UAV global pose estimation by matching forward-looking aerial images with satellite images

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1 The 2009 IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems October -5, 2009 St. Lous, USA UAV global pose estmaton by matchng forward-lookng aeral mages wth satellte mages Kl-Ho Son, Youngbae Hwang, and In-So Kweon Abstract A global pose estmaton method of an Unmanned Aeral Vehcle (UAV) by matchng forward-lookng aeral mages from the UAV flyng at low alttude wth down-lookng mages from a satellte s proposed. To overcome the lmtaton of sgnfcantly dfferent camera vewponts and characterstcs, we use buldngs as a cue of matchng. We extract buldngs from aeral mages and construct a 3D model of buldngs, usng the fundamental matrx. We estmate the global pose of the vehcle by matchng 3D structure of buldngs wth satellte mages, usng a partcle flter. Expermental results show that the proposed approach s a promsng method to the global pose estmaton of the UAV wth forward-lookng vson data. I. INTRODUCTION OSE estmaton of an aeral vehcle s a fundamental and Pchallengng ssue n the aerospace communty. A global postonng system (GPS) s usually used for the localzaton of a vehcle. However, the GPS s unstable when there s jammng around the vehcle. Even though an nertal measurement unt (IMU) system can be appled to estmate the pose of the vehcle, The IMU system accumulates errors as tme goes on. Also, the system can only estmate a local pose of a vehcle wth reference to an ntal pose. A camera system can be a complementary soluton to overcome the above lmtatons. Although a camera system also has ts lmtatons, such as an aerosol, a weather condton and an llumnaton, t s not affected by jammng around the vehcle or the accumulaton of errors. In addton, t s the global localzaton method, f we can match aeral mages wth satellte mages, whch are geometrcally referenced. Varous works have been presented for the UAV pose estmaton usng a camera. Snopol et. al. proposed a localzaton algorthm, usng a GPS, an IMU and a camera system []. They estmated an ntal pose of the vehcle wth the GPS and IMU system and refned t wth a camera. Although ther results were good, the GPS and IMU have ther lmtatons, as descrbed above. A localzaton method matchng dgtal elevaton maps wth aeral mages has been suggested [2], and relatve and absolute UAV localzaton Ths research was supported by ADD project, A Study on IR Image matchng for estmatng UAV poston (No. UD069009ED), and by the Defence Acquston Program Admnstraton and Agency for Defense Development, Korea, through the Image Informaton Research Center at KAIST under the contract UD070007AD Kl-Ho Son s wth the ADD, Daejeon, Korea (correspondng author to provde phone: ; e-mal: khson@add.re.kr). Youngbae Hwang s wth the KAIST, Deajeon, Korea (e-mal : uncorn@rcv.kast.ac.kr). In-So Kweon s wth the KAIST, Daejeon, Korea (e-mal : skweon@ee.kast.ac.kr). (c) Fg.. Advantages of forward-lookng camera: down-lookng aeral mage; forward-lookng aeral mage; and (c) Amount of ground nformaton for each camera system. Fg. 2. SIFT matchng results (green rectangles are the SIFT descrptors and red lnes represent correspondng ponts). methods by matchng between satellte mages and down-lookng aeral mages have been studed [3]. Caballero et. al. estmated a relatve poston of the UAV by calculatng homographes among down-lookng aeral scenes wth the assumpton that the ground s a plane[4][5]. All these methods showed good results wth down-lookng camera systems because matchng between satellte mages and down-lookng aeral mages s feasble as a result of usng smlar vewponts. However, mages taken by a down-lookng camera tend to have blurred effects and lttle ground nformaton when a UAV navgates at low alttude and hgh speed, especally as shown n Fgure a and c. Although short exposure tme can reduce the blurred effect, mages can be too dark to obtan adequate nformaton from them. A forward-lookng camera system, however, can take well-focused and brght mages wth more ground nformaton (Fg. b and c). We propose a method of UAV global pose estmaton by /09/$ IEEE 3880

2 Fg. 4. Results of vertcal lne detecton: constructed ground quas-plane and ts normal vector; and vertcal lnes about the ground planes. Fg. 3. An llustraton of a matchng system for global pose estmaton of a UAV. matchng forward-lookng aeral mages wth satellte mages. The man problem of the matchng s the sgnfcant dfference n characterstcs, such as type of cameras and a wde baselne between forward-lookng mages and down-lookng satellte mages. Conventonal matchng schemes by the scale nvarant feature transform (SIFT) [6] algorthm usng appearance nformaton does not work well because of the wde baselne between two mages, as shown n Fgure 2. We detect SIFT descrptors n an aeral mage and fnd the best correspondng ponts n a satellte mage. It shows that most correspondence s false. Matchng two mages only usng appearance nformaton s dffcult because forward-lookng aeral mages contan sdes of buldngs, whereas down-lookng satellte mages have only rooftops of buldngs. We suggest a semantc matchng method between forward-lookng aeral mages and down-lookng satellte mages based on nformaton of buldngs to estmate a global pose of a UAV, as shown n Fgure 3. Frst, we detect buldngs n aeral mages based on cues that columns of buldngs are normal to the ground and buldngs nclude man-made regons and repeated patterns. Next, we construct a 3D model of the detected buldngs and fnd the relatve pose of the camera, usng structure from moton (SFM) [7]. Then, we project the 3D structure of buldngs to make mages, usng the azmuth and elevaton angles of the satellte. Fnally, buldng nformaton from the aeral mages and satellte mages s used to match the mages, and we estmate the global pose of a UAV. The paper s organzed as follows: Secton 2 explans the detals of the buldng detecton method n aeral mages; Secton 3 descrbes a method for 3D constructon and reprojecton of buldngs; Secton 4 dscusses the matchng method by consderng errors of estmatng ntrnsc and extrnsc camera parameters; Secton 5 presents the expermental results; and the concluson s dscussed n Secton 6. II. BUILDING DETECTION To detect buldngs from aeral mages, we generate canddates wth a cue that columns of buldngs are normal to the ground plane. Buldngs are then detected based on the observaton that buldngs are parts of the man-made regons and have repeated patterns. A. Detecton of the ground plane and ts normal vector We cannot construct an accurate 3D model of buldngs wth a seres of aeral mages by usng an SFM method because the dstance between the camera and the buldng s too long compared wth the sze of the buldng. However, we can construct the 3D ponts of the ground as a quas-plane through the SFM method, as shown n Fgure 4a [7]. Let ax + by + cz + d = 0 be the ground plane equaton. Then, ( abc,, ) s a normal vector of the ground plane. P, P2... Pk... PN( Pk = [ xk, yk, zk]) are the N number of constructed 3D ponts of the ground plane usng the SFM method. Then, all ponts have to satsfy the followng equaton: a b A = 0 c d, A P P PN 2 =. () Equaton () s the over constraned case of smultaneous equatons. We can solve the equaton usng sngular value decomposton (SVD). Once we estmate the normal vector of the ground plane, we can fnd the drecton of vertcal lnes to the ground plane n aeral mages by projectng the normal vector to the mage plane. Some 3D ponts from the buldngs wll result n erroneous results for detectng the normal vector of the ground plane, because the constructed 3D ponts of the ground plane are not plane but quas-plane. We therefore nclude a ± 5-degree error when detectng vertcal lnes n aeral mages. Fgure 4a shows the SFM results wth aeral mages that contan 3D ponts of the ground (blue ponts) and pose of the camera (red ponts) and a normal vector of the ground plane. If we estmate how the normal vector of the ground plane projects to the aeral mages, we can fnd the vertcal lnes about the ground plane n aeral mages, as shown n Fgure 4b. Our method detectng a drecton of 388

3 Gradent orentaton hstogram Bn Fg. 5. Tranng data for man-made detecton: ten representatve orentaton hstograms of tranng data for man-made regons; and Ten representatve orentaton hstograms of tranng data for the regons of the nature Gradent Orentaton Hstogram Bn vertcal lnes to the ground plane n aeral mages can be appled to the roll movement of the UAV because we estmate a drecton of vertcal lnes through fndng ground planes n aeral mages B. Man-made regon detecton Gven an nput mage, the man-made regon detecton can be consdered as a classfcaton problem for each patch (block, ste). Each patch can be classfed nto the man-made regon or the non-man-made ones. Let Y be the observed data as Y = ( y ) M th m m=, where ym s the data from the m ste. Let the correspondng labels at the mage ste be gven by X = ( x ) M m m=, where x m = {0,}. 