SPATIAL DATABASE UPDATING USING ACTIVE CONTOURS FOR MULTISPECTRAL IMAGES: APPLICATION WITH LANDSAT7

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1 SPATIAL DATABASE UPDATING USING ACTIVE CONTOURS FOR MULTISPECTRAL IMAGES: APPLICATION WITH LANDSAT7 Sylvi Jodouin, Layachi Bntabt, Djml Ziou, Jan Vaillancourt Départmnt d Mathématiqus t d Informatiqu Univrsité d Shrbrook, Canada {jodouin, bntabt, ziou, vaillanc}@dmi.ushrb.ca KEY WORDS: Activ contours, snaks, multi-spctral imagry, spatial data intgration. ABSTRACT This papr prsnts a fully automatd systm for ara dtction basd on satllit imags and topographic faturs from a databas. Th surfacs issud from th databas ar rfind using activ contours (also calld snaks according to updatd information providd by th multi-spctral imags. Th snak is rformulatd using finit lmnts, allowing for th procssing of smallr structurs thus low tim procssing. W propos a nw rnal nrgy masur through a formula by combining statistical and radiomtry faturs. Usually th snak modl is controlld by various paramtrs that ar difficult to st by a trial-and-rror procss. W propos an automatic stting of ths paramtrs and an updat of th snak topology. Th proposd updats allow th snak to b dformd in ordr to provid accurat localization. Our approach is validatd in a sris of tsts on LANDSAT7 imags. 1 INTRODUCTION Spatial databass ar gaining popularity as a rfrnc tool in many filds of application. Th spatial information providrs ar currntly concrnd by how to maintain data updatd and also how to incras its accuracy with limitd rsourcs. This problm could b ovrcom through imag procssing tchniqus, which allows incrasing accuracy of both gomtric and tmporal faturs. An incrasing numbr of mthods to updat spatial information basd on imag procssing bgan to appar in th latst yars. From th proposd mthods, w ar mostly intrstd with thos basd on th snaks. Th proposd approachs dal with diffrnt typ of imags, mainly with singl band imags issud from satllit or airborn and from diffrnt typ of snsors such as radar or optical (Auclair-Fortir t al 001, Bntabt t al 001, Horritt, Th snak modl is dfind according to th gomtry of th targt fatur. Som works prsnt linar snaks to sarch linar faturs such as roads (Auclair-Fortir t al 001, Bntabt t al 001 and othrs prsnt closd snaks to obtain a dscription of ara faturs such as watr rgions (Horritt, In this papr, w propos a mthod to updat xisting ara faturs from a givn spatial databas by th us of multi-spctral imags. Th availabl databas vctors provid an intrsting initialization for th ara localization procss. In this cont, th closd snak approach was prsntd as a natural solution. Th first contribution of this work is th formulation of th rnal nrgy of th snak that combins statistical and radiomtry information. Scondly, th snak paramtrs ar fixd automatically from th spatial databas and ar updatd during th localization procss. Finally, an fficint implmntation of th snak using finit lmnts provids accurat localization with low tim procssing. APPROACH A snak is dfind as a paramtric curv v(x,y=v(x(s,t,y(s,t which is allowd to dform from som arbitrary initial location within an imag towards th dsird final location. Thus, th us of snaks involvs a two stps procss bing an initialization and th itrativ minimizing procss. To initializ th snak, w first prform th 48

2 discrtization of th databas vctors. This opration is prformd using a finit lmnt mthod togthr with th approximation of th snaks with Hrmit polynomials. Th final snak location is obtaind through minimization procss acting upon an intrnal and an rnal nrgy function dfind as follows (Kass t al E ( t E ( t E ( t = int (1 tot + whr E (t is th rnal nrgy, E int (t th intrnal nrgy. As dscribd in classical snak modling approach (Auclair-Fortir t al 001, Bntabt t al 001, Horritt, 1999, Kass t al 1988, th intrnal nrgy acts as a stabilizr to th rnal data irrgularitis. Th standard intrnal formulation is givn as follow: E int ( ' ( + '' t v s, t β v ( s, t = ds α ( whr α and β ar rspctivly th lasticity and rigidity paramtrs. In this papr, w will laborat in mor dtail about th rnal nrgy and th stting of th snak paramtrs. 3 EXTERNAL ENERGY Th rnal nrgy rprsnts th imag forcs E (t attracting th snak. This nrgy is calculatd as follow: ( t F ( v( s t E =, ds (3 whr F (v(s,t is th calculatd forc attracting th snak towards th boundary of th rgion. In our cas, this forc is dfind through a combination of radiomtry and statistical information. Th radiomtry fatur is obtaind from a multi-band dg dtctor (Drwniok, This dtctor taks as input all bands of th multispctral imag and provids a singl dg map. Th statistical proprtis of th targtd ara ar computd assuming th rgions of intrst bing normally distributd. If w considr a population givn by th pixls within th initial ara providd by th databas through n bands, th man vctor and th covarianc matrix will b dfind as follow: T { } { x} C = E ( x m( x m m = E and (4 whr x is a radiomtry vctor of dimnsion n, E{arg} is th xpctd valu of th argumnt, T indicats vctor transposition. Th dimnsion of th matrix C is n n. Considring th radiomtry and statistical information issud for th imag, w obsrv th advantags and drawbacks of ach fatur. Indd, th dg dtctor allows accurat location of ara boundaris, but givs fals dgs for turd rgions and wk rspons insid th rgion. Th statistical fatur, it provids a good modl for turd rgions, but wk localization of ara boundaris. Within th actual framwork, th two faturs ar complmntary in thir strngth and waknss. Indd, th statistical information givs good information insid th rgion compard to th dg map that provids accurat location of th rgion limits whn w gt closr to th contour. Considring ths facts, th rnal forcs applid on th snak ar obtaind by a wightd combination of both statistical and radiomtry basd valus. For clarity in th following formulas, w will work for a givn tim t=t 0 and omit this tim argumnt. Th rnal forc at th curvilinar abscis on th snak is dfind as follows: F ( v( s Grad max 1 Grad ( v( s ( 1 Dist( v( s man,0 = τ τ (6 49

3 whr τ [0,1] is a calculatd wighting combination valu, Grad(v(s is th multi-band dg dtctor rspons, Grad man is th man valu of th gradint valuatd for th spcific typ of rgion according to th hol imag. Th Dist(v(s valuats th proximity of a pixl to th statistical proprtis of th rgion. From this formulation, w can obsrv that whn a masur of th rnal nrgy is takn insid th rgion, th first trm of quation (6 (radiomtry masur is clos to on. Thus, th statistical masur is prioritizd. Also, whn th masur is takn nar a high dg valu, th first trm is clos to zro and cancls th ffct of statistical. This obsrvation allows th following dynamic formulation for th τ argumnt: ( v( s Grad τ = k min, 1 (7 Grad man whr k [0,1] is a wighting constant. Th Dist(v(s function in quation (6 can b dfind using th Mahalanobis distanc. Th Mahalanobis distanc not only looks at variations (varianc btwn th rang for on spctral band, but also at th intr-spctral lvl (covarianc. Thus, th Mahalanobis distanc dfins a multi-dimnsional mtric spac whos boundaris dtrmin th rang of variation that is accptabl for unknown sampls to b classifid as mmbrs of th population. This Mahalanobis distanc for a sampl x from m is dfind as follow: T 1 ( x-m C ( x-m (8 Sinc w assum that x follows a gaussian distribution, w know that th Mahalanobis distanc follow a distribution (Saporta, 1990 with n dgrs of frdom (n bing th numbr of bands for th multi-spctral imag. Thus, w can st a thrshold valu basd on som confidnc valu (1% for instanc. This thrshold valu will srv to normaliz th calculatd Mahalanobis distanc for tstd sampls and also to idntify outlirs. Thus, th Dist(v(s function is dfind as follow: χ Dist ( v( s = T 1 ( v( s m C ( v( s m thrsholddist (9 whr thrsholddist is givn by th χ tabl valu according to th dimnsion of th data and to th dsird confidnc valu. 4 FINITE ELEMENTS As mntiond arlir, th databas vctors srv to initializ th snak using a finit lmnts approach. Th finit lmnts approach offrs accurat discritization of drivativs and optimizs tim procssing sinc it has fwr lmnts to cop with. Th intrstd radr will find all dtails in Bntabt t al (001. To summariz, th discrtizing of th paramtric curv v(s into finit lmnts lads to an xprssion for ach lmnt givn by: v s = N s V (10 ( ( [ ] whr L dnots row vctors and [ L ] matrics or column vctors. N(s is th st of intrpolation curvs. In our cas, w usd a Hrmit basis functions N ( s N ( s,, N ( s 1, K m dfining th form of th intrpolating curv. V is a two-column matrix [ ] Y X, of control nods insrtd at rgular intrvals of th initial curv issud from th databas. Th global nrgy minimization is prformd using th Eulr Lagrang quation ( E tot =0. This lads to th following diffrntial quation: 50

4 ( s,t v t αv '''' ( s,t + βv ( s,t E = ( v( s,t '' γ (11 whr γ controls th spd of volution of th snak. Equation (11 is discrtizd using th finit lmnts dtaild in Bntabt t al (001. Th final itrativ quation is givn as follow: 1 T ( = + γ V n+ 1 T I K VnT FnT (1 γ T whr I is th N N idntity matrix. K is an N N matrix which dpnds on α, β and th shap of th intrpolating curvs. Th Hrmit polynomial bas dtrmin th lmnts of K. V nt givs th location of th lmnt nods at itration n. v 5 SNAKE PARAMETERS From th xprinc of xisting works, it has bn stablishd that it is difficult to st th rigidity and th lasticity paramtrs of th intrnal nrgy of th snak corrctly (Horritt, Indd, thy ar usually fixd within a lngthy trial-and-rror tsting procss. In this work, w stimat th rigidity paramtr β from th avrag curvatur of th initial databas vctors as follow: ( 1 curv β = (13 β max whr β max is th maximum valu assignd to th rigidity parmtr, curv is a masur of th avrag curvatur of th snak initialization using th sgmnt of th databas. β is valuatd knowing that th rigidity paramtr is invrsly proportional to th snak curvatur. This paramtr stting mthod was proposd and is dscribd in mor dtail by Bntabt t al (001. Th lasticity paramtr α is st to a valu nar zro in ordr to allow th snak to strtch according to th rnal nrgy only. Whil th minimization procss is running, th snak paramtrs ar dcrasd in paralll in ordr to nabl th snak to fit accuratly to th high curvd parts of th ara bordrs. Multiplying thm with a constant factor smallr than on (0.75 for instanc allows th dcras of th snak paramtr valus. Also, updating th control nods of th snaks optimizs th itrativ nrgy minimization procss. Indd, thr principal oprations ar prformd: addition of nw control points as th snak xpands, dltion of control points according to th local curvatur of th snak and lastly, th stopping of control points whn th optimal locations ar rachd. 6 ALGORITHM Th proposd algorithm taks as input th ara vctor databas coordinats and a multi-spctral imag of th sam rgion. This algorithm can b summarizd as follow: Prform multi-spctral dg dtction; For vry ara vctor to updat from th databas: Comput th statistics of th rgion using quation (4; St th initial α paramtr and comput th initial β paramtr using quation (13; Until th snak nrgy is not minimum: Comput th rnal forc of th snak from quation (6; Comput th nw location of th rgion using quation (1; Dcras th snaks paramtrs; If ndd: Adjust th snak topology by r-sampling control points and/or stopping control points. 51

5 7 EXPERIMENTAL RESULTS Th proposd approach was xprimntd on Landsat7 imags using 7 bands to updat faturs of th Canadian National Topographic Databas (NTDB. Th prsntd rsults in figur 1 show two kinds of pattrnd aras. Th rgion 1 and rprsnt watr rgions that ar charactrizd by a low varianc and a high valu for th gradint. In contrast, rgion 3 dfins a claring in a forstd ara. This surfac is charactrizd by a high varianc and low gradint. Th flxibility of wighting btwn statistics and gradint allowd us to dal with ths two kinds of pattrnd aras providing gratr localization accuracy. Th final snak locations ar drawn ovr th fourth radiomtric band of th Landsat imag portion. To visually valuat ths rsults, on should considr that othr radiomtric bands of th imag might contain complmntary information that cannot b sn on th imag whr th rsults ar displayd. 8 CONCLUSION Our work dmonstrats th importanc of using snaks and multi-spctral imags for updating xisting spatial ara information. W combind statistics and radiomtry for th rnal nrgy. An fficint implmntation using finit lmnts has bn proposd providing accurat localization. REFERENCES Auclair-Fortir, M.F., D. Ziou, C. Armnakis and S. Wang, 001. Automatd Corrction and Updating of Road Databass from High-Rsolution Imagry, Canadian Journal of Rmot Snsing, Vol. 7, no. 1, pp Bntabt, L., S. Jodouin, D. Ziou and J. Vaillancourt, 001. Automatd Updating of Road Databass from SAR Imagry: Intgration of Road Databass and SAR Imagry information, Procdings of th Fourth Intrnational Confrnc on Information Fusion, Vol. WA1, pp Drwniok, C., Multi-Spctral Edg Dtction: Som Exprimnts on Data from Landsat-TM, Intrnational Journal of Rmot Snsing, Vol. 15, no. 18, pp Horritt, M.S., A statistical activ contour modl for SAR imag sgmntation, Imag and Vision Computing, Vol. 17, pp Kass, M., A. Witkin, and D. Trzopoulos, Snaks: Activ Contour Modls, Intrnational Journal of Computr Vision, Vol. 1, no. 4, pp Saporta, G., Probabilité analys d donnés t statistiqu, Édition Tchnip, ISBN:

6 Band-1 Band- Rgion 1 Rgion Band-3 Band-4 Rgion 3 Band-5 Band-6 Band-7 Snak Localization Figur 1: Exprimntal rsults with Landsat 7 imags for two typs of ara. Dpartmnt of Natural Rsourcs Canada. All rights rsrvd. 53