gre cre ws lso e whe erpreg he es resuls for gve po. If ouler s cluded wdow of d he he lelhood h he predced po P flls close o he rue poso ws g decresed. Oe wy o couer hs possble scero ws o form he sme d seco o hree wdows 0 0 d. Compug d esg he predced pos P P P 3 s show Equo 7 we were ble o coclude h f oe of he hree predced pos pss he he observed mesureme M psses d ws o reed s ouler. Ths sregy effecvely dels wh he suo where more h oe ouler exsed gve wdow. Oulers whch occurred eher mmedely before he observed mesureme M or mmedely fer he observed mesureme M he dscree me seres dd o cuse flse deeco o occur. Whe oulers exsed boh mmedely before he observed mesureme M d mmedely fer he observed mesureme M flse deeco sll lely occurred. 3. Curved Surfce Fg CSF 3.. The CSF Algorhm The geerc model of qudrc curved-surfce ws gve by f L 0 x y = x y 3 4 x y 5 x 6 y 7 x 8 y 9 0 = 0 8 where x y s he coorde of po o he surfce d j j = K 0 re he prmeers. Due o he mbguy he surfce deermo roduced by he prmeer 0 ws ecessry o cosr he e prmeers by

7 Remoe Ses C = = 9 Gve he mesuremes x y of po wh s 3x3 vrce mrx D d he pproxme 0 0 vlues K of he e prmeers oe obs he lered form of Equo 8 s where The vlues 0 x y A v B w = 0 0 K K K vx v y v K K K T K K K x y K K K x y x y x y x y w 0 F 0 x y v = A = B = 3 = K 0 4 Equo represe he prl dervves of Equo 8 wh respec o he gve mesuremes of po. Uder he ssumpo h ll of he mesureme pos re o correled o ech oher oe defes { v v v } v = A v = x x y y 5 o cree equvle sgle mesureme o he mesured hree coorde compoes of po so h Equo 5 ws smplfed o for = K. v B w = 6 As c be see he combo of he lered form of Equos 8 9 d 6 s sdrd prmerc djusme model wh cosr. There s o eed o provde furher del for s soluo. For more dels refer o [7]. Due o he lelhood h oe or more oulers my creep o he po cloud smple beg used o form he polyoml surfce ws good de o provde ssc chec o he goodess-of-f for ech clculed surfce. By comprg he poseror vrce wh he pror vrce we produced such ssc whch follows he Ch-Squred dsrbuo s show Equo 7: V T P LL 0 V χ ~ 0 I order o es f po s poel ouler wo dffere es sscs c be cosruced. Whe po ws cluded he polyoml surfce fg he Tu dsrbuo [8] ws used o es he resdul of po s show Equo 8 es ssc. v T = ~ τ 0 8 ˆ 0 qv V where v ws he resdul of po ˆ 0 ws he poseror vrce of u wegh d ws he cofcor of v. The Tu es ws used es ssc due o he fc h v d ˆ 0 vrbles. qv V 7 re deped

8 Remoe Ses Alervely whe po ws o cluded he polyoml surfce fg he Sude dsrbuo ws used o es he dscrepcy bewee po d he surfce s show Equo 9 es ssc. where deermed d T w = ~ 0 9 w w ws compued by pluggg po o Equo 8 fer he surfce prmeers hve bee w ws he esmed sdrd devo of w. Usg he specfed pch se d surroudg ech dvdul po exmple po cloud ws used o cree curved surfce. The surfces were vlded usg Equo 7 d oulers were splly deeced usg Equo 9 s he predcor. 3.. Ouler Deeco he Spl Dom Vewg he LDAR d s srcly spl ey he relve poso of po wh respec o s eghbors ws used o defy oulers. Coducg serch roud ech po po cloud represeve smple of eghborg pos ws obed. Ths represeve smple ws used o form surfce. Comprg hese pos o he surfce oulers were defed by her spl sepro from he foremeoed surfce. Ths cocep s llusred Fgure 4. Fgure 4. Polyoml surfce pch he mmede eghborhood of he po beg esed. The qudrc curved-surfce fg lgorhm geeres smll surfce pches he eghborhood of ech po Fgure 4. Ths s ouler deecor he spl dom whch reles o he ssumpo h he pos mmedely djce o ouler wll hemselves le o he surfce d o be oulers s well. The umber of pos o use he polyoml pch fg ws vrble h eeds o be deermed. O oe hd les 0 pos re requred o derve he bes f surfce. O he oher hd he lrger he umber of coordes used he greer he probbly h oher oulers wll be corpored o he clculo of he surfce Fgure 5. I fc whe dscussg LDAR he codos whch cuse ouler wll lso grely crese he lelhood h oher oulers le close by. Therefore cre hd o be e whe seg pch se. The es ssc gve Equo 7 by gvg us mesure of he f of he surfce o he d pch ws used s d o deermg wheher oulers re cluded wh he seleced pch d.

