RIGOROUS GENERATION OF DIGITAL ORTHOPHOTOS FROM EROS A HIGH RESOLUTION SATELLITE IMAGES

Transcription

1 ISPRS SIPT IGU UCI CIG ACSG Table of contents Table des matères Authors ndex Index des auteurs Search Recherches Ext Sortr RIGOROUS GENERATION OF DIGITAL ORTHOPHOTOS FROM EROS A HIGH RESOLUTION SATELLITE IMAGES Lang-Chen CHEN and Tee-Ann TEO Center for Space and Remote Sensng Research, Natonal Central Unversty, 3 Chung-L, TAIWAN Tel: ext76 Fax: Emal: lcchen@csrsr.ncu.edu.tw Commsson IV, WG IV/7 KEY WORDS: EROS A Satellte Images, Orbt Adjustment, Least Square Flterng, Orthorectfcaton ABSTRACT: As the resoluton of satellte mages s mprovng, the applcatons of satellte mages become wdespread. Orthorectfcaton s an ndspensable step n the processng for satellte mages. EROS A s a hgh resoluton magng satellte. Its lnear array pushbroom mager s wth.8meter resoluton on ground. The satellte s sun-synchronous and samplng wth asynchronous mode. The man purpose of ths nvestgaton s to buld up a procedure to perform orthorectfcaton for EROS A satellte mages. The major wors of the proposed scheme are:() to set up the transformaton models between on-board data and respectve coordnate systems, () to perform correcton for on-board parameters wth polynomal functons, (3) to adjust satellte s orbt usng a small number of ground control ponts, (4) to fne tune the orbt usng the Least Squares Flterng technque and, (5) to generate orthomage by usng ndrect method. The experment ncludes valdaton for postonng accuracy usng ground chec ponts.. INTRODUCTION The generaton of orthomages from remote sensng mages s an mportant tas for varous remote sensng applcatons. Nowadays, most of the hgh resoluton satelltes are usng lnear pushbroom arrays, such as IKONOS, Qucbrd, EROS and others. From the photogrammetrc pont of vew, base on the collnearty condton equatons; bundle adjustment may be appled to model the satellte orentaton (Guaan and Dowman 988, Chen and Lee 993). Ths approach needs a large number of ground control ponts (GCPs). Chen and Chang (998) used on-board data and a small number of GCPs to buld up a geometrc correcton model for SPOT satellte mages. Smlarly, we wll propose to use the on-board orbtal parameters and GCPs to calbrate the satellte orbt. After orbt modellng, we wll develop an ndrect method to do the mage orthorectfcaton.. CHARACTERISTICS OF EROS A SATELLITE EROS A was launched by ImageSat Internatonal (ISI) on the 5 th of December,. It s expected to have at least four years of lfetme. Its orbt alttude s 48m wth 97.3 degrees orbt nclnaton, whch mae the satellte sun-synchronous. Usng ts body rotaton functon, the satellte s able to turn up to 45 degrees n any drecton. Its lnear array pushbroom mager s wth.8meter resoluton on ground and.5degree of feld of vew. Table shows the characterstcs of EROS A satelltes. EROS A satellte taes mages wth asynchronous mode. It allows the satellte to move n a faster ground speed than ts rate of magng. The satellte actually bends bacwards to tae ts mages n an almost constant, predetermned angular speed, enablng ts detectors to dwell longer tme over each area. In ths way, t wll be able to get lghter, and mprove contrast and the satellte orbt s longer than the samplng area. In the best condton, the rato of satellte orbt to samplng area s about to 5 Table I. The characterstcs of EROS A satelltes ITEM Orbt Alttude Orbt Inclnaton Orbt Pass rate Body Rotaton Mode of Operaton Scannng Mode Stereo pars Sensor Type Swath Wdth Ground Samplng Dstance Focal Length Slant Angles Feld of Vew EROS A Specfcaton 48m 97.3 Deg 5.3 orbts/day Yes Push Broom Scannng Asynchronous (up to 75 lnes/sec) In Trac, Cross Trac CCD.5m.8m (PAN) 3.4 m 45 Deg.5 Deg Pxels-n-lne 78 Spectral Band Panchromatc:.5 to.9 µm Samplng Depth Transmtted Bts condtons for optmal magng. Fg (a) llustrates the synchronous mode vs. asynchronous one. Referrng to fg. (b), Symposum on Geospatal Theory, Processng and Applcatons, Symposum sur la théore, les tratements et les applcatons des données Géospatales, Ottawa

2 Swath (a) Satellte Orbt Satellte Orbt Satellte Ground Trac 3.. Intalzaton Of Orentaton Parameters: The onboard ephemers data and GCPs are n dfferent coordnate systems. Before the orbt adjustment, t s essental to buld up the coordnate transformaton, so that the orbt adjustment wll be performed n WGS84 as unfed coordnate system. Those coordnate systems nclude nertal frame, WGS84, GRS67, Geodetc Coordnate System, TWD67, Orbtal Reference Frame and EROS A Body Frame. In whch, GRS67 used the Kaula ellpsod (a=63786m, f=/98.47). The Geodetc Coordnate System s n longtude and lattude. Based on the datum of GRS67, the TWD67 system s a Transverse Mercator Projecton usng λ =E as the central merdan. There wll be three steps between TWD67 and WGS84 transformaton. Frst, we project TWD67 nto the Geodetc Coordnate System, then the Geodetc Coordnate System s projected nto GRS67. Fnally, the GRS67 system s transformed nto WGS84. The camera model was provded by ISI Internatonal. Swath PhotoGraphc Tme (b) Fgure. Illustraton for scannng modes (a) Synchronous (b) Asynchronous 3. METHODOLOGY The proposed method comprses two major parts. The frst part s to buld up the satellte orentaton by usng the ground control ponts. The second one s to use the orbt parameters to perform the orthorectfcaton. 3. Orentaton Modelng Satellte Ground Trac The major step n valdatng the postonng accuracy for an mage s to model the orbt parameters and the atttude data. Once those exteror orentaton parameters are modeled, the correspondng ground coordnates for an mage pxel can be calculated. Due to the extremely hgh correlaton between two groups of orbtal parameters and atttude data, we only correct the orbtal parameters. That means, we wll use the atttude nformaton n the on-board ephemers data as nown values. Three steps are ncluded n ths nvestgaton. The frst step s to ntalze the orentaton parameters usng on-board ephemers data. We then ft the orbtal parameters wth seconddegree polynomals usng GCPs. Once the trend functons of the orbtal parameters are determned, the fne-tunng of an orbt s performed by usng Least Squares Flterng (also called Least Squares Collocaton ) technque. 3.. Prelmnary Orbt Fttng: Because the on-board data ncludes errors to a certan degree, GCPs are needed to adjust the orbt parameters. Referrng to fg., the observaton vector (Ua) provded by the satellte wll not pass through the correspondng GCP due to errors the on-board data. Thus, correcton of the orbt data from (x, y, z ) to (x, y, z) may be performed under the condtons X = x(t ) S u Y = y(t ) S u x Y Z = z(t ) S u x ( t y ( t z ( t ) = x ) = z ) = y Z a c b a c b a b c (a) (b) (c) (a) (b) (c) X, Y,Z are object coordnates of the th GCP, u x, u y,u z are components of the observaton vector, x(t ), y(t ),z(t ) are the satellte s coordnates of the th GCP after correcton, x,y,z are the satellte s coordnates before correcton, a, b and c (=,,) are coeffcents for orbt correctons, t represents samplng tme, and S s the scale factor. Ua ( x,y,z ) () ( x,y,z) GCP Fgure. Prelmnary fttng for satellte orbt After Intal Satellte

3 3..3 Least Squares Flterng: Because the least squares adjustment s a global treatment, t cannot correct for the local errors. Therefore, the least squares flterng (Mhal and Acermann, 98) has to be used to fne tune the orbt. By dong ths, we assume that the x, y, z-axs are ndependent. Thus, we use three one-dmensonal functons to adjust the orbt. The model of least squares flterng s shown as ρ = Σ ν [ ] ε (3) s x,y,z axs ρ r s the correcton value of the nterpolatng pont, ν s the row covarance matrx of the nterpolatng pont wth respect to GCPs, Σ r s the covarance matrx for GCPs, and ε s the resdual vectors for GCPs. The basc consderaton n ths nvestgaton s to mnmze the number of requred GCPs. Thus, usng a large amount of GCPs to characterze the covarance matrx s not practcal. In ths paper, we use a Gaussan functon (shown as fg. 3) wth some emprcal values as the covarance functon. The Gaussan functon s shown as Covarance = ce µ (.46 ( r n ) c = µ d d ) max, f d, f d = d s the dstance between an ntersecton ponts and a GCP, dmax s the dstance between an ntersecton pont and the farthest GCP, μ s the varance of GCPs resdual, and rn s the flterng rato, n whch we use rn=. n experment. The emprcal value.46 s selected so that the covarance lmt s % of.(- rn)μ when d=dmax (Chen & Chang, 998). (4) 3D object pont on to D mage space. It s nown that the ndrect method performs better than the drect method n terms of effcency and qualty (Mayr and Hepe 988,Chen and Lee 993). We select the ndrect method to determne the correspondng mage pxels from a ground element. Once the orentaton parameters are determned and a DTM s gven, the correspondng mage poston for a ground pont may be determned by the ndrect method. Fg. 4 shows the geometry of ndrect method. Gven a ground pont A, we can create a vector r(t) from ground pont A to mage pont a. The vector r(t) vector s located on the prncple plane and n(t) s the normal vector on the prncpal plane. The mathematcs show that, at tme t, r(t) s orthogonal to the normal vector n(t). When r(t) s perpendcular to n(t), the nner product of r(t) and n(t) s zero. The functon f(t) s defned to characterze the coplanarty condton f(t)=r(t) n(t )= (5) We apply Newton-Raphson method to solve the nonlnear equaton (5), to determne the samplng tme t for ground pont A. The teraton s expressed n the equaton (6), ( ) f tn f ( tn ) tn = tn = tn (6) f '( t ) [ f ( t t) f ( t t)]/ t n n when n=,,.. untl t n -t n < -5 sec s satsfed. For an mage pont sampled at tme t, we can decde a prncpal plane, the along trac mage coordnate can be calculate by Lne=(t-t)/(ntegraton tme) (7) t s samplng tme for the frst scan lne. Integraton tme s the samplng nterval. Z Satellte Orbt after precson correcton Satellte CCD array scannng surface n normal vector n(t) r(t) a Projecton Center Prncpal plane Covarance µ c r n µ A Y Ground surface d /d max FIGURE 4. Illustraton of ndrect method X Fgure 3. Covarance functon of least squares flterng 3. Orthorectfcaton There are two ways to do the orthorectfcaton. The frst one s the drect method. A technque called Ray-Tracng (O Nell and Dowman, 988) was developed to solve the problem by drect method. It projects a D mage pont on to a 3D object model. The second one s ndrect method, whch projects the The across trac mage coordnate may be determned, as shown n fg. 5. In the fgure, V f s the pontng vector of frst CCD n lne, and V l s the pontng vector of last CCD n lne. The across trac coordnate for the pxel s Sample=(S/FOV)*743 (8) S s the angle between V f and r(t). FOV s feld of Vew angle, and 743 s number pxel n a lne.

4 V v f Projecton Center Fgure 5. Illustraton for determnng across-trac mage coordnate 4. EXPERIMENTS The experments nclude two parts of valdaton. The frst one s to chec for the determned orentaton parameters. The second one s to examne the accuracy for the generated orthomage S FOV r(t) V v l Table II. Related nformaton of test mages ITEM Parameters Scene ID TAW-e993 Date /4/5 Integraton Tme 3.7msec Ground Samplng Dstance.9m Test Area 3.38m *.48m Image sze 743* 657 pxel Place KaoHsung, Tawan Pontng Angle.6 Deg Orbt Arc 7KM(about :3) The DTM used n the orthorectfcaton was acqured from the Topographc Data Base of Tawan. The pxel spacng of DTM s resample from 4m to m. Fg. 7 llustrates the terran varaton. The elevaton ranges from m to 34m. 4.. Test Data The test area s n KaoHsung, whch s located n the southern part of Tawan as shown n fg.6. Scene ID s TAW-e993, whch were sampled on Apr. 5,. The asynchronous rato of the satellte orbts to samplng area s :3. The GCPs and chec ponts (CHKPs) were measured from : scale topographc maps. The poston accuracy s better than 5 centmeters. The dstrbutons of those ponts are shown n fg. 6. In the fgure, trangles represent the GCPs whle boxes are the CHKPs. The total number of GCPs and CHKPs are 53. Other related nformaton s shown n Table II. Fgure 7. The DTM used n orthorectfcaton 4.. Accuracy VS. Number of GCPs The Ray-Tracng method s appled to evaluate the orbt accuracy. Gven the satellte orentaton and mage pont, we calculate the ntersecton pont of DTM and ray drecton. Fg.8 ndcates the RMSEs when dfferent numbers of GCPs were employed n the test data. Table III lsts the fgures to ndcate the trend n detal. It s obvous that the RMSEs.e., (3.53m, 4.7m) tend to be stable when 9 or more control ponts were employed. Notce that the coordnate system s n TWD67 wth Transverse Mercator projecton. ImageSat Internatonal. Fgure 6. The test mage.

5 RMSE RMSE_E RMSE_N Number of GCP Fgure 8. RMSEs for the dfferent number of GCPs Table III. RMSEs for dfferent number of GCPs No. of GCPs RMSE E (m) RMSE N (m) (a) 4.3. Accuracy Analyss Of Orbt Modelng We further evaluate the error behavours n the two dfferent phases. Fg.9(a) depcts the error behavour after prelmnary orbt fttng n TWD67 coordnate system. We could see that the system errors are obvous. Fg.9(b) llustrates the results after precson correcton,.e., least squares flterng. The coordnate system s also n TWD67. After usng least squares flterng to fne tune the orbt, the major system errors have been compensated. We provde Table III for the summary of accuracy. Table IV llustrates the accuracy performance of GCPs and CHKPs, when 9 GCPs were employed. After prelmnary orbt fttng, the RMSE of CHKPs s about 6meter and 4meter n two drectons. After least squares flterng, the RMSE of CHKPs are reducng to 3.3meter and 4.3meter respectvely. (b) Fgure 9.Error vectors of orbt modelng (a)error vectors of the prelmnary orbt fttng (b) Error vectors after least squares flterng Table IV. Root-Mean-Square Error of orbt modelng RMSE E (meter) RMSE N (meter) Prelmnary orbt fttng GCPs (9) CHKPs (44) Least Squares Flterng GCPs (9).47.7 CHKPs (44) Accuracy Evaluaton Of Orthorectfcaton The generated orthomage s shown n fg.. In order to evaluate the qualty of orthomage, we chec t manually. Fg. llustrates that the RMSE of ground chec pont s slghtly

6 better than pxels. It s observed that the error vectors are smlar to the result after least square flterng. Table V shown the Root-Mean-Square Error of orthoretfcaton. The RMSEs of CHKPs are 3.meter and 3.7meter n E and N drectons respectvely. the geometrcal relatonshp between mage space and object space. After that, we use least squares predcton to fne-tune the orbt. Fnally, we use ndrect method to generate the orthophotos. Expermental results ndcate that the proposed scheme may reach an accuracy of better than two pxels n the mage scale for an mage sampled wth an asynchronous rato of 3. Because of the measurement error, the results of orthorectfcaton and least squares flterng are slghtly dfferent. The DTM used n the orthorectfcaton was resampled from the one wth 4m resoluton. Due to ts error, the precson of the proposed method could be underestmated. 6. REFERNENCES Chen, L.C., and Chang, L. Y., 998, Three Dmensonal Postonng Usng SPOT Stereostrps wth Sparse Control, Journal of Surveyng, ASCE 4(): pp Chen, L.C., and Lee, L.-H. 993, Rgorous Generaton of Dgtal Orthophoto from SPOT Images. Photogrammetrc Engneerng and Remote Sensng, 59(5), Fgure. Generated orthophoto Gugan, D.J., and Dowman, I. J. 988, Accuracy and completeness of topographc mappng from SPOT magery. Photogrammetrc Record, (7), Mhal E.M and F. Acermann, 98, Observaton and Least Squares, Unversty Press of Amerca, New Yor, pp.4. Mayer, W. and C. Hepe, 988, A Contrbuton to Dgtal Orthophoto Generaton, Internatonal Archves of Photogrammetry and Remote Sensng, 7(B):IV43-IV439. O Nell, M.A., and Dowman, I. J., 988, The Generaton of Eppolar Synthetc Stereo Mates for SPOT Images Usng a DEM, Internatonal Archves of Photogrammetry and Remote Sensng, Kyoto, Japan, 7(B3): pp Fgure.Error vectors for the generated orthophoto Table V. Root-Mean-Square Error of orthoretfcaton Orthorectfcaton RMSE E (meter) RMSE N (meter) GCPs (9).8 3. CHKPs (44) CONCLUSIONS We have proposed a procedure to perform geometrc correcton for EROS A satellte mages usng a small number of GCPs. The correctons for orbtal data are modeled as functons of tme. The GCPs are appled to correct the on-board data to mantan