THE PRACTICE OF AUTOMATIC SATELLITE IMAGE REGISTRATION

Transcription

1 THE PRACTICE OF AUTOMATIC SATELLITE IMAGE REGISTRATION Yao Janchao and Cha Ten Chern Sgnal Processng Laboratory, DSO Natonal Laboratores Scence Park Drve, Sngapore 1183 Tel: 65) Fax : 65) {yjancha,ctenche}@dso.org.sg KEY WORDS: Iage Regstraton, Intensty Matchng, Projectve Model, Levenberg-Maruardt Algorth, Robust Estaton ABSTRACT: In ths paper, a new algorth for satellte age regstraton was developed. The an characterstc of the algorth s to algn two ages autoatcally, wthout requrng ether control ponts or sensor s paraeters. Two knds of odels, charactersng the age varablty between ages, were utlsed. One s projectve odel, accountng for geoetrcal varaton. The other s the polynoal llunaton change odel, accountng for the varaton n llunaton at dfferent te. These two odel paraeters can be sultaneously estated va the ntensty atchng, usng the Levenberg-Marquardt nsaton fraework ncorporated wth ult-resoluton and ultple odel strategy. The algorth has been verfed by an ntensve experent on a great nuber of real ages, taken by satellte, dgtal and frae caera. The Experental result deonstrates the robustness, effcency and accuracy of the algorth. 1. INTRODUCTION Satellte Iage regstraton s a crucal underlyng process for applcaton such as osackng, change detecton, cloud reoval and dgtal elevaton odel reconstructon. Coercal software, such as ErDas, utlses control ponts or sensors nforaton to pleent age regstraton. However, nforaton on the control ponts or sensors nforaton ay not be readly avalable or accurate enough, the regstraton based on such nforaton s therefore lted and ay even be naccurate. Another dsadvantage of usng control ponts for age regstraton s that too uch anual work s nvolved. It s ndeed a tedous work for user to nput so any correspondences on both of the ages va an nteractve way. Therefore, the functonalty of autoatc satellte age regstraton s uch requred. Although the autoatc regstraton technques have been well developed for the applcaton of vdeo osack Gregory D al 1998, LG Brown 199, P.Anandan 1988, R.Szelsk al. 1997), a challenge was faced when these technques are appled for regstraton of aeral photograph or satellte age, due to the followng reasons. In the frst place, snce the satellte ages to be algned are usually taken at dfferent te or even dfferent da and dfferent locaton, the brghtness constancy assupton, whch underles the coon ntensty atchng approach, s volated. Therefore, we have to take the llunaton change nto account for successful regstraton of two satellte ages contanng llunaton varatons. Although the generalsed brghtness odel to account for unfor photoetrc varaton.e. αi+β, where α and β are the llunaton ultplcaton and bas factors) was wdely used n vdeo/age processng, ths odel cannot however account for spatally varyng change of llunaton exstng n satellte age par. Secondly, because satellte ages are taken at dfferent te, there ay be soe envronent change durng the nterval. For nstance, the cloud ay be present when the frst age was captured, and t ay have dsappeared when the second age was taken. In such a case, the algorth should have certan knd of echans to detect autoatcally whch pxel s an outler correspondng to cloud), and whch pxel s an nler, n order to do a successful regstraton. To overcoe these probles, a generalsed dynac age odel s used n the paper, whch assues the llunaton ultplcaton and bas factor to be functons of locaton. We assue that these two llunaton factors are slowly varyng functons of locaton, thus they can be well approxated by low-order polynoals of poston varables. The satellte age regstraton s then forulated as an energy nsaton proble to estate the projectve transforaton paraeters accountng for the age varablty caused by poston change of caera, as well as llunaton polynoal coeffcent accountng for varaton n llunaton at dfferent te. The fraework and new algorth for estatng such a set of paraeters were developed. In order to ncrease the speed of estaton, the ult-resoluton and ult-odel schee was pleented. In addton, the robust estaton fraework was ntegrated n the algorth so that the erroneous easureent or the easureents not consstent wth ajort s treated as outlers and ther nfluence on estaton s reduced. In ths way, the algorth has the capablty of dealng wth partal occluson and ultple oton. The experental results deonstrated that the algorth s of robustness, effcency and accuracy.