9 Remoe Ses Fgure 5. Polyoml surfce pch geered usg d seco cog oulyg pos. Blue les dce oulers used o compue he surfce. The Red le dces he po beg esed s ouler. 4. Tess d Resuls 4.. The Lyx Moble Mpper: Hrdwre d Sofwre MFIS d CSF were esed usg prs of wo d ses colleced wh he Lyx Moble Mpper. The Lyx Moble Mpper cossed of wo LDAR sesors wo clbred pssve mgg cmers d he Applx POS LV 40 durg d colleco. Ths sysem s desged o collec rch survey-grde LDAR d mge d from vehcle movg rffc speeds. For ech es se clbro of he Applx POS sysem ws ccomplshed mmedely before he d collec. GAMS GPS muh mesureme subsysem prmeers for he Applx POS sysem were deermed he dy of he d colleco o esure ccurcy. For ech es re he d secos used esg were seleced from he sme d used o deerme he LDAR sysem boresgh vlues. The sysem lever rms d boresgh vlues were obed usg he LDAR mufcurer s recommeded procedure. Processg he rw POS d proceeded usg he sofwre pcge POSPAC. The resul of hs processg ws SBET Smoohed Bes Esmed Trjecory fle. Ths SBET fle ws he used cojuco wh he boresgh vlues prevously obed o process he rw LDAR d. Ths ws ccomplshed usg he sofwre pcge Dshmp. The processed LDAR d ws oupu o ASCII form. 4.. Descrpo of D Four secos of Lyx po clouds A B C d D show Fgures 6 d 7 were seleced for esg. Tble gves specfcs bou he coes of hese po clouds. Tble. Specfcos for po clouds used lgorhm esg. Po Cloud A B C D Tol No. of Pos Tol No. of Oulers Tol % of Pos Whch re Oulers

10 Remoe Ses D wh Smple Geomery Po cloud A ws obed o seco of sphl from geerc prg lo over whch mulple drve psses were performed. Po cloud B ws colleced dr lo where mulple psses were lso performed. Po cloud A coed umerous oulers wo lrge groups wh oher oulers spred hroughou he d. As show Tble he oulers mde up 0.30% of he ol po cloud. Ths d ws colleced o dy where he sphl ws we bu he emperure ws jus bove 0 Celsus. The prevlg cold we codos cused codeso from he vehcle s exhus ppe o combe wh vryg hgh d low esy reurs from he sdg pools of wer. Ths cused mulple lser reflecos o be recorded bove he sphl surfce. I cors po cloud B ws colleced lumber yrd wh upved rough fshed mosly ve cly drvg re h hd bee ped d grooved by he pssge of hevy vehcles. The mbe emperure durg he collec ws bou 5 Celsus d he groud surfce ws dry. These codos produced po cloud wh comprvely few oulers 0.06% from Tble. My of he oulers whch dd exs hs d se were wh cemeers of he groud surfce. I hs lso bee observed h severl of he oulers hs po cloud were colleced from dffere poso h he groud surfce d herefore le ou of emporl seres wh much of he d. Fgure 6. Po clouds of smple geomery e from wo sepre prg los used durg esg of he wo ouler lgorhms prevously descrbed. Po cloud A cos umerous oulers evely dsrbued bove sphl surfce; b Po cloud B cos oulers dsrbued evely cross bre sol surfce. b

11 Remoe Ses D wh Complex Geomery Po cloud C ws e from he sme d se s po cloud A. A wo secod seco of he vehcle rjecory ws soled d ll he LDAR d colleced durg h me ws exrced o form po cloud C. Smlrly po cloud D ws e from he sme d se s po cloud B. Ag wo secod seco of he vehcle rjecory ws soled d ll LDAR d colleced durg h me ws exrced o form po cloud D. Po cloud C cos complex scee cludg pr of buldg wh wdows crs sphl rod sdewl curb wo smll rees bushes d pr of url feld. As Tble dces he umber of oulers po cloud C comprse bou.09% of he d. Po cloud D cos oher complex scee cludg pr of buldg wh wdows overhed wres bre erh drvg surfce d bre erh moud. Ule po cloud C po cloud D cos o vegeo d s such he umber of pos h c be clssfed s oulers s much lower 0.0% of he d Tble. Fgure 7. Po clouds of complex geomery e from wo sepre prg los used durg esg of he wo ouler lgorhms prevously descrbed. Po cloud C cos umerous oulers log wh buldg wll sdewl curb rod feld d vegeo; b Po cloud D cos oulers log wh buldg wll overhed wres bre sol surfce d sol moud. b

12 Remoe Ses Alyss of Ouler Deeco Uly Rel D Boh of he lgorhms descrbed Secos d 3 were mplemeed uder Mcrosof Vsul C 6.0. To esure h he roue ws worg s expeced d o ssess he effecveess of he roue relsc d le of d ws exrced from po cloud A Fgure 8. Fgure 8 shows le of d wh oe of he pos lyg fr ou of spl poso from he res. The lbels Sr of Iervl d Ed of Iervl gve dco of he order whch he pos were colleced. Those pos colored gree were colleced before he ouler po d hose pos colored red were colleced fer he ouler po. Fgure 8. The movg fxed ervl smoohg mehod ppled o seco of moble erresrl LDAR po cloud colleced wh he Lyx Moble Mpper. As wh he movg fxed ervl smooher qudrc polyoml surfce fg ws used o seco of po cloud B Fgure 9. As before hs ws doe o esure h he roue ws worg s expeced d o ssess he effecveess of he roue relsc d. The resuls re llusred Fgure 8. Selecg pch se of 00 pos roud he po Fgure 8 defed s Ouler Po polyoml surfce ws clculed. Compug he shores dsce bewee 'Ouler Po' d he surfce we fd h he po les 0.95 m from he surfce. Geerg he sscs descrbed Seco. we fd h he surfce does f he d well bu he po s fr ousde he llowble devo from he surfce. Loog cross seco of he surfce d d Fgure 9 he devos of he pos roud he clculed surfce become cler. The devo of he po lbeled Ouler Po s obvously fr greer h he devo of y oher po.

13 Remoe Ses Fgure 9. Seco of moble erresrl LDAR po cloud colleced wh he Lyx Moble Mpper. Objec s beg vewed from he Souh Resuls As prevously meoed Seco. he oupu from he moble erresrl LDAR llowed for rw gle-rge mesuremes gle-rge mesuremes djused by he sysem clbro formo d/or coorde vlues o be pu o he MFIS lgorhm s he dscree observos. Durg esg ll hree opos were red wh d of boh smple d complex geomery however he resuls obed from he rw gle-rge d were umpressve d hey were excluded from hs seco. Severl rls were coduced o fd he opmum wdow se for MFIS ech po cloud. Tble gves he resuls of he bes rl rug he MFIS lgorhm usg he LDAR rge vlues fer hey hd bee djused for he scer s cos rge offse vlue d he dvdul rge correcos for vryg esy reurs. Tble 3 gves he resuls of he bes rl rug he MFIS lgorhm usg he oupu esg orhg d up coordes. Beg h wo es sscs were derved for he CSF roue oe requrg he po beg esed o be cluded he d used o cree he surfce pch Equo 8 d oe requrg he po beg esed o be excluded from he d used o cree he surfce pch Equo 9 boh sceros were esed. Severl rls were coduced o fd he opmum pch se for CSF ech po cloud for boh es ssc Equo 8 d es ssc Equo 9. The resuls of he bes rl from ess coduced usg po clouds A B C d D re gve Tble 4 for es ssc d Tble 5 for es ssc.

14 Remoe Ses Tble. Resuls from rls coduced usg djused LDAR rges he Movg Fxed Iervl Smooher MFIS o po clouds A B C d D. Po Cloud A B C D Wdow Se pos No. of Oulers Idefed No. of No-Oulers Idefed Flse Idefco No. of Oulers Mssed % of Oulers Idefed % of Po Cloud Idefed % of Po Cloud Idefed Icorrecly Flse Idefco Re Tble 3. Resuls from rls coduced usg XYZ coordes he Movg Fxed Iervl Smooher MFIS o po clouds A B C d D. Po Cloud A B C D Wdow Se pos No. of Oulers Idefed No. of No-Oulers Idefed Flse Idefco No. of Oulers Mssed % of Oulers Idefed % of Po Cloud Idefed % of Po Cloud Idefed Icorrecly Flse Idefco Re Tble 4. Resuls from rls coduced usg Qudrc Polyoml Surfce Fg CSF o po clouds A B C d D usg es ssc Equo 8. Po Cloud A B C D Pch Se pos No. of Oulers Idefed No. of No-Oulers Idefed Flse Idefco No. of Oulers Mssed % of Oulers Idefed % of Po Cloud Idefed % of Po Cloud Idefed Icorrecly Flse Idefco Re Tble 5. Resuls from rls coduced usg Qudrc Polyoml Surfce Fg CSF o po clouds A B C d D usg es ssc Equo 9. Po Cloud A B C D Pch Se pos No. of Oulers Idefed No. of No-Oulers Idefed Flse Idefco No. of Oulers Mssed % of Oulers Idefed % of Po Cloud Idefed % of Po Cloud Idefed Icorrecly Flse Idefco Re <0.0 <

15 Remoe Ses The combo of he MFIS d CSF mehods ws performed where he reduced po cloud produced by he MFIS mehod ws he lyed wh he CSF mehod. Ths combed MFIS/CSF roue ws performed usg he esg orhg up coorde verso of he MFIS mehod d he es ssc verso of he CSF mehod. The resuls for hs es coduced usg d srps A B C d D re gve Tble 6. Tble 6. Resuls from rls coduced usg he Movg Fxed Iervl Smooher MFIS precedg Qudrc Polyoml Surfce Fg CSF o po clouds A B C d D. Po Cloud A B C D MFIS Wdow Se pos CSF Pch Se pos No. of Oulers Idefed No. of No-Oulers Idefed Flse Idefco No. of Oulers Mssed % of Oulers Idefed % of Po Cloud Idefed % of Po Cloud Idefed Icorrecly Flse Idefco Re As furher corol o he resuls po clouds A B C d D were mpored o he Polywors IMSurvey module d he bul- ouler deeco roue ws used. Ths ouler roue s precursor o he wrp mesh fuco used he creo of rgulr rregulr ewor TIN models. The ouler roue Polywors requred us o se vlues for he mxmum po o po dsce d he mxmum cluser se. Severl emps were mde o opme hese pus o he commercl roue. The resuls of he bes rl usg he Polywors sofwre re summred Tble 7. Tble 7. Resuls from rls coduced usg Polywors IMSurvey s Verso.0.30 Rejec Oulers roue o po clouds A B C d D. Po Cloud A B C D Mx Spo Spce Mesured m M Spo Spce Mesured m Mx Po-o-Po Dsce Used m Mxmum Cluser Se Used m No. of Oulers Idefed No. of No-Oulers Idefed Flse Idefco No. of Oulers Mssed % of Oulers Idefed % of Po Cloud Idefed % of Po Cloud Idefed Icorrecly Flse Idefco Re Alyss d Dscussos From he rls of he MFIS roue ws cler h for smple geomery usg he coorde vlues cossely produced beer resuls h usg he djused rges. Ths ws mos clerly

16 Remoe Ses show from he rl wh po cloud B where 9.9% of he oulers were foud by usg rges s opposed o he 87.4% oulers foud by usg coordes. The rls lso showed h he coorde verso of he MFIS roue hd much smller flure re defyg.58% of po cloud B correcly s oulers. The rge verso of he MFIS roue correcly defed 3.45% of po cloud B erly double he mou of he coorde verso. The resuls usg coordes from po cloud B were eresg becuse my of he oulers po cloud B occur emporlly fer he l sc d herefore do o follow he me seres per. Loog more closely he resuls we foud h my of hese oulers po cloud B fl he esg or orhg compoes d o s s he cse po cloud A he up compoe. I s sgfc h he esg d orhg compoes were ble o sve he MFIS roue po cloud B eve hough my of he oulyg d pos le ou of emporl sequece wh oher splly close d. Upo roducg complex geomery o he MFIS roue po clouds C d D we fd h he flse defco re drmclly creses o bewee 6% d 0% of he ol po cloud. Ieresgly eough he use of djused rges he MFIS roue ws ble o mch he performce whe he coorde vlues were used boh po clouds C d D. The coorde mehod sll shows slghly smller mou of flse defcos bou % h whe he djused rges were used po clouds C d D; however he dfferece he umber of correc defcos s o s sr s hd bee whe usg smple geomery. The o-oulers h were wrogly defed by he MFIS roue occur res of he po cloud where he regulry of he me seres ws dsruped by rough objecs such s vegeo or mholes. Where mhole ws ecouered he d desy ws suffce o model he rsed surfces o he mhole s ld. Also res of he po cloud where he sysem ws collecg d whle sory occlusos d chges surfce dreco seemed o cuse flse deecos. CSF performed bes o po clouds B d D defyg 5.36% d.39% of he oulers respecvely whe es ssc ws used d 7% d 83% of he oulers respecvely whe es ssc ws used. Po clouds A d C hd oly 4.36% d 9.0% of her oulers defed respecvely whe es ssc ws used d 9% d 5% of her oulers defed respecvely whe es ssc ws used. Overll es ssc cossely produced beer resuls h es ssc. Tes ssc lwys foud more oulers h es ssc. I s eresg o oe h he umber of flse defcos from es ssc dd sgfcly crese wh complex geomery somehg h co be sd bou he resuls obed from es ssc. The CSF roue performed excepolly poorly o d where he oulers were clumped closely ogeher s ws he cse po clouds A d C. Exmg he ch squred es ssc we see h res where he d s clumped ogeher he f of surroudg polyoml surfces re que poor. Addolly whe complex geomery ws roduced by po clouds C d D he ch squre ssc shows us h he polyoml surfces f very poorly res were he po cloud rsoed from oe objec o oher. Ths roue hd much greer success o po clouds B d D where he oulers re more spred ou o he rod surfce d buldg. I fc he spl ure of he mehod showed self s beg que well sued for po clouds where oulyg d pos my o le sequel emporl order. Combg MFIS d CSF usg smple geomery showed h boh po clouds A d B we foud lmos 90% of he oulers wh relvely few flse lrms bou.5% of he ol po cloud

17 Remoe Ses se. The resuls proved slghly beer po cloud A whe he roues were combed sce smll umber of oulers o defed by MFIS were defed by CSF. O he oher hd po cloud B sw much less beef from he combo of he mehods. The vs mjory of pos foud po cloud B were foud by he MFIS roue. I fc oly ew ouler ws defed by he CSF roue whe he combed MFIS/CSF roue ws ppled o po cloud B. Wh he roduco of complex geomery po clouds C d D we fd h g we could defy greer h 90% of he oulers however he cos flse defcos cresed o roud 0%. The resuls from he commercl sofwre pcge Polywors show h ws ble o defy fewer oulers po clouds A d B. The cos o defy hese oulers ws much greer h h from eher he MFIS lgorhm or he CSF lgorhm. Where MFIS defed roud.5% d CSF defed less h 0.0% of he po cloud correcly s oulers Polywors defed s much s 6.9% of he po cloud correcly s oulers. However whe complex geomery ws roduced po cloud C we fd h he commercl sofwre cheved comprble resuls wh he MFIS roue. The commercl sofwre defed bou 97% of he ow oulers whle wrogly elmg oher 4% of he ol po cloud. The MFIS roue foud over 90% of ow oulers whle elmg bou 0% of he po cloud correcly. The complex geomery of po cloud D g sepres he commercl sofwre from he combed MFIS/CSF roues. Wh po cloud D he commercl sofwre defed roud 75% of he oulers he po cloud whle g defyg bou 0% correcly. The combed MFIS/CSF roue ws ble o fd 97% of he oulers po cloud D wh smlr flure of pproxmely 0% of he po cloud beg defed correcly. Le he resuls obed from po clouds A d B he resuls from po cloud D demosre sgfc mproveme over he commercl sofwre. 5. Cocluso Ths pper preseed he resuls of combg wo dffere ypes of lgorhms for he deeco d flerg of oulers po clouds colleced usg moble erresrl LDAR. These roues hve e dvge of he exr formo h s geerlly vlble from hs ype of equpme. The wo mhemcl models preseed here llowed for he creo of wo compuer roues whch perform ouler deeco moble erresrl po cloud d. I hs bee show h dvdully ech mehod of ouler deeco hs dffculy deecg oulers whe cer codos re me. Uder rel world codos vros surfce quly from objecs such s vegeo or mholes c cuse problems. The possbly lso exss h o ll pos whch le splly close o ech oher wll hve bee colleced relvely smlr mes. Due o he moble ure of hs LDAR vr s possble h he vehcle crryg he LDAR hs looped bc o s prevous poso or h he scers hve see he sme po from dffere prs of s rjecory. Eqully he codos whch cuse oulers ed o cree mulple oulers wh prculr rego. Creg surfce pch from d h cos oulers resuls poor fg surfce d problemc ouler deeco oucome. Whle ech mehod hs prove o hve s ow sreghs d weesses hey hve ech prove cpble of deecg d removg oulers from cul LDAR d. Wheher he po cloud cos relvely smple geomery or cos d comprsg more complex scee hese mehods hve

18 Remoe Ses successfully defed oulers rel LDAR d. Whe compred o commercl sofwre he combed roues hve prove o exceed he commercl roue performce. More wor s eeded o opme he pus o he roues specfclly o deerme ccure error esmes for he po cloud coordes. Acowledgemes The uhors would le o h he Nurl Sceces d Egeerg Reserch Coucl NSERC of Cd for he fcl suppor. Refereces. Aov G. Precse Mppg wh 3D Lser Scg. I Proceedgs of he Ierol Coferece o Crogrphy d GIS Boroves Bulgr 5 8 Jury Mller M.M.; Meeres C.; Phllps D.; Rub C.; Ely L.; Pr-Sul B. Collborve Reserch MRI: Acquso of Terresrl Lser Scg Sysems for Erh Scece Reserch; Proposl Submed o EAR Mjor Reserch Isrumeo; UNAVCO: Boulder CO USA 009. Avlble ole: hp:// MRI_TLS_EAR009_UNAVCO-CWU.pdf ccessed o 7 Mrch Lu C.T.; Che D; Kou Y. Algorhms for Spl Ouler Deeco. I Proceedgs of he 3rd IEEE Ierol Coferece o D Mg ICDM 03 Melboure FL USA 9 November Sooodeh S. Ouler Deeco Lser Scer Po Clouds. I Proceedgs of he ISPRS Commsso V Symposum Imge Egeerg d Vso Merology Dresde Germ 5 7 Sepember 006; Volume XXXVI Pr 5 pp Be-Gl I. Ouler deeco. I D Mg d Kowledge Dscovery Hdboo: A Complee Gude for Prcoers d Resercher; Mmo O. Rocch L. Eds.; Sprger: New Yor NY USA 005; Volume Chper pp Breug M.; Kregel H.; Ng R.; Sder J. LOF: Idefyg Desy-Bsed Locl Oulers. I Proceedgs of he Ierol Coferce o Mgeme of D ACM SIGMOD 000 Dlls TX USA 6 8 My Ls M.; Kdel A. Auomed Deeco of Oulers Rel-World D. I Proceedgs of he Secod Ierol Coferece o Iellge Techologes Bgo Thld 7 9 November Ppdmrou S.; Kgw H.; Gbbos P.B.; Flousos C. LOCI: Fs Ouler Deeco Usg he Locl Correlo Iegrl. I Proceedgs of he 9h Ierol Coferece o D Egeerg Bglore Id 5 8 Mrch Zheg M.-Q.; Che C.-C.; L J.-X.; F M.-H.; Jscó T. A Algorhm for Spl Ouler Deeco Bsed o Deluy Trgulo. I Proceedgs of he Ierol Worshop o Compuol Iellgece Secury for Iformo Sysems CISIS 08 Geov Ily 3 4 Ocober Wg J.G. Pre-Processg of INS-D wh he Help of he α-β-γ-fler; Ierl Repor; Isue of Geodesy UBw Much: Neubberg Germy July 997; Germ.

19 Remoe Ses Ah S.J.; Ruh W.; Cho H.S.; Wece H.J. Orhogol dsce fg of mplc curves d surfces. IEEE Trs. Per Al. Mch. Iell Gsc M.; Suer T. Polyoml erpolo severl vrbles. Adv. Compu. Mh Xu Y. Polyoml erpolo severl vrbles cubure formule d dels. Adv. Compu. Mh Grue A.; Ac D. Les squres 3D surfce d curve mchg. ISPRS J. Phoogrmm. Remoe Ses Ac D. Mchg of 3D surfces d her eses. ISPRS J. Phoogrmm. Remoe Ses Chu C.K.; Che G. Klm Flerg wh Rel-Tme Applcos 4h ed.; Sprger-Verlg: Berl/Hedelberg Germ Wg J.G. Les Squres Qudrc Surfce Fg wh he help of Sscl Tess A Cse Sudy Idusrl Surveyg. I Proceedgs of Ierol Geomcs Forum Qgdo Ch 9 30 My Cspry W.F. Coceps of Newor d Deformo Alyss; Moogrph School of Surveyg UNSW Sydey NSW Ausrl Augus by he uhors; lcesee MDPI Bsel Swerld. Ths rcle s ope ccess rcle dsrbued uder he erms d codos of he Creve Commos Arbuo lcese hp://crevecommos.org/lceses/by/3.0/.