EPIPOLAR GEOMETRY OF LINEAR ARRAY SCANNERS MOVING WITH CONSTANT VELOCITY AND CONSTANT ATTITUDE

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1 EPIPOLAR GEOMETRY OF LINEAR ARRAY SCANNERS MOVING WITH CONSTANT VELOCITY AND CONSTANT ATTITUDE M. Morgan a, K. Km b, S. Jeong b, A. Habb a a Department of Geomatcs Engneerng, Unversty of Calgary, Calgary, Unversty Drve NW, Calgary, AB, TN N, Canada - (mfmorgan@ucalgary.ca, habb@geomatcs.ucalgary.ca b Electroncs and Telecommuncatons Research Insttute (ETRI, 6 Gaeong-Dong, Yuseong-Gu, Daeeon, -, Korea (kokm, PS WG III/: Sensor Pose Estmaton KEY WORDS: Photogrammetry, Analyss, Drect, Modellng, Pushbroom, Sensor ABSTRACT: Image resamplng accordng to eppolar geometry s a prerequste for a varety of photogrammetrc tasks such as mage matchng, DEM and ortho-photo generaton, aeral trangulaton, map complaton, and stereoscopc vewng. The resamplng process of magery captured by frame camera has been establshed and mplemented n current Dgtal Photogrammetrc Workstatons (DPW. Scannng analogue mages or drectly usng dgtal cameras can produce dgtal mages, whch are the nput meda for DPW. So far, there s no dgtal frame camera capable of producng radometrc and geometrc resolutons that are comparable to those assocated wth analogue ones. To overcome such a lmtaton, lnear array scanners have been developed to capture scenes through multple exposures of few scan lnes along the focal plane. Ths magng scenaro makes the perspectve geometry of lne cameras more complcated than that of frame mages. Moreover, establshed procedures for resamplng frame mages accordng to eppolar geometry are not sutable for scenes captured by lnear array scanners. In ths paper, the geometry of eppolar lnes n scenes captured by lnear array scanners movng wth constant velocty and constant atttude s analyzed. The choce of ths model s motvated by the fact that many scanners can be assumed to follow such traectory durng the short duraton of scene capture (especally when consderng space borne magng platforms. The paper starts by establshng the mathematcal model descrbng the shape of eppolar lnes n the captured scenes from a platform movng wth constant velocty and constant atttude. The paper proceeds by presentng smulated expermental results usng scenes captured accordng to SPOT, IKONOS and three-lne camera magng confguratons, where we show the effect of dfferent stereo-coverage methodologes (.e., tltng the sensor across the track drecton SPOT, tltng the sensor along track IKONOS, and usng three lnear array scanners on the shape of the eppolar lnes. For these scenaros, a measure s ntroduced to quantfy the devaton of the resultng eppolar lnes from straghtness. Small devatons from straghtness wll allow for better capablty of resamplng the captured scenes accordng to eppolar geometry and thus lead to more straghtforward subsequent processng (e.g., DEM generaton, stereo-vewng, etc... INTRODUCTION Scenes captured from lnear scanners (also called pushbroom scanners or lne cameras have been ntroduced for ther great potental of generatng ortho-photos and updatng map databases (Wang, 999. The lnear scanners wth up-to onemeter resoluton from commercal satelltes could brng more benefts and even challenges to tradtonal topographc mappng wth aeral mages (Frtz, 99. Careful sensor modellng has to be adapted n order to acheve the hghest potental accuracy. Rgorous modellng descrbes the scene formaton as t actually happens, and therefore t s the most accurate model. Thus, t has been adopted n a varety of applcatons (Lee and Habb, ; Habb et al., ; Lee et al., ; Wang, 999; Habb and Beshah, 998; McGlone and Mkhal, 98; Ethrdge, 977. On the other hand, other approxmate models exst such as ratonal functon model, RFM, drect lnear transformaton, DLT, self-calbratng DLT and parallel proecton (Tao and Hu, ; Ono et al., 999; Wang, 999; Abdel-Azz and Karara, 97. Selecton of any approxmate model, as an alternatve of rgorous modellng, has to be done based on the analyss of the acheved accuracy. In ths paper, rgorous modellng of lnear array scanners s adopted. Eppolar resamplng of frame mages s a straghtforward process (Cho et al., 99. However, resamplng lnear array scanner scenes accordng to eppolar geometry s not a trval task. The dffcultes n resamplng the scenes can be, to a certan degree, attrbuted to the shape of eppolar lnes. Therefore, ths paper s dedcated to the shape analyss of eppolar lnes, and how close they are to straght lnes. Km ( nvestgated the eppolar geometry of lnear array scanner scenes. The author concluded that scanners movng accordng to second order polynomal functons n poston and headng angle, and frst order polynomal functons n roll and ptch angles do not produce straght lnes. In ths paper, Secton contans background nformaton regardng frame mages as well as lnear array scanner scenes. The choce of constant-velocty-constant-atttude as the rgorous sensor model and ts utlzaton n dervng the eppolar lne equaton are the subects of Secton. Secton s dedcated to the analyss of the shape of eppolar lnes. Expermental results are then presented n Secton. Fnally Secton 6 ncludes the conclusons and recommendatons for future work.