2 . THE FORMULATION OF IMAGE REGISTRATION The conventonal age regstraton algorths, n partcular age ntensty atchng approach, are based on the brghtness constancy assupton gven as follows: g x, y ) = f x, 1) Where f and g are the age ntensty functons at te t 1 and t respectvely. Soe prevous work utlsed a generalsed brghtness odel to account for unfor photoetrc varaton,.e., g x, y ) = α f x, + β ) Note that the constants α and β are the llunaton ultplcaton and the bas factors respectvely. However, ths odel cannot account for spatally varyng llunaton varatons. To overcoe ths restrcton, a generalsed dynac age odel s proposed S. Negahdarpour, 1998) by assung the llunaton ultplcaton and bas factor α and β) to be functons of locaton x,. In ths paper, we assue these two llunaton factors are slowly varyng functons of locaton, thus they can be well approxated by low-order polynoal of poston varables x, as follows. g x, y ) = α x, f x, + β x, 3) Where α x, and β x, are the low-order polynoal functons wth the coeffcents represented by = 1 p 1 = 1 p 1 α α, α, α ) and β β, β, β ) respectvely. In our pleentaton, for splcty, we eployed a blnear odel for the llunaton ultplcaton functon and a constant functon for the llunaton α = bas. In ths sple case, α, α, ) and β ). It can be readly extended to a ore coplcated 1 α β = case. The coeffcents of these two polynoal functons can be deterned sultaneously wth the geoetrc transforaton paraeters. The geoetrc transforaton n the age atchng for planar objects can be strctly represented by a projectve transforaton. For projectve transforaton, The poston relatonshp between a par of correspondng ponts can be wrtten as: o x + 1 y + = x + y x ; y = 4) 6 7 x + y + x + y Where = {, 1, h7} s the paraeter vector for a projectve odel. The error functon between two fraes after projectve transforaton wll be represented as: g x, y ) x, y ) f x, y ) β x, y ) α 5) The algnent of two ages s to fnd such optal paraeters,α, that nse a weghted su of errors,.e., E = w x y g x, y ) α x, y ) f x, y ) β, )) 6) It should be notced that w s the weght assocated wth the data constrant coputed at the locaton x, y ). The weghtng allows us to ncorporate robust estaton nto our nsaton fraework, whch s accoplshed by dynacally adjustng the weght for each constrant approprately based on ts resdue. Snce equaton 6) s a nonlnear nsaton proble, we have to use the teratve non-lnear nsaton algorth, say Levenberg- Marquardt algorth, to obtan the optal values of,α, β β. As we know, n order to ake the algorth to converge to global nu, the ntal estate of,α, should be close to the soluton. In our approach, the ntal paraeters s obtaned by pseudo sulated annealng approach ncorporated wth ultresoluton and ultple odel strategy, t s then refned va Levenberg-Marquardt algorth based on ntensty-based atch. 3. THE DESCRIPTION OF THE ALGORITHM 3.1 Robust estaton Va Dynac Weghtng β

3 Snce ages ay contan partal occluson, ultple oton and perturbaton nose, robust estaton technque was used n the paper. In the robust estaton approach, the quadratc functon of resdue used n least-squares estaton s replaced by a ρ-functon, whch assgns sall weghts for the constrant wth larger resdues. There are a few eber of ρ-functons used n age processng, we used Lorentzon functon n the paper, whch s gven as follows: ρ x x, σ ) = log1 ) σ LO + where x s the resdue of data constrant and σ s the scale paraeter. When usng the ρ-functon for odel fttng, the nfluence for each data constrant to the soluton s charactersed by an nfluence functon, whch s the dervatve of the ρ-functon. If we take the dervatves of the above functon, we can obtan the nfluence functon as follow x ψ x, σ ) = σ + x The nfluence functon decrease as the agntude of the resdue ncreases. For the least-square estaton, the nfluence functon s lnearly ncreasng as the agntude of the resdue ncreases. Therefore the least-square estaton s ore senstve to outlers than the robust estaton. To use robust estaton n our nsaton fraework, we can sply replace the quadratc functon n 6) by above ρ-functon, Ths yelds the followng new objectve functon E, α, β ) = w ρ r, σ ) = w g x y x y f x y x y LO ρ LO, ) α, ), ) β, ), σ ) 7) 3. Optsaton Algorth Once the ntal estate of both projectve and llunaton odel paraeter were gven, we can solve the nsaton proble of 7) by usng Levenberg-Marquardt algorth. The algorth requres coputaton of the partal dervatves of r defned n 7) wth respect to projectve odel paraeters {, 1, 7} and α = llunaton paraeters α, α, ) and β ). These are straghtforward to copute. For exaple, r r α 1 α β = x g r y g g =,, = ; x + y D x 7 D x y r r = f x, y ), = x f x, y ), = 1 α β Where x + y 1 1 g g D = and, ) x y s the age ntensty gradent of g at x, ). Fro these partal dervatves, we constructed the followng teratve procedure based on the Levenberg-Marquardt algorth: = α β 1. Intalse odel paraeter c,, ) based on ntal value estaton procedure dscussed later. The ntal σ was selected to be large enough so that the robust estaton s very uch lke the least-squares estators at begnnng. Set the teraton ndex k=;. Copute the resdues r and the assocated gradent vector gad 3. Copute the weght τ assocated wth each data constrant by r = c based on equaton 8). τ = w ρ r ) r 4. For the weghted Hessan atrx and the weghted gradent vector H gad gad, b = r gad τ. y = τ 8) T

4 5. Update the oton paraeter estate c by an aount stablsaton paraeter. 6. Update the scale paraeter σ = / 7. Set τ r τ c k + 1 = c k + c and k=k+1; f = c, stop ; else go back to step 1 c = H + λ I) b, where λ s a te-varyng The advantage of usng Levenberg-Marquardt over straghtforward gradent descent s that t converges n less teraton. 3.3 Intal value estaton In order to provde the algorth wth good stablty and lockng capabltes, a coarse-to-fne strategy s eployed n whch we construct a pyrad of spatally fltered and sub-sapled ages. In our pleentaton, fve-level of pyrad representaton of age was constructed. At the coarse level, we used translaton only odel; at second, thrd and fourth level, we used affne odel; and at orgnal resoluton of age, we used projectve odel. As n the fgure 1. Orgnal Iage 1 Projectve odel Regstraton Orgnal Iage 1st level lower resoluton Iage 1 nd level lower resoluton Iage o 1 3rd level lower resoluton Iage 1 Lowest resoluton Iage 1 o 5, 1,, 3, 4, Affne Model Regstraton 5, 1,, 3, 4, Affne Model Regstraton, 1,, 3, 4, 5) Affne Model Regstraton 5, ) Translaton Model regstraton Guaasan flter ) ) 1st level lower resoluton Iage nd level lower resoluton Iage 3rd level lower resoluton Iage Lowest resoluton Iage Fgure 1. Mult-resoluton and ultple odel strategy for age regstraton In the coarsest level, n order to estate the translaton ters and 5 correctly, we used pseudo sulated annealng approach. The paraeter space of and 5 was dvded nto non-overlappng subspace. The paraeter space of translaton s lted by age sze of that level, snce t s possble to fnd a translaton that s larger than age sze. In each subspace, the central pont of the subspace s taken as ntal value and runnng Gauss- Newton algorth sultaneously, the optal translaton paraeter s then obtaned va search for the nu energy aong converged ponts of all the subspace. The next level n the pyrad s then processed. The ntal estates at ths level are 1,,,,1, 5 ). These paraeter s further refned va LM algorth decrbed before. The output of ths level for the optal affne paraeters s {, 1,, 3, 4, 5}. There s the sae procedure for the thrd and fourth level. Fnally, the ffth level n the pyrad s processed at orgnal resoluton of age). The ntal estated at ths level s {, 1,, 3, 4,5,,}. These values s agan refned va LM algorth at ths level to output the fnal result of projectve odel paraeters. That s what we requred. 4. EXPERIMENTAL RESULT Fgure shows an exaple of algnent of two ages taken by aeral dgtal caera. The ages were taken under dfferent llunaton condton. In addton, geoetrc varaton between two ages s qute large. The orgnal denson of the age s 154x11. For such knd of ages, t s qute dffcult to algn the accurately by usng conventonal ultple odel and ult-resoluton algorth, snce ntal paraeter values of a odel are

5 far away fro zero. By usng our algorth, the regstraton result s shown n fgure c). The ultple odel paraeter value estated at dfferent resoluton s shown n table 1. Although these two ages contan large varaton n geoetry and llunaton, the algorth algns the precsely. Fgure 3 shows an exaple of algnent of two SPOT satellte ages. These two ages coe fro Pal Sprngs, Calforna. They are both SPOT panchroatc ages wth 1-eter resoluton. Autoatc regstraton of these two ages nvolves two cascaded steps. In the frst step, we got the projectve paraeter algnng frst pcture wth second one. The result s { }. Due to too uch age varablty between the, the transfored age or warped age) s not well algned wth second age. Therefore, n the second step, we conducted algnent between the warped age and second one agan. The estated paraeters s { }. Cobnng these two sets of projectve odel paraeters together, we obtan the ore accurate projectve odel paraeters that brngs the frst age to be algned wth second one precsely. The result s shown n fgure 3. c). 5. CONCLUSION In the paper, a new algorth for satellte age regstraton was developed. The algorth has the followng characterstcs. 1). The regstraton process s totally autoatc, wthout requrng ether control ponts or sensors paraeters. ). The robust estaton echans was ncorporated nto the algorth, thus allowng partal occluson and ultple oton; 3) Illunaton odel based on low-order polynoal functons used n our approach enhances the robustness of the algorth aganst llunaton changes. The Experental result deonstrates the robustness, effcency and accuracy of the algorth. REFERENC Gregory D. Hager, Peter N.Belhueur, Effcent Regon Trackng wth Paraetrc Models of Geoetry and Illunaton. IEEE trans. PAMI, vol., No. 1, pp L.G Brown, 199. A survey of age regstraton technques. ACM Coputng Surveys, Vol. 4, No. 4, pp M.J.Black and A.D. Jepson, 1998, EgenTrackng: Robust Matchng and Trackng of Artculated Objects Usng A Vew-based Representaton. Int. J. Coputer Vson, Vol 6, No. 1, pp P.Anandan, 1988., A coputatonal fraework and an algorth for the easureent of vsual oton. Int. J. Coputer Vson, Vol., No. 3, pp R. Szelsk and J. Coughlan, Splne-based age regstraton. Int. J Coputer Vson, Vol., No.3, pp S. Negahdarpour, Rovsed defnton of optcal flow : ntegraton of radoetrc and geoetrc cues for dynac scene analyss.. IEEE Tran. Patt. Anal. Mach. Intel. Vol., No. 9, pp 961~979 Table 1. Model paraeter estaton at dfferent level of pyrad Orgnal Resoluton st level lower Res nd level lower Res rd level lower Res Lowest Resoluton a) b)

6 c) Fgure. a)b) The orgnal ages, c) The algnent of frst age wth second one a) b) c) Fgure 3. a)b) Two SPOT satellte ages; c) The algnent of frst age wth second one