LIGHT DETECTION AND RANGING (LIDAR) DATA COMPRESSION

Transcription

1 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 LIGHT DETECTION ND RNGING (LIDR DT COMRESSION waj radha * Sadp Kumar Shar Maor bdul Rahma Raml ad bdul Rahd Mohamd Sharf Iu for dvacd Tcholog (ITM Faculy of Egrg Uvry ura Malaya 434 UM Srdag Slagor Darul Eha Malaya Dparm of Mchacal Egrg Iu of Tchology aara Hdu Uvry (HU Varaa 5 Uar radh Ida STRCT Lgh Dco ad Ragg (LIDR daa compro ha b a acv rarch fld for la fw yar bcau of larg orag z. Wh LIDR ha larg umbr of daa po h urfac grao rprd by rpolao mhod may b ffc boh orag ad compuaoal rqurm. Th papr pr a wly dvlopd compro chm for h LIDR daa bad o cod grao wavl. w rpolao wavl flr ha b appld wo p amly plg ad lvao. I h plg p a ragl ha b dvdd o vral ub-ragl ad h lvao p ha b ud o modfy h po valu (po coorda for gomry afr h plg. Th h daa comprd a h drd locao by ug cod grao wavl. Th qualy of gographcal urfac rprao afr ug propod chqu compard wh h orgal LIDR daa. Th rul how ha h mhod ca b ud for gfca rduco of daa. KEYWORDS: Lgh Dco ad Ragg (LIDR Dlauay ragulao Tragulad rrgular work (TIN Gographcal formao ym Lfg chm Scod grao wavl. INTRODUCTION Rcly mo of h mhod for mag compro ar bad o wavl ad rlad chqu. Wavl approach for mag compro d o ouprform Fourr approach bcau of ably o rpr boh paally localzd faur ad mooh rgo a mag. Th upror compro capably of wavl combd wh hr aural mulroluo rucur mak hm a good rprao for org mag. Whl workg wh dyadc wavl dcompoo dgal mag ar rprd by wavl coffc. Th yp of rprao dyadc wavl dcompoo ar kow a lar dcompoo ovr a fxd orhogoal ba. Th o-lary h approxmao of mag by wavl roducd by h hrholdg of h wavl coffc. Th yp of approxmao ca b vwd a mldly olar. Rcly vral hghly olar mhod for capurg h gomry of mag wr dvlopd uch a wdgl []; a wll a dgadapd olar mulroluo ad gomrc pl approxmao []. Th papr pr a w approach for LIDR daa compro mhod ug cod grao wavl. radom of po ha b approxmad o rpr a *Corrpodg auhor. Tl: Fax: E-mal: bwaj@malcy.com 55

2 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 urfac by Dlauay ragulao. Th hory compuao ad applcao of Dlauay ragulao ad Voroo dagram hav b dcrbd dal h lraur [-8]. Th pr work dcrb a fa algorhm bad o Ta Covx Hull Iro algorhm [7-8] for h coruco of Dlauay ragulao of arbrary collco of po o h Euclda pla. Th orgal algorhm ha b mprovd furhr for a far compuao of gomrc rucur. Th ourc cod ha b wr FORTRN complr. Oc h ragulad rrgular work ha b crad from h radom of po wa furhr ubjcd o compro by ug cod grao wavl. Rul wr how a comparav udy ba for h TIN daa compro a dffr lvl of roluo.. DELUNY TRINGULTION May rarchr [3 9-] hav uggd dffr way o coruc ragulao wh h local qularal propry. wll kow coruco calld h Dlauay Tragulao mulaouly opmz vral of h qualy maur uch a max-m agl m-max crcumcrcl ad m-max m-coam crcl. Th Dlauay ragulao DT of a po h plaar dual of h famou Voroo dagram. Th Voroo dagram a paro of h pla o polygoal cll o for ach pu po o ha h cll for pu po a co of h rgo of h pla clor o a ha o ay ohr pu po. So log a o four po l o a commo crcl h ach vrx of h Voroo dagram ha dgr hr ad h DT whch ha a boudd fac for ach Voroo vrx ad vc vra wll dd a ragulao. If four or mor po do l o a commo crcl h h po wll b h vrc of a largr fac ha may h b ragulad o gv a ragulao coag h DT Voroo dagram ad Dlauay ragulao hav b gralzd umrou drco. For mor formao o Dlauay ragulao ad Voroo dagram h urvy by Foru ad urhammr []. Thr a c rlaohp bw Dlauay ragulao ad hr dmoal covx hull. Lf ach po of h pu o a parabolod hr-pac by mappg h po wh coorda (x y o h po (x y x y. Th covx hull of h lfd po ca b dvdd o lowr ad uppr par: a fac blog o h lowr covx hull f uppord by a pla ha para h po from (. I ca b how ha h DT of h pu po h projco of h lowr covx hull oo h xy -pla a dpcd Fgur. Fally a drc characrzao: f a ad b ar pu po h DT coa h dg { a b } f ad oly f hr a crcl hrough a ad b ha rc o ohr pu po ad coa o pu po ror. Morovr ach crcumcrbg crcl (crcumcrcl of a DT ragl coa o pu po ror. Som propr of Dlauay ragulao hav b dcud a follow: L Y do a f plaar po. Dlauay ragulao D (Y of Y o uch ha for ay ragl D(Y h ror of crcumcrcl do o coa ay po from Y. Th pcfc propry rmd a Dlauay propry. Th Dlauay ragulao D(Y of Y uqu provdd ha o four po Y ar co-crcular. Sc hr h X of pxl or ub afy h codo w ally prurb h pxl poo ordr o guara ucy of h Dlauay ragulao of X ad of ub. Each prurbd pxl corrpod o o uqu uprurbd pxl. From ow o w do h of prurbd pxl by X ad h of uprurbd pxl by X. 56

3 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 Z Uppr covx hull Dlauay ragulao Lowr covx hull Fgur Th lfg raformao map h DT o h lowr covx hull For ay y Y D(Y \ y ca b compud from D(Y by a local upda. Th follow from h Dlauay propry whch mpl ha oly h cll C(y of y D(Y d o b rragulad. Rcall ha h cll C(y of y h doma cog of all ragl D(Y whch coa y a a vrx. Fgur how a vrx yd(y ad h Dlauay ragulao of cll C(y. D(Y provd a parog of h covx hull [Y] of Y. Fgur Irrgular of po Fgur 3 Th TIN daa rucur ug Dlauay ragulao 3. INTEROLTION WVELET FILTERS FOR TIN rpolao wavl flr for TIN l ubdvo proc whch ha wo p []. O a plg p; h ohr o a lvao p. I h plg p a ragl dvdd o vral ub-ragl. Th lvao p o calcula h po valu (po coorda for gomry afr h plg. L u dcu h paro p mahmacally. 57

4 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 Codr a daa o b parod o wo group calld ad. Ug o xpr h po coorda o ca coruc a mao of bad o. ~ E( ( Th mao fuco (flr E ca b a local mao or global mao. global mao grally compuaoally xpv; hrfor a local mao ug oly ghborg po prfrrd. fr h mao p a wavl rm W ad a approxmao rm for h orgal daa ca b corucd a: W ( C(W Th corrco fuco C a cuomzabl fuco bad o dffr opmzao rqurm. vr raform ca b corucd a: ~ C(W W E( (3 If h orgal po ca b parod o a d group h h abov proc ca b ravly appld o dffr h group. d group ha h flowg rucur: N N (4 N do h f rprao of h gomry. ca b parod o ad N ; h N ca b parod o N ad N ad o o ul parod o ad. No ha h uprcrp ar ud o rpr dffr roluo (largr umbr rpr fr roluo. ad o h d (or hrarchcal rucur of h paro o ca coruc wavl ad approxmao of h daa a: N N W E( ( C(W N ( N N N Hr a rmda ymbol o rpr h parog rul. parod o ( ( wo compo: ad whch blog o ad rpcvly. ad o quao (5 h orgal daa N dcompod o W.. W N. Equao (5 h aaly raform whch dcompo h fr rprao o a coarr rprao plu dal. Th yh raform h vr raform ad how quao (6. Th rcorucd.. N ( N yld a mulroluo rprao of h orgal daa. (5 58

5 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 C(W ( ( N E( W (6 N N I h abov drvao of a wavl rprao [3-8] h proc do o dpd o a rgular g for h daa; hrfor ca b ud boh h rgular ad rrgular g ca. Th a mpora advaag of h lfg chm [7-8]. If h flr ad ar h am for vry po a a gv lvl h chm a uform chm. If hy alo do o chag wh h roluo h chm a aoary chm a wll. Howvr quao (5 ad (6 ar gral formula. No-aoary ad o-uform chm ca b wr h form wh dc o E ad C. Nvrhl ho chm could co mor compug rourc ad may b l ffcv for daa compro GIS applcao. C E 3. N EXMLE Emao of 3 fr corrco Fgur 4 xampl ha llura h bac da of h wavl flr coruco proc Fgur 4 how a xampl ha llura h bac da of h abov coruco proc. Hr ad dpd o ad hrfor a o-aoary ad o-uform raform. Gv rrgular daa o po h o p paro ad wavl raform ar: E C } { W W C(W ( W ( ( } { } { (7 59

6 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 I h xampl a lar maor ad corrcor ar ud for E ad C. If ad ar.5 h corrco p mak h orm dfd quao (8 ak a mlar valu ha h ucorrcd valu. (No ha quao (8 ( for j rfr o h j mao valu E( a. Th a xampl of h opmzao h corrco p. j Equao (7 h aaly raform for h fr p. Th yh raform ca b drvd by rplacg h maor ad h corrcor quao (6. j j j orm ( ( ( (8 4. ROOSED LGORITHM Th chm dcrbd prvou co 3. o yp of flr bad o h lfg chm. Th calld a approxmao flr whch vry po valu wll chag afr ach rao. Th ohr yp of flr bad o h lfg chm a rpolao flr whch a po valu rach fal poo oc calculad. For GIS rra daa howvr rpolao grally prfrrd bcau po valu ar of mor uful ha a gral hap. Thrfor rpolao wavl flr wll b ud h rarch for procg hr-dmoal rra daa. Fr h approxmao of h fuco wa drmd larly. Th h lfg chm wa ud o drm h b ba fuco ad h coffc. Normally pracc h urfac daa co of may frqucy bad ad ra. For lmd ampl boudary flr ar prfrrd ovr ohr chqu. Th lfg chm ha b mployd o provd h boudary hgh ad low pa flr. Th grag proc for h LIDR daa compro a follow:. Du o radomly drbud raw daa po h daa rpolad by ma of a lar fuco. I amg o abl procg wh rgularly drbud grd daa.. Ug h Dlauay algorhm h TIN modl of h urfac ha b calculad. For ach ragl h TIN modl h coorda of h vrc ad hr rpcv hgh valu of h hr po ha compo wr calculad. 3. Th adjaccy marx ha formd by h boudd dg for all ragl ha b calculad. 4. Th coorda of h vrc ad ragl dg hav b rwr WTIN daa rucur. 5. Th wavl flr for ach ragl ha b calculad bad o h ara mhod a dcrbd co 4.. Wavl coffc hav b drmd o chck ad compar h ara of ach ragl bad o lfg chm (pla co 4.. If h wavl coffc valu much hghr ha h hrhold valu h ha vrc wr rad. If h dffrc fall blow a prdfd hrhold h orgal po ar lcd. Th proc compld wh h umbr po addd durg h prd rao ad wa coud ll all h po wr chckd. 6. y ug rav procg h orgal LIDR po wr compard wh h comprd daa ad hr rpcv ak Sgal o No Rao (SNR valu wr calculad for boh mag o compar h compro rao. 5

7 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc CODING SCHEME y 3 o 3 Fgur 5 urfac howg h ara of h ragl o calcula h wavl coffc Th algorhm ca b dcrbd a h Fgur 5. Th mag o b codd ca b rgardd a a dcr urfac.. a f of po hr-dmoal (3-D pac by codrg a o-gav dcr fuco of wo varabl F(x y ad ablhg h corrpodc bw h mag ad h urfac x y c c F(x y o ha ach po corrpod o a pxl h mag; h coupl (x y gv h pxl poo h XY pla whl c h po hgh. Our goal o approxma by a dcr urfac x y d d G(x y dfd by ma of a f of po. L T b a grc ragl o h XY of vrc: (x y (x y 3 (x 3 y 3 d l c F(xy c F(x y c3 F(x3y3 (9 Whr ad ar rprd a 3 ( x yc (x y c (x 3 y3c3 L O b h crod of h ragl whch ma a w po afr addg o h ragulao. L ad 3 b h ara of h hr ragl. Th h oal ara ca b rprd a:. x 3 ( Th dal coffc ca b rprd a quao. d Z (Z ( h Whr d h dal coffc a h lvl ad (Z h prdcd valu a lvl ad Z h valu a h odd ampl. h Th quao abov ca b rwr a gral form for lvl a h 5

8 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 Z Z v C(d ( whr C(d 3 (3 T C Thu by chagg h corrco facor C quao 3 w ca lc h wavl coffc. Th wavl coffc wll drm h umbr of gfca po ha ca b rmovd from h ragulao. Th gfca po wll b ud o rpr h urfac. 5. EXERIMENTL RESULTS ll algorhm wr codd Vual Forra ad MTL ad xcud o a um IV 56 M RM mach. Th opmzd cod abou l of Vual Forra ad 5 l of MTL. To valua h prformac of h wavl bad ragulao compro mhod vral daa wr ud. Th wavl bad ragulao compro mhod gv coly br prformac for h LIDR daa ha w ud. Th co pr om rul of h algorhm o LIDR daa ug h wavl bad ragulao compro mhod a dffr lvl of qualy. I our a ach rcuro p abou 5% of h vrc ar rmovd by ug h cod grao wavl ad lfg chm. Th umbr of ragl h hrarchy a mo oly hr m largr ha h umbr of ragl of h al ragulao. W x xam h orag ovrhad caud by h maac of h hrarchy. Th oal amou of orag by of h daa rucur dcrbd prvou co whch may clud mulpl cop of h am ragl oly 4 o 5 m largr ha h orag of h al ragulao. I our mplmao h gav a oal mmory rqurm for h hrarchcal rprao of a rra of daa po of roughly O( log by. Th daa rucur of Dlauay ragulao dffr from h daa rucur of Wavl compro wo way. Fr w o logr or mulpl cop of h am ragl ad w or for ach ragl h lvl a whch wa crad. Scod w roduc h rmda od whch rduc h oal umbr of por h rucur. Toghr h wo chag rduc h orag rqurm by o hrd whch ma ha h orag abou 3.5 m a much a h orag for h al rra. If h cra orag would ll b oo much pobl o hav a rad-off bw h z of h rucur ad h dffrc bw ubqu lvl. I parcular ad of rqurg h dld vrc o form a dpd w ca rqur ha hy form dpd group of a cra z. 5. DT USED Two dffr of LIDR daa hav b collcd o chck h ffccy of h compro program. Th daa wr SCII forma dcrbg h x y ad z valu for h po. I h fr p h TIN modl for h urfac ug h Dlauay algorhm ha b calculad. Fgur 5 how h LIDR daa rprd rm of TIN. I ca b obrvd ha mo of h ragl grad by h program follow h Dlauay crro. Th abov Fgur how h TIN modl for 5 po. O h op lf poro of h Fgur 6 how 5

9 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 h ad fla ragl. Th wa du o h lack of rmda po bw bcau of h vally. Fgur 6 Th TIN modl (Rd colord l ar h dg of h ragl ad blu po ar h vrc ha mak h ragl. Th orgal LIDR daa wa a rrgular faho. Dlauay ragulao mhod for h crao of h TIN ha b appld o h orgal daa. w algorhm ha b dvlopd for h crao of h TIN. Furhrmor TIN wa comprd ug h cod grao wavl. w algorhm for cod grao wavl compro propod. ad o h al cofgurao of h orgal TIN dffr roluo ar corucd durg wavl aaly. Fgur 7a 7b ad 8a 8b how h rul compud ug h wavl bad lfg chm algorhm. Fgur 7a how h orgal daa. Fgur 8a how h rul afr % compro ad Fgur 9a how afr 3% compro. Fgur 9b how h ragulao of h mag afr compro. Dffr compro chm uch a Huffma codg ca b appld o h wavl coffc o furhr rduc h orag z. Th work alo provd curr mplmao of wavl coffc durg h compro oprao. Th propod algorhm ha h mulroluo capably ad ay o compr du o larg umbr of wavl coffc wh mall magud whch uabl for drbud GIS applcao uch a wb dplayg. 53

10 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 Fgur 7a Ial Trra (Gouraud hadd Fgur 7b Tragulao for h al rra (5 po Fgur 8a Trra compro a % Fgur 8b Tragulao for h rra a % (Gouraud hadd (3 po Fgur 9a Trra comprd a 3% Fgur 9b Tragulao of h rra a 3% (Gouraud hadd (87 po 54

11 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc CONCLUSION Th coruco of Tragulad Irrgular Nwork ug Dlauay ragulao for h LIDR daa ha b how. Th approach u fa ad ffc cod grao wavl algorhm for mulroluo aaly of GIS daa compro. Th algorhm ay o prform h mahmacal ad compuaoal oprao wh mmal m rrpcv of h larg daa. Our algorhm chm prrv hgh-grad rgo ha mgh x a gv daa. W hav d our mhod wh varou daa. Th compuaoal co of our algorhm dpd o h dffr approach ud. Th al ragulao ca b do O ( log h grad approxmao ca b do O( log. Th dvdual rfm p ha o chck all h orgal daa po lyg h volvd ragl o h complxy of ach p O (. How of h rao p xcud dpd o h rror valu gv h pu. a gral rul h auhor hav aumd ha o mor rao hould b do ha hy ar orgal daa. So h ovrall complxy O (. W ar currly vgag h dald rror aaly for h dffr of daa a dffr cal. 7. CKNOWLEDGEMENTS uhor would lk o hak varou aoymou rvwr for hr crcal uggo ha mprovd h qualy of h maucrp. LIDR daa wa provdd by wa Raja ara. REFERENCES [] Dooho D. 999 Wdgl: Narly-Mmax Emao of Edg al of Sac [] Dmar L. Dy N. Floar M.S. ad Ik. 4 dapv Thg for Trra Modllg ad Imag Compro. I: Dodgo N.. Floar M.S. ad Sab M.. Ed. dvac Mulroluo for Gomrc Modllg. Sprgr-Vrlag Hdlbrg pp [3] Lawo C.L. 97 Grao of a Tragular Grd wh pplcao o Coour log. Calfora Iu of Tchology J olluo Laboraory Tchcal Mmoradum No. 99 [4] Sbo R. 978 Locally Equagular Tragulao Compur Jour. ( [5] Kao T. Mou D.M. ad Saalfld. 99 Dyamc Maac of Dlauay Tragulao. roc. uo-caro I almor Marylad [6] uppo E. Dav L. DMho D. ad Tg Y.. 99 aralll Trra Tragulao. roc. 5h Ir. Sympoum o Spaal Daa Hadlg V. Charlo Souh Carola pp [7] Ta V.J.D. ad Vodroh.. 99 Gralzd lgorhm for h Coruco of Dlauay Tragulao Euclda -pac. roc. GIS/LIS '9 V. laa Gorga pp [8] Ta V.J.D. 993 Fa Topologcal Coruco of Dlauay Tragulao ad Voroo Dagram Compur & Gocc 9( [9] Eva W. Krkparck D. ad Towd G. Rgh-Trgulad Irrgular Nwork lgorhmca. Spcal Iu o lgorhm for Gographcal Iformao Sym 3( [] báolo M.J. la J. ad d Gu. Hrarchal Tragulao for Mulroluo Trra Modl Th Joural of Compur Scc & Tchology (JCS&T 3. [] Foru S. 99 Voroo Dagram ad Dlauay Tragulao. I: Hwag F.K. ad Du D.Z. Ed. Compug Euclda Gomry. World Scfc. 55

12 KMITL Sc. Tch. J. Vol. 5 No. 3 Jul. Dc. 5 [] Kma J..K. ad ähr H.-. Wavl Compro ad h uomac Clafcao of Urba Evrom ug Hgh Roluo Mulpcral Imagry ad Lar Scag Daa Goformac [3] Wu J. ad marauga K. 3 Wavl Tragulad Irrgular Nwork Iraoal Joural of Gographcal Scc 7( [4] Dy N. Lv D. ad Grgory J.. 99 urfly Subdvo Schm for Surfac Irpolao wh To Corol CM Traaco o Graphc [5] Coh. ppld ad Compuaoal pc of Nolar Wavl pproxmao. I: Dy N. Lvaa D. Lv D. ad ku. Ed. Mulvara pproxmao ad pplcao. Cambrdg Uvry r Cambrdg pp [6] Malla S. 989 Thory of Mulroluo Sgal Dcompoo: Th Wavl Rprao IEEE Traaco o ar aly ad Mach Illgc [7] Swld W. 994 Coruco ad pplcao of Wavl Numrcal aly.. Upublhd hd. h Dp. of Compur Scc Kaholk Uvr Luv lgum. [8] Swld W. 996 Th Lfg Schm: Cuom-dg Coruco of orhogoal Wavl ppld Compur Harmoc aly 3(