0 means that the selected patch s a natural regon, and means the patch s a man-made regon. We use a gradent orentaton hstogram classfer because man-made objects usually contan structures, such as lnes, corners and Y junctons, whch have a domnant edge. To capture these characterstcs, the nput mage s convolved wth the dervatve of Gaussan flters to yeld the gradent magntude and orentaton at each pxel. Then, for an mage patch, the gradents are combned to yeld a hstogram over gradent orentatons. We weght each count by the gradent magntude at each pxel and normalze the hstogram nstead of ncrementng the counts n the hstogram [8]. Then, the hstogram s shfted n order to make the domnant orentaton drecton be n the frst bn. Ths shft procedure makes features be orentaton nvarant. We defne C as: ( H H M < H α H C( y ) = 0 ( H H M H α H α = arg mn H H k M k β = arg mn H H k N k where H s a vector that contans the orentaton hstogram of the -th patch. HM s a set of representatve hstogram vectors extracted from tranng data correspondng to man-made regons where H M s a k-th vector. k H N s a set of vectors and H N s the k-th vector correspondng to the k natural regons. To extract 0 representatve hstograms, we elmnate the outlers, usng a cross-valdaton algorthm, and make 0 representatve models of a hstogram by the K-mean Nβ Nβ ) ) (2) (3) (4) (c) Fg. 6. Results of man-made regon detecton: aeral nput mage; man-made regon detecton before ICM; and (c) man-made regon detecton wth ICM and normal lnes about the ground plane n the man-made regon. clusterng algorthm. Equaton (2) means that an nput patch s classfed nto the man-made regon f ts orentaton hstogram s closer to 0 man-made representatves than natural ones. Fgure 5 shows the 0 representatves of tranng data. Note that the hstograms of man-made regons have more than one sgnfcant peak n the hstogram because of the structures n patches. In contrast, the results from natural patterns are dstrbuted evenly. A sgnfcant dfference n hstograms between man-made and natural regons makes the classfer strong. We apply the terated condtonal modes (ICM) algorthm to use neghborhood nformaton because man-made regons usually gather together [9]. Fgure 6b s an nput mage and Fgure 6b showss detected results whose black regons mean non-man-made regons before applyng ICM. Fgure 6c shows the fnal results of man-made regon detecton wth ICM and normal lnes about the ground plane n man-made regons, as explaned n the prevous chapter. Because the sdes of buldngs are generally rectangles, we can generate canddates of buldngs wth two vertcal lnes. We construct all buldng canddates by combnng two vertcal lnes n man-made regons, as shown n Fgure7. C. Buldng decson algorthm among the remanng hypotheses We propose a buldng decson algorthm that selects true buldngs among the remanng buldng hypotheses. By observng that the buldng texture has repeated patterns due to the wndows or the brcks n the wall, we can use the man orentaton around the corner to detect buldngs. We rank all hypotheses that contan a common lne because an extracted lne can be a part of only one buldng. The score s estmated as below: 3882

4 Fg. 7. Rectangle-shaped buldng canddates wthn man-made regons. Score = # of corners whose man drecton s smlar to the man drecton of the sum of the orentaton hstogram around corners - # of corners whose man drecton s dfferent to the man drecton of the sum of the orentaton hstogram around corners. Fgure 8a shows corners and ther man orentaton after excludng the ground normal orentaton drecton wthn the rectangle canddates, and Fgure 8b shows the sum of orentaton hstograms around the corners. The rectangle canddate s determned as a buldng because the man orentatons of the corners are smlar to the man drecton of the sum of orentaton hstograms around the corners. Fgure 9 shows the outler case. Not only the sum of orentaton hstograms s randomly dstrbuted but also the man orentatons of the corners are almost random. III. 3D CONSTRUCTION AND REPROJECTION OF BUILDINGS A. Estmatng ntrnsc parameters n aeral mages We fnd the ntrnsc parameter usng mages that are collected from the UAV. If we assume that the ntrnsc parameter of the camera s fxed and the UAV moves n varous motons when t captures mages, we can estmate the ntrnsc parameter usng the dual absolute quadrc [9]. B. Estmatng extrnsc parameters n aeral mages We assume that the UAV navgates at low alttude to allow robust computaton of the fundamental matrx between consecutve aeral mages. We fnd the correspondng ponts among a sequence of aeral mages, usng the KLT algorthm [0]. After estmatng a fundamental matrx wth the correspondng ponts, we calculate the extrnsc parameters of the camera by decomposng the fundamental matrx and estmate the 3D structure of the buldngs by trangulaton [7]. Although the correspondng ponts between aeral mages have subpxel errors, there are some errors n the 3D structures of the buldng ponts because the ponts are trangulated usng only the fundamental matrx. We therefore consder these errors when defnng a cost-functon matchng between extracted buldng nformaton n aeral and satellte mages. The defnton of cost functon s explaned n secton 4. Orentaton hstogram Orentaton Fg. 8. Buldng detecton result: corner ponts and ther man orentaton except for the ground normal drectons; and sum of orentaton hstogram around the corner ponts. Orentaton hstogram Orentaton Fg. 9. Outler regons: corner ponts and ther man orentaton except for the ground normal drectons; and sum of orentaton hstogram around the corner ponts. We construct the 3D structure of extracted buldngs and relatve aeral camera poses, as shown n Fgure 0a. The orgn of the coordnate s the poston of the camera. The drecton of the postve z-axs s the prncpal axs of the camera. Rectangles show the 3D poston of buldngs. C. Projecton of constructed buldngs and cameras We can fnd azmuth and elevaton values of the satellte camera from the meta data of satellte mages. We project the constructed 3D structure of buldngs to the ground plane wth the azmuth and elevaton values of the satellte camera so that we can extract 2D nformaton of buldngs whose vewponts are the same as satellte mages, as shown n 3883

5 between the aeral camera and the buldngs s extremely long n a forward-lookng camera system. Therefore, we defne the cost functon, consderng the factors that severely affect 3D constructon, to estmate a homography: Fg. 0. Projecton of constructed buldngs and cameras: constructed 3D model of buldngs and relatve pose of an aeral camera; and mage of buldngs and a camera projected to the ground plane wth azmuth and elevaton of the satellte camera Fgure 0b. The trangle s the pose of an aeral camera and lnes show the buldng nformaton extracted from the aeral mages. IV. BUILDING MATCHING BASED ON NONLINEAR OPTIMIZATION The buldng nformaton from the satellte mages s extracted manually. We match two types of mages based on extracted buldng nformaton, such as a scale, poston and orentaton of buldngs. We also defne the cost-functon consderng errors n the 3D constructon of buldngs and mnmze t to match the buldngs extracted from aeral mages and satellte mages, usng nonlnear optmzaton methods. A. Cost functon, consderng 3D constructon error Once we fnd the 2D buldng nformaton from aeral mages and satellte mages, matchng problems can be translated to 2D 2D regstraton problems (.e., all we need to estmate s a homograhpy between two scenes that contan a scale, a rotaton and a translaton value). We defne the cost functon to fnd a homography. Although correspondng ponts between the aeral mages have a subpxel error, we have to consder that constructon of 3D buldngs from aeral mages can have erroneous results because we do not know the exact ntrnsc parameters and because the dstance between aeral cameras and buldngs s too long. Ths means that trangulaton results can have erroneous results. If we assume that there s no skew n an aeral camera, then there are two mportant factors affectng 3D constructon n ntrnsc parameters: a focal length n terms of pxel dmenson n the x and y drecton and a prncpal pont offset [7]. Problems n focal length n terms of a pxel dmenson result n the 3D constructon results havng a dfferent scale error n the x and y drecton. A prncpal pont offset error affects all the results of constructed buldngs. However, f scene depth s too large, prncpal pont error does not have much of an effect n constructng 3D models of buldngs [7]. The dstance between aeral cameras and buldngs s so great that we can neglect the error of prncpal ponts. If depth of the scene s too large, results of the trangulaton method are very senstve to the error of correspondng ponts, even though the correspondng error s n the subpxel range. We must consder trangulaton error because the dstance close α S( H l)/ S( l ) M close H = arg mn + βdh ( l l ) (5) H close + γ AH ( l) Al ( ) b b2 Tx H = b2 b22 T y (6) 0 0 b b2 B = b2 b (7) 22 B = R φ Λ R φ (8) ( ) ( ) cosφ snφ R ( φ ) = snφ cosφ λ 0 Λ= 0 λ 2 x x 2 l = y y2 (9) (0). () l s the extracted buldng lnes from aeral mages, where x and x 2 are the x coordnates of lnes at endponts and y and y2 are the y coordnates of lnes at endponts. A homography conssts of a scale ( Λ ),rotaton ( R ) and translaton ( T x, T y ) factors, as shown n Equaton (6). φ s a relatve angle of prncpal axs, and λ and λ2 are scale factors n the x and y drecton, respectvely. The scale factors complement error n focal length n the pxel range. M s the total number of the constructed buldngs from aeral mages. close l s a boundary lne of buldngs manually extracted n satellte mages and s the closest one to the -th lne of the buldngs constructed from aeral mages. We place the weght termsα, β andγ to be dependent on the depth of the -th buldng so that the cost functon compensates for the error of the trangulaton method. α β, γ and the others are defned as follows: α = β = γ = (2) Z 2 2 Sl ( ) = ( x, y) ( x, y) (3) D( l ) = ( x, y ) + ( x, y ) (4) 2 2 y y2 = x x2 Al ( ) tan ( ). (5) 3884

6 Z s the depth of the -th buldng. Functon S s used to calculate the length of lnes and functon D calculates the dstance between lnes. Functon A s used to compute the relatve orentaton angle of buldngs. Equaton (5) conssts of three smlarty measures of two types of buldngs, whch consder the scale, poston and orentaton of buldngs. The frst term n equaton (5) decreases f the sze of the buldngs s smlar to each other. The second and thrd terms also decrease f the poston and orentaton of buldngs are analogous to each other. B. Nonlnear optmzaton Our optmzaton problem has sx degrees of freedom. We cannot apply gradent methods to fnd the mnmum value of the proposed cost functon because t s not a convex. Therefore, we apply the partcle flter method, whch s an algorthm for samplng the probablty dstrbutons to fnd the global mnmum of the cost functon [2]. We ntalze the partcles accordng to the buldngs, whch are manually extracted from the satellte mage (.e., we construct the same number of partcles as the number of buldngs from a satellte mage). Each partcle s ntalzed by algnng the constructed buldng lne that s closest to the aeral camera wth a lne of buldngs n the satellte mage. For each partcle, we calculate a local mnmum value of the cost wth the gradent method. We then make new partcles n the form of a Gaussan dstrbuton, where the number of partcles defned accordng to the cost and varaton of the partcles s dependent on the number of the teraton of the gradent method. We teratvely do ths procedure several tmes. We do ths teraton fve tmes emprcally. Mnmum value of the cost functon n ths procedure determnes fnal matchng results. The uncertanty of n poston estmaton s defned as follow: U = #of partcles when generatng mnmum cost value total#of partcles. (6) V. EXPERIMENTS AND ANALYSES We tested our proposed method wth QuckBrd satellte mages, whch are rectfed wth shuttle radar topography msson (SRTM) as a dgtal elevaton model (DEM) and ground control ponts (GCP) for geo-referencng [3]. We appled our system to a set of aeral mages that has 56 by 34 resolutons. Fgure shows the results of buldng detecton. Rectangles n the mage are the detecton results of buldngs from the aeral mages. The proposed method detects the buldngs robustly as long as the buldngs satsfy the condtons. A number of UAV localzaton papers proposed verfcaton methods usng GPS or IMU systems [3]. However, t s very dffcult to obtan varous sensor data smultaneously, and synchronzaton of the sensors s not easy. Therefore, we manually verfed our methods. Fgure 2a and 2c show automatcally detected buldngs and ther labeled numbers for each buldng n aeral mages. Rectangles n Fgure 2b and 2d are the manually detected buldng data from satellte mages, and numbers n the mage are also the Fg.. Buldng detecton results from a seres of aeral mages labelng numbers of each buldng. Buldngs labeled as 9, 5, 6 and 7 n aeral mages are matched wth buldngs labeled as 9, 5, 6, and 7 n the satellte mage respectvely, as shown n Fgure2a and 2b. It s apparent that the automatcally extracted buldngs n an aeral mage and the manually extracted buldngs n a satellte mage are well matched. Red crcles n Fgure 2b and 2d are the estmated pose of the camera and ts uncertantes. The bgger crcles mean the hgher uncertantes. We appled our algorthms to key frames that are selected when correspondng ponts are frstly below 50 between aeral mages. Fgure 3 shows the fnal estmated results of the camera poses and ts uncertantes. Fgure 3b shows a set of aeral mages, wth numbers n the crcles of Fgure 3j beng correspondng camera poses. The closer the buldngs are to the camera, the more the pose of the camera become stable because the trangulaton error s reduced as the scene depth decreases. In Fgure 3, uncertantes are decreased as the pose of the camera s close to the buldngs except for the msmatchng case n aeral mage 7 (Fg. 3). If the buldng detecton method does not work well because the columns of buldngs are not detected, our algorthm fals, as shown n aeral mage 7 (Fg. 3). Lttle nformaton on the buldngs from aeral mages also results n method falure. Our method compared wth the GPS usng other aeral mages that has 320 by 240 resolutons, as shown n Fgure 4. The UAV fled to the buldngs that are detected n aeral mages and collected key frames from to 0 sequentally. Although buldngs n satellte and aeral mages are matched well, a proposed pose estmaton method s unstable compared wth GPS and has offset errors. Ths s manly because the trangulaton errors accordng to the scene depth. We can observe that the closer the UAV s to the buldngs, the more the pose of the UAV become stable and also the errors are reduced. VI. CONCLUSIONS We desgned a semantc matchng algorthm between forward-lookng aeral mages and down-lookng satellte mages based on relatonal nformaton of buldngs to estmate a global pose of a UAV. We detect buldngs n forward-lookng aeral mages by observng that the columns of buldngs are normal to the ground plane and the buldngs are part of man-made regons and have a repeated pattern. 3885

7 Fnally, we proposed a cost functon to match the buldng nformaton from aeral mages and manually detected connectons of buldngs from satellte mages, consderng errors n 3D constructon of aeral mages. Our system works well wth assumptons that the UAV fles around buldngs and the ground plane s flat. Also, our system s not real tme. Even though there are lmtatons to our algorthm, our proposed approach shows a promsng soluton to pose estmaton of a UAV wth only forward-lookng camera data. For more accurate and robust pose estmaton, we wll carry out addtonal studes on how to combne road nformaton wth our current work. (c) REFERENCES [] Bruno Snopol, Maro Mchel, Ganluca Donato, T. John Koo, Vson Based Navgaton for an Unmanned Aeral Vehcle, Internatonal Conference on Robotcs and Automaton, 200. [2] Kumar. R., Sawhney. H. S., Asmuth. J. C. Pope. A. Hsu. S., Regstraton of vdeo to geo-referenced magery, Fourteenth Internatonal Conference on, 998. [3] D.-G. Sm, R.-H. Park, R. C. Km, S. U. Lee, and I. C. Km, Integrated poston estmaton usng aeral mage sequences., IEEE Trans, Pattern Anal. Machne Intell., Vol. PAMI-24 no., pp. -8, Jan [4] Fernando Caballero, Lus Merno, Joaqun Ferruz and Anbal Ollero, Improvng Vson-based Planar Moton Estmaton for Unmanned Aeral Vehcles through Onlne Mosacng, Internatonal Conference on Robotcs and Automaton, [5] Fernando Caballero, Lus Merno, Joaqun Ferruz and Anbal Ollero, Homography Based Kalman Flter for Mosac buldng. Applcaton to UAV pose estmaton, Internatonal Conference on Robotcs and Automaton, [6] D. G. Lowe, Object Recognton from Local Scale-Invarant Features", n Proceedngs of the IEEE Internatonal Conference on Computer Vson, 999. [7] R. I. Hartley and A. Zsserman. Multple Vew Geometry n Computer Vson. Cambrdge Unversty Press, Second Edton [8] S. Kumar and Martal Hebert, Man-Made Structure Detecton n Natural Images usng a Causal Multscale Random Feld", n Proceedngs of the IEEE Internatonal Conference on Computer Vson, [9] J. Besag, On the statstcal analyss of drty pctures, Journal of the Royal Statstcal Socety, 986. [0] Janbo Sh, Carlo Tomas, Good features to track, 994 IEEE Conference on Computer Vson and Pattern Recognton (CVPR'94), 994, pp [] B. Trggs. Autocalbraton and the absolute quadrc. IEEE Computer Socety Conference on Computer Vson and Pattern Recognton, pages , 997. [2] J.S. Lu, Monte Carlo Strateges n Scentfc Computng, Sprnger, 200 [3] (d) Fg. 2. Matchng results wth buldng nformaton: detected buldngs n aeral scene ; matched results between buldngs n aeral scene and buldngs n satellte mages; (c) detected buldngs n aeral scene 2; and (d) matched results between buldngs n aeral scene 2 and buldngs n satellte mages. uncertantes of pose for each aeral mage 3886

8 aeral mage (c) aeral mage 2 (d) aeral mage 3 (e) aeral mage 4 (f) aeral mage 5 (g) aeral mage 6 (h) aeral mage 7 () aeral mage 8 (j) UAV localzaton results accordng to aeral mages Fg. 3. Fnal results; uncertantes of UAV pose for each aeral mage; ~() red rectangles are detected buldngs and numbers are buldng label numbers; (j) numbers n crcles are the correspondng aeral mage number and crcles show the pose of the forward-lookng aeral camera. Red crcles are the results of the camera pose when the buldng match s successful, and blue crcles are the results of the camera pose when the buldng match has faled. Fg. 4. GPS and proposed results; yellow lnes are GPS results and red lnes are proposed results. Numbers are key frame number n aeral mages; errors between GPS and proposed results n Eucldan dstance. 3887