2 . BACKGROUND. Eppolar Geometry of Frame Cameras.. Defntons It s mportant to lst some terms wth ther defntons before gong nto any detaled dscusson (Cho et al., 99. These terms wll be used throughout the analyss of the eppolar geometry of frame mages. Fgure shows two frame mages, relatvely orented smlar to that at the tme of exposure. O and O are the perspectve centres of the left and rght mages at the tme of exposure, respectvely. eppolar lne I p left mage O base lne eppolar plane p O p I p rght mage p eppolar lne Where: x, y are the mage coordnates of a pont n the mage; x, y, c are the Interor Orentaton Parameters, IOP, of the frame camera; X, Y, are the poston of the exposure staton; R s the rotaton matrx of the mage; X k, Y k, k are the coordnates of the obect space pont; λ k s the scale factor. Consderng Fgure, two sets of collnearty equatons can be wrtten for pont p by settng the scale factor λ k to two arbtrary values. Ths results n two arbtrary obect space ponts, P and P, along the ray Op. The two obect ponts are then reproected nto the rght mage wth known orentaton parameters. The resultng ponts, p and p, form the eppolar lne. Method : Coplanarty Condton Wthout Vstng the Obect Space P The coplanarty condton (Kraus, 99, Equaton can be drectly used to determne the eppolar lne equaton. Fgure. Eppolar geometry n frame mages Eppolar plane: The eppolar plane for a gven mage pont p n one of the mages s the plane that passes through the pont p and both perspectve centres, O and O. Eppolar lne: The eppolar lne can be defned n two ways. Frst, t can be defned as the ntersecton of the eppolar plane wth an mage, whch produces a straght lne. Secondly, the eppolar lne can be represented by the locus of all possble conugate ponts of p on the other mage (by changng the heght of the correspondng obect pont. The latter defnton wll be used when dealng wth lnear array scanners. It should be noted that no DEM s needed to determne the eppolar lne. Selectng several ponts along the ray (Op,.e., choosng dfferent heght values of the obect pont, wll yeld the same eppolar lne (I p n the other mage, Fgure. Another mportant property of eppolar lnes n frame mages s ther exstence n conugate pars. Consder Fgure, where I p s the eppolar lne n the rght mage for pont p n the left mage, and p, p are two dfferent ponts n the rght mage selected on I p. The eppolar lnes of ponts p and p wll be dentcal, denoted as I p, and wll pass through the pont p. Ths can be easly seen from the fgure snce all these ponts and lnes should be n the same plane (the eppolar plane... Eppolar Lne Determnaton n Frame Images Method : Collnearty Equatons Through the Obect Space The collnearty equatons (Kraus, 99, Equaton, relate a pont n the obect space and ts correspondng pont n the mage space. X Y k k k X Y P x x + R y y λk c ( ( ' Op O' p' OO o ( Where: OO s the vector connectng the two perspectve centres; Op s the vector connectng the pont of nterest p n the left mage wth ts perspectve centre, O; O p s the vector connectng the correspondng pont n the rght mage wth ts perspectve centre; and, symbolze vectors cross and dot products, respectvely. Snce only the coordnates of the correspondng pont n the rght mage (.e., x and y are unknown, Equaton becomes the eppolar lne equaton. One has to note that n ths method, the obect space pont, or ts possble locaton, has not been dealt wth. Next secton deals wth lnear array scanners as alternatve to frame cameras.. Lnear Array Scanners.. Motvatons for usng Lnear Array Scanners Two-dmensonal dgtal cameras capture the data usng twodmensonal CCD array. However, the lmted number of pxels n current dgtal magng systems hnders ther applcaton towards extended large scale mappng functons. One-dmensonal dgtal cameras (lnear array scanners can be used to obtan large ground coverage and mantan a ground resoluton comparable wth scanned analogue photographs. However, they capture only one-dmensonal mage (narrow strp per snap shot. Ground coverage s acheved by movng the scanner (arborne or space-borne and capturng many D mages. The scene of an area of nterest s obtaned by sttchng together the resultng D mages. It s mportant to note that every D mage s assocated wth one-exposure staton, and therefore, each mage has ts own set of Exteror Orentaton Parameters (EOP. A clear dstncton s made between the two terms scene and mage throughout the analyss of lnear array scanners. An mage s defned as the recorded sensory data assocated wth one exposure staton. In case of a frame mage, t contans only one exposure staton, and consequently t s one complete mage. In case of lnear array scanner, there are many D

3 mages, each s assocated wth dfferent exposure statons. The mathematcal model that relates a pont n the obect space and ts correspondng pont n the mage space s the collnearty equatons, whch uses EOP of the approprate mage (n whch the pont appears. In contrast, a scene s the recorded sensory data assocated wth one (as n frame mages or more exposure statons (as n lnear array scanners that maps near-contnuous obect space n a short sngle trp of the sensor. Therefore, n frame mages, mage and scene are dentcal terms, whle n lnear array scanners, the scene s an array of consecutve D mages. Consequently, t s mportant to dstngush between the scene and mage coordnates. As shown n Fgure b, and y are the scene coordnates, whle n Fgure a, x and y are the mage coordnates for mage number. Only x and y can be used n the collnearty equatons, whle ndcates the mage number or the tme of exposure. y x y y x (a n (b y Fgure. A sequence of D mages (a consttutng a scene (b.. Stereo Coverage One of the man obectves of photogrammetry s to reconstruct the three-dmensonal obect space from D mages/scenes. Ths s usually acheved by ntersectng lght rays of correspondng ponts n dfferent vews. Therefore, dfferent vews or stereo coverage s essental for dervng D nformaton regardng the obect space. In lnear array scanners, stereo coverage can be acheved usng one of the followng ways: x One scanner and across track stereo coverage usng roll angles: Stereo coverage can be acheved by tltng the camera sdeways across the flght drecton (dfferent roll angles, Fgure a. Ths has been adopted n SPOT. A drawback s the large tme gap between mages of the stereo par, and consequently changes may occur between the two scenes (Wang, 999. One scanner and along track stereo coverage usng ptch angles: In ths case the camera s tlted forward and backward along the flght drecton (dfferent ptch angles, Fgure b. Ths type of stereo coverage s used n IKONOS. Ths method has the advantage of reducng the tme gap between the scenes consttutng the stereo par. Three scanners (three-lne cameras: In ths case, three scanners are used to capture backward-lookng, nadr, and forward-lookng scenes, Fgure c. Contnuous stereo or trple coverage can be acheved along the flght lne wth reduced tme gaps. However, dfferent radometrc qualtes exst between the scenes. Ths method s mplemented n MOMS and ADS (Hepke et al., 996; Sandau et al., ; Fraser et al.,. y n x n Column # or tme (a Fgure. Stereo coverage n lnear array scanners acheved by roll angle rotaton n two flyng paths (a, ptch angle rotaton n the same flyng path (b, and three-lne cameras (c... Rgorous Modellng Rgorous (exact modellng of lnear array scanners descrbes the actual geometrc formaton of the scenes at the tme of photography, that requres the knowledge of IOP of the scanner and the EOP of each mage n the scene. Usually, EOP do not abruptly change ther values between consecutve mages n the scene, especally for space-based scenes. Therefore, most rgorous modellng methods adapt polynomal representaton of EOP (Lee et al., ; Wang, 999. The parameters, descrbng the polynomal functons, are ether gven (drectly from the navgaton unts such as GPS/INS mounted on the platform, or ndrectly estmated usng ground control n bundle adustment (Lee and Habb, ; Habb et al., ; Habb and Beshah, 998. Other methods (Lee et al., ; McGlone and Mkhal, 98; Ethrdge, 977 use pecewse polynomal model for representng the flght traectory and the platform atttude. Ths opton s preferable f the scene tme s large, and the varatons of EOP do not comply wth one set of polynomal functons. For ndrect estmaton of the polynomal coeffcents usng ground control ponts, nstablty of the bundle adustment exsts, especally for space-based scenes (Fraser et al., ; Wang, 999. Ths s attrbuted to the narrow Angular Feld of Vew (AFOV of space scenes, whch results n very narrow bundles n the adustment procedures. To avod the polynomal representaton of EOP, Lee and Habb ( explctly dealt wth all EOP assocates wth the scene. Lnear feature constrants were used to ad ndependent recovery of the EOP of the mages as well as to ncrease the geometrc strength of the bundle adustment. (b (c. Eppolar Geometry of Lnear Array Scanner Scenes Km ( modelled the changes of EOP as second order polynomal functons n scanner poston and headng, and frst order functons n ptch and roll angles. Ths model s called Orun and Nataraan model as cted from (Orun and Nataraan, 99. The author proved that the eppolar lne s no longer a straght lne, rather has hyperbola-lke shape. In addton, the author proved that eppolar lnes do not exst n conugate pars. The next secton nvestgates the eppolar geometry of lnear array scanners usng constant-velocty-constant-atttude EOP model, whch s a subclass of Orun and Nataraan model. But frst, eppolar lne determnaton n lnear array scanners has to be explaned. As dscussed earler, scanner at successve exposure statons has dfferent perspectve centres and dfferent atttude, therefore, EