AN EXPLICIT GROWTH MODEL OF THE STEREO REGION GROWING ALGORITHM FOR PARALLEL PROCESSING

Transcription

1 Intenatonal Achves of Photogammety, Remote Sensng and Spatal Infomaton Scences, Vol. XXXVIII, Pat 5 AN EXPLICIT GROWTH MODEL OF THE STEREO REGION GROWING ALGORITHM FOR PARALLEL PROCESSING Dongoe Shn*, and Jan-Pete Mulle Imagng Goup, Mullad Space Scence Laboatoy, Depatment of Space and Clmate Physcs, Unvesty College London, Holmbuy St. May, Dokng Suey, RH5 6NT (ds2, pm@mssl.ucl.ac.uk Commsson V, WG V/4 KEY WORDS: Dense econstucton, Steeo Regon Gowng, Paallel Pocessng, Adaptve Least Squae Coelaton, GOTCHA ABSTRACT: GOTCHA s a well-ted and tested steeo egon gowng algothm, whch teatvely apples Adaptve Least Squae Coelaton (ALSC matchng to the adacent neghbous of a seed pont n ode to acheve a dense econstucton wth sub-pxel pecson. It s, howeve, a computatonally expensve algothm as evey seed pont collected by the ALSC matchng poduces quadants o octants of new matchng canddates. Accodngly, the computatonal complexty nceases exponentally as the steeo matchng egon gows. To expedte the matchng pocess of a tadtonal GOTCHA, ths pape poposes a paallelsed steeo egon gowng algothm called a MT-GOTCHA. To acheve data paallelsm, the poposed method ntally dvdes a steeo mage fom abtay dstbuted seed ponts, whch ae able to employ multple GOTCHA s. In addton, snce t estmates a cluste of neghbous usng a non-lnea dffuson equaton and pefoms multple ALSC pocesses n paallel to vefy local matchng canddates, moe teponts ae obtaned wthn less pocessng tme. Expemental esults demonstate the poposed method can educe the pocessng tme of a dense econstucton at a easonable cost of memoy consumpton. 1. INTRODUCTION A mao goal of shape fom steeo s geneally concluded to obtan accuate and complete econstucton fom an ovelappng mage pa. Howeve, t s often dffcult to satsfy both condtons at the same tme, patculaly when dealng wth mages contanng a matchng ambguty (e.g., sgnfcant scene dstoton due to a wde baselne sepaaton o contanng ethe a epettve patten o homogeneous textue. Thus, matchng accuacy tends to tade off aganst matchng completeness and vce vesa dependng on the applcaton. Fo example, a tadtonal matchng appoach fo close-ange developed fo dense econstucton n the compute vson communty explots the eppola constant (.e., a coect coespondence should only be found wthn an eppola lne n the othe mage. Consequently, Dynamc Pogammng (DP has seved as a standad method fo dense econstucton but t often ncludes outles as the eppola constant s not suffcent to defne a tepont at tmes (.e., DP esults only satsfy the global matchng constant defned wthn an eppola lne and not fo each and evey potental pxel pa. Moeove, matchng consstency between eppola lnes s not guaanteed wthout a pope post-pocess (Schasten and Szelsk, 2002; Ohta and Kanade, On the othe hand, the emote sensng (fa-ange communty has developed a steeo egon-gowng algothm to acheve a dense econstucton fom dffeent easons, such that some matchng dffcultes notced n close ange mages ae not geneally found but the lnea eppola constant no longe holds. Fo nstance, occluson and sgnfcant geometc (e.g., poectve dstoton ae hadly obseved n obtal steeo pas. Howeve, t s dffcult to defne a lnea fundamental matx that maps a pont to a lne n satellte magey fom a push boom senso (Otto, 1988; Km, One good example of a steeo egon gowng algothm s the Guen-OTto-CHAu (GOTCHA algothm (Otto and Chau, 1989, whch s based on the Adaptve Least Squae Coelaton (ALSC (Guen, 1985 combned wth a 2D egon gowng algothm. Fo example, gven ntal matchng esults, efeed to as seed ponts n (Km and Mulle, 1996, GOTCHA can ncease the numbe of matchng pas consdeably as t does not lmt gowng dectons wthn an eppola lne as a seed pont can gow n both the x and y dectons f ALSC confms that the accuacy of a matchng canddate s acceptable. Howeve, thee s one mao dsadvantage whch s that the computatonal complexty of the GOTCHA algothm s sgnfcant compaed wth ts countepat DP matchng. Ths s patly because ALSC needs to be pefomed sequentally at evey neghboung pxel of a new gowng poston. Also, gowng esults need to be odeed wth espect to matchng smlaty n ode fo GOTCHA to decde the next best gowng pont. Consequently these two pocedues (.e., ALSC followed by sotng become a mao bottleneck of the GOTCHA pocess as the numbe of seeds nceases. To addess ths poblem, ths pape poposes a modfed GOTCHA algothm called MT-GOTCHA, whch expedtes the gowng pocess by employng multple pocesses n paallel. To ealse a paallel pocess, the poposed method dvdes an mage nto multple gowng egons so that each egon has ts own ndependent pocess. Addtonally, multple ALSC pocesses assocated wth a sngle seed pont ae also paallelsed. Ths means that the poposed method could acheve mco and maco level paallelsm, e.g., multple * Coespondng autho. 543

2 Intenatonal Achves of Photogammety, Remote Sensng and Spatal Infomaton Scences, Vol. XXXVIII, Pat 5 GOTCHA s can opeate at a maco level wth multple ALSC pocesses at a mco level. To acheve ths, MT-GOTCHA models the gowth of a seed pont by two boundaes called nte and nta bounday espectvely,.e., the ntesecton of two boundaes defnes the fnal gowng egon of a seed pont. Ths pape s ogansed as follows. Secton 2 evews moe detals about the ALSC and GOTCHA algothm and dentfes potental poblems. In Secton 3, the poposed steeo egon gowng method s explaned patculaly egadng how the gowng boundaes ae defned n MT-GOTCHA. Fnally, expemental esults and conclusons ae pesented n Secton 4 and 5, espectvely. 2.1 ALSC 2. STEREO REGION GROWING Adaptve Least Squae Coelaton s the coe-matchng algothm used n GOTCHA. It can estmate a tue coespondence fom an appoxmated tepont by changng the shape of a matchng wndow teatvely. Thus, f a gven seed pont s located close enough to the tue coespondence, ALSC can move the ntal poston and convege at the tue coespondence. Suppose I l ( x s a functonal whch maps a 2D postonal vecto x [x y] T to an ntensty scala value of a left mage, and also assume that t s contnuous and dffeentable at any pont wthn a left mage doman. Then, a tepont can be defned as a pont pa ( x, x whch satsfes I l ( x I ( x N( x (1 whee N( x s a Gaussan functonal that epesents mage nose at a pont x and smlaly I ( x s an ntensty functonal defned n a ght mage. If the ght poston of an ntal tepont s gven aound the tue poston and assume the eo between the tue and the ntal poston s ntoduced by a local affne dstoton, then the eo vecto can be found by mnmsng a cost functon, d I ( x ˆ d I( x ˆ I( x ˆ dx I( x ˆ dy (4 x y whee dx and dy s delveed fom (3. Thus, a closed fom soluton of (2 s found n the least squaes sense and ALSC ecusvely apples (2 wth the updated soluton untl t conveges at a cetan pont. It s also mpotant to menton that the cost functon shown n (2 appeas to fnd a 2D vecto but t s, n fact, paametesed by (3 so that at least thee ponts pas (.e., each pa povdes two condtons fo an affne tansfom ae equed to avod a sngula system of equatons. These pont pas ae found fom a matchng wndow and (2 s theefoe nomally ove-detemned. Fg. 1 demonstates the pefomance of ALSC, whch stated fom an ncoect ght poston (see a geen coss n the ght mage but found the coect poston afte 15 teatons. One can notce that ALSC apdly conveges at the tue pont and a squae box shown n both mages epesents an ntal matchng wndow and multple ectangles shown n the ght mage vsualses how ALSC dstots the squae shape teatvely fom the ntal matchng wndow. d mn I l ( x I ( x ˆ d (2 d whee x ˆ denotes an appoxmate ght poston gven ntally and d s the offset between the tue poston and ts appoxmaton such that x x ˆ d and a pont pa ( x, x defned n a tepont s elated by a local affne tansfom,.e., x l a 11 a 12 x a 21 a t x 22 t y whee a denotes affne dstoton paametes and t x and t y epesents a tanslaton n x and y decton. By employng Taylo s theoem up to the fst ode tem, the second tem of the cost functon (2 can be expanded wth espect to the appoxmated ght poston, x ˆ,.e., (3 544 Fgue 1 Example of ALSC, whee an ntal pont maked as a geen coss n both mages. The ght mage shows an updated coespondng pont afte 15 teatons as a yellow coss whlst ntemedate ght postons ae hghlghted as a ed colou. 2.2 GOTCHA GOTCHA can be seen as an extended veson of a geneal 2D egon gowng algothm used n mage segmentaton. Smla to a tadtonal bnay segmentaton, GOTCHA gows a seed

3 Intenatonal Achves of Photogammety, Remote Sensng and Spatal Infomaton Scences, Vol. XXXVIII, Pat 5 pont by addng adacent neghbous to a seed pont ecusvely. A dffeence s t uses neghbou pont pas to deal wth a steeo mage and avods a false neghbou pa whch fals to poduce a efned coespondence wthn pedefned ALSC matchng eo. Suppose that a set of ntal teponts s gven as T {t k ( x k, x k : I l ( x k I ( x k } (5 whee s a matchng theshold, then the 8-connected neghbous of the k th tepont ae defned as N 8 (k {n l ( x m, x n : x m x k 1, x n x k 1} (6 In ths case, ntal seed pont pas of GOTCHA (.e., the fst place fom whch the algothm begns to gow s defned as all neghbous of an ntal tepont set,.e., whee S (0 epesents a set of seed ponts and the numbe n the paenthess wtten as a supescpt denotes the numbe of teatons that GOTCHA takes to gow. Once an ntal seed set s eady, GOTCHA ecusvely adds a new seed pont pa f any pont pa n S ( poduces a satuated esult fom ALSC and ths teaton contnues untl S ( 0. To explan ths moe clealy, a pseudo code of GOTCHA algothm s pesented n Fg. 2 whee ALSC(. shown on lne 7 epesents a functon that etuns the dssmlaty of ALSC matchng, a epesents a matchng theshold of ALSC, s k on lne 8 epesents an updated seed pont pa of s k by ALSC, and sot(. n lne 12 s a sotng functon whch odes seed elements wth espect to the matchng smlaty so that a seed pont havng the hghe smlaty s tested eale n the next gowng pocess. As notced fom lnes 7 to 10 n Fg. 2, ths algothm nceases a seach space exponentally. Also, ecusve sotng shown n lne 12 makes the gowng pocess slowe as S nceases. Please also note that the pseudo Fgue 2 A pseudo code of GOTCHA code pesented n Fg. 2 s used to hghlght how data n T and S n (5 and (7 change ncementally. The moe effcent algothm s theefoe possble by mnmsng the numbe of tempoay vaables. As a dssmlaty measue of ALSC matchng, a tadtonal ALSC uses the lagest egenvalue of the covaance matx of the estmated dt x and dt y. Thus, f an updated soluton has a lage dssmlaty, ths means that the soluton s not satuated (7 at the fxed pont as the ncement of the tanslaton paametes s lage. Ths measue nomally pefoms bette than the sum of ntensty dffeences o coelaton scoe when matchng wndows contan homogeneous o epettve textue that can also gves small ntensty dffeence at any pont wthn a matchng wndow. 3. PARALLELISED STEREO REGION GRWOING One of the staghtfowad appoaches to expedte the gowng pocess shown n Fg. 2 s pefomng multple ALSC matchng pocesses (see fom lne 5 to 7 n Fg. 2 smultaneously. Otto and Chau mplemented ths dea n the Mult-Instucton steam and Mult-Data steam (MIMD paallel pocessng achtectue, whee multple pocessos establsh a fam of woke pocessos to whch a cental contol pocesso (.e., the man CPU of a Unx system connects va data ppelnes (Otto and Chau, In ths method, the man contolle pocesso owns a global GOTCHA pocess, opeatng as a maste pocess such as sendng multple ALSC tasks to each woke pocesso and managng both the poty of the pocessng queue and mage data equed fo ndvdual ALSC matchng, whlst each woke pocesso smply pefoms a sngle ALSC matchng and etuns the esult to the maste. Howeve, ths appoach only woks f the sze of an mage s small enough due to the naow data bandwdth of the data ppelnes at that tme. To addess ths, Holden et al. (1993 poposed a Geometcally Paallel Steo Matche appoach (also efeed to as GPSM, whch dvdes an nput mage nto multple ovelappng ectangula tles and ntates multple GOTCHAs afte povdng each woke pocesso wth elevant tles fo matchng (Holden et al., Accodngly t can also acheve data paallelsm and ths mnmses data tansfe ate. Fo example, snce each woke pocesso has an mage tle to whch a seed pont belongs as well as the ovelappng egons fom adacent tles, each woke pocess s ndependent and nte-pocesso communcatons ae sgnfcantly mnmsed. Howeve, GPSM eques a tool that can egeneate unfomly dstbuted seed ponts to ntate evey GOTCHA pocess successfully. Unlke these pevous effots, the poposed method s moe concentated on task paallelsm as the hadwae constant studed n the eale paallel computng methods has been changed sgnfcantly, e.g., the amount of memoy and data tansfe bandwdth ae even eady fo the cloud computng. Theefoe, a hadwae-elated ssue of paallel computng (e.g., balancng computng load of the mult-pocessng coes and managng communcatons between pocessos s not nvestgated n ths pape. Instead we focus on dentfyng ndependent sub-tasks fom the gowng algothm and how to pefom them smultaneously wthout shang any nput data. Theefoe, the fundamental dea of the poposed method s to defne ndependent pocessng tasks wth as many as we can. Fo example, the poposed method s desgned to have multple GOTCHA pocesses, whch also use multple ALSC matches when testng neghbous. Thus, to some extent, ths can be consdeed as a way to combne two pevous effots (.e., one of whch uses mult-alsc and the othe of whch uses mult- GOTCHA. As a pelmnay equement of the poposed method, an nput steeo mage needs to be dvded appopately accodng to the dstbuton of ntal seed ponts,.e., a lage gowng aea s 545

4 Intenatonal Achves of Photogammety, Remote Sensng and Spatal Infomaton Scences, Vol. XXXVIII, Pat 5 assgned to a seed pont havng hghe matchng smlaty, and we call the bounday between seed ponts an nte-bounday. In addton, we defne anothe bounday (called an nta-bounday wthn the nte-bounday. Ths s used to defne a cluste of local neghbous fom a seed pont accodng to a matchng confdence. Consequently, nta-bounday can povde moe than 8 neghbous f a seed s suounded by stong matches. Othewse, t only poduces small numbe of neghbous, whch ae tested by multple ALSCs n paallel. 3.1 Inte-bounday estmaton The nte-bounday s the bounday between multple seed ponts and t s estmated by a modfed Voono tessellaton that povdes a lage aea to a seed pont havng a hghe matchng smlaty. To ealse ths dea, the ntal postons of seed ponts move accodng to the sum of gavty pulls between seed ponts befoe applyng Voono tessellaton and an ntal matchng dssmlaty s used as the mass of a seed n the computaton of a gavty pull. Voono tessellaton, whch s also known as a dual of Delaunay tangulaton, s a method pattonng a plane nto convex subegons based on the neaest neghbouhood ule (Auenhamme, 1991 fom nput ponts (called stes. Fo example, a Voono egon of the th pont x of a ste set V s defned as whee R { p : x p x p } (8 p s a pont n an mage and x V { x }. Although thee ae sophstcated mplementatons of Voono tessellaton whch can mpove the computatonal effcency consdeably such as Fotune s algothm (Fotune, 1986 n whch the computatonal complexty s known as O( V ln V, we adopt the smplest algothm estmatng a Voono egon by ntesectng half planes constucted between stes. Fo example, a half plane used to estmate R fom two stes x and x s a half nfnte plane that contans x and lmted by an othogonal lne ntesectng the mddle of the lne ( x, x. Thus, the constucton of a half plane s affected by the geometcal dstbuton of nput stes. In ou case, a ste set V s eplaced wth a set of ntal seed pont pas T (0, so that the postons of T (0 need to be modfed accodng to the matchng dssmlaty values befoe tessellaton. We model the moton of the ntal pont as a esult of the nteconnected gavty pull. Fo example, f a pont x has a hghe dssmlaty then t ceates a stong pullng foce esultng n that othe ponts move towad the pont. Consequently, the mddle ponts that defne half planes move close to the pont x and R estmated by ntesectng evey half-plane contanng becomes smalle. x Suppose that thee ae two teponts t k and t l T (0, whee t k ( x a, x b and t l ( x c, x d then a gavty foce that pulls fom t k to t l n a left mage s defned as f left (t k,t l g ALSC(t k ALSC(t l x a x 2 ( x a x b (9 b 546 whee g epesents a gavty coeffcent. Addtonally, a gavty map F(T can be defned as a netwok of gavty pulls between evey pa of teponts, e.g., an element of F at the k th ow and the l th column, f k,l s f (t k,t l. Thus, f k,l = -f l,k and ts dagonal values should be 0 as self-pullng s avoded,.e., 0 F(T,t 1 L f (t T 1,t 1 0 M M O f (t 1 L 0 (10 Once a gavty map s eady, the total gavty that a sngle pont has can be easly found by summng elements of a ow (o column vecto of F. (a (b Fgue 3 Example of an nte-bounday estmaton fom fou nput teponts, whee ntal left postons of teponts (t 1 -t 4 hghlghted as ed dots ae moved to t 1 -t 4 maked as blue dots (a and updated teponts ceates fou pattons fom Voono tessellaton (b. Fg. 3 vsualses an example of Voono tessellaton fom fou ntal teponts denoted as t 1 -t 4. Fg. 3(a s the left mage of a test steeo data so that dots n Fg. 3(a epesent left teponts. Usng (10, each tepont moves fom ts ntal poston fom the ed to the blue befoe pattonng the mage. Consequently, each tepont owns a Voono egon R whee GOTCHA s pefomed late (see Fg. 3 (b. 3.2 Inta-bounday estmaton The nta-bounday s the confdence bounday of a seed pont, whch can estmate how much a seed pont possbly gows wth

5 Intenatonal Achves of Photogammety, Remote Sensng and Spatal Infomaton Scences, Vol. XXXVIII, Pat 5 gven dssmlaty value afte the n th teaton of GOTCHA. A dffuson equaton has been adopted to model ths non-lnea shape of a confdence bounday. Accodngly, the poposed method can nclude ethe non-adacent neghbous of a seed pont o a smalle numbe of neghbous dependng on matchng dssmlaty of the cuent state. In fact, an nta-bounday povdes a way fo GOTCHA to contol the numbe of neghbous and ths can be futhe exploted to balance computng load adaptvely. Fo example, t s potentally possble that GOTCHA optmses the numbe of ALSC pocesses dependng on the computng load by updatng dffuson polcy, e.g., a stcte dffuson ule s enfoced f less neghbous ae equed. An nta-bounday s modelled usng a dffuson equaton, by assumng that the confdence at cuent state flows out fom souces (.e., coect matches up to the cuent state untl t eaches equlbum. Ths s a moe accuate assumpton to c( x,0 1 ALSC( x (12 a Afte samplng contnuous tme t, (11 can be appoxmated as c( x,n 1 c( x,n {L x c( x,n L y c( x,n} (13 whee L x and L y epesent Laplacan opeatos n tems of x and y and n denotes the n th dscete tme. In the poposed method, a 7x7 wndow cented at a seed pont s used to defne a suppotng aea of dffuson,.e., the pevous matchng esults n ths wndow ae also taken nto consdeaton when defnng the neghbouhood of a cuent seed pont, and a degee of dffuson s contolled by and the numbe of teatons,.e., n n (13. Fg. 4 demonstates a esult of an nte-bounday estmaton. Fg 4(a shows a confdence map of 1793 teponts obtaned fom a egon R 1 (see Fg. 3(b afte 618 teatons of a GOTCHA pocess. The whte box shown n both mages llustates a wndow used to defne a suppotng aea of a seed pont at (268, 780. The seed pont poduces 13 neghbous when n = 5 and they ae shown as hghest confdence values n Fg. 4(b fo vsualsaton. 4. EXPERIMENTAL RESULTS (a (b The poposed method has been mplemented n JAVA and the algothm tested n a mult-coed sngle pocesso system. Thus, n ode to test paallelsed tasks wth a sngle pocesso, the poposed method has been desgned to un a sngle pocessng task wth multple theads. Also, snce we ae only focussed on the task paallelsm and do not nvestgate the effect of computatonal load balancng and the delay fom the data tansfe, dect compason wth the esult fom a C mplemented paallel algothm n MIMD achtectue s unavalable. Howeve, t s stll possble to pedct ts mpact fom the nomalsed pefomance gaph shown n Fg. 5. To compae a tadtonal GOTCHA wth MT-GOTCHA s havng a dffeent numbe of seed ponts, we fxed the numbe of GOTCHA teaton, = 200 (see Fg. 2 and aveaged pocessng tme was measued to count the total pocessng tme of MT-GOTCHA because some of the GOTCHA s may temnate eale than othes n the poposed method. Fou pefomance measues, such as peak memoy usage (Max. 823 Fgue 4 Example of a cluste of local neghbous, whee a confdence map of R 1 obtaned fom Fg. 3(b (a and local neghbous found by an nte-bounday at pont (268, 780 (b. descbe the gowth of a seed than a geneal dea that a matchng possblty of a pont pa s exponentally educed as t goes away fom known tue matches. Suppose c( x, t s a functon that estmates a matchng confdence at tme t and assume t s dffeentable, then a dffuson of confdence s gven as c( x,t 2 c( x,t t (11 whee s a dffuson coeffcent and matchng ntal confdence at x s defned as Fgue 5 Pefomance esults of the MT-GOTCHA algothm 547

6 Intenatonal Achves of Photogammety, Remote Sensng and Spatal Infomaton Scences, Vol. XXXVIII, Pat 5 [MB], the numbe of added ponts (Max [pts], total pocessng tme (Max [sec], and a ato of tepont addton (Max [pts/sec], has been used to evaluate the pefomance of algothms and Fg. 5 epesents them as *,,O, and, espectvely. Fom the test esults we can conclude that a tadtonal GOTCHA pefoms wost n tems of the ato of the tepont addton (381 [pts] / [sec], whlst all MT- GOTCHA s poduce smla esults. Howeve, GOTCHA shows the smallest peak memoy (339 [MB], whch s nceased as the numbe of seeds nceases n MT-GOTCHA. Fo example, MT- GOTCHA wth 4 seed ponts can acheve a 597% ncease n the numbe of added teponts at cost of a 143% ncease n peak memoy usage. To demonstate econstucton completeness, the poposed paallel egon-gowng algothm has been appled to steeo mages fom NASA Mas Exploaton Rove msson. Fg. 6 shows that the esultng dssmlaty maps (a-(b and dspaty maps (c-(d fom GOTCHA and MT-GOTCHA. In Fg. (a-(b the bghte ed ndcates smalle dssmlaty whlst Fg.6 (a- (b uses a bghte colou to epesent a lage dspaty. poposed MT-GOTCHA can acheve consdeable speedup at easonable cost of memoy consumpton. ACKNOWLEDGEMENT The eseach has eceved fundng fom the Euopean Communty s Seventh Famewok Pogamme (FP7/ unde gant ageement n "PRoVsG" REFERENCES Auenhamme, F., Voono dagams - a suvey of a fundamental geometc data stuctue. ACM Computng Suveys, 23(3, pp Foutune, S., A sweeplne algothm fo Voono dagams. In: Poceedngs of the second annual symposum on Computatonal geomety, pp Guen, A. W., Adaptve least squaes coelaton: a poweful mage matchng technque. South Afcan Jounal of Photogammety, Remote Sensng and Catogaphy, 14, pp (a (b Holden, J., M. J. Zemely, and J.-P. Mulle Paallel steeo and moton estmaton. John Wley & Sons, Inc., New Yok, Amstedam, pp Km, T. and J.-P. Mulle, Automated uban aea buldng extacton fom hgh esoluton steeo magey. Image and Vson Computng, 14(2, pp Km, T., A Study on the eppolaty of lnea pushboom mages. Photogammetc Engneeng & Remote Sensng, 66(8, pp Ohta, Y. and Takeo Kanade, Steeo by nta- and ntescanlne seach usng dynamc pogammng. IEEE Tans. Patten Analyss and Machne Intellgence, 7(2, pp Otto, G. P., Rectfcaton of SPOT data fo steeo mage matchng. In: Intenatonal Achves of Photogammety and Remote Sensng, 27(B3, pp (c (d Fgue 6 An example of dssmlaty map fom GOTCHA (a and MT-GOTCHA (b; a dspaty map (c fom (a and (d fom (b The completeness atos ae 52.93% and 52.88%, espectvely, so that GOTCHA s slghtly bette but t ncludes false teponts n the aea adacent to the sky and MT-GOTCHA wth a sngle seed s 3.5 tmes faste than GOTCHA. Otto, G.P. and T.K. W. Chau, Regon-gowng algothm fo matchng of tean mages. Image and Vson Computng, 7(2, pp Schasten, Danel and Rchad Szelsk, A taxonomy and evaluaton of dense two-fame steeo coespondence algothms. Intenatonal Jounal of Compute Vson, 47(1, pp CONCLUSIONS Ths pape has pesented a paallelsed steeo egon gowng algothm, focussng on task paallelsm fo GOTCHA. In the poposed method, multple GOTCHAs ae pefomed afte pattonng a steeo mage accodng to the estmated ntebounday of ntal seed ponts. Also, t has been desgned to employ multple ALSC opeatons smultaneously n each GOTCHA. The numbe of ALSCs s contolled nta-bounday of a seed pont, whch s estmated by the poposed confdence dffuson equaton. The expemental esults demonstate the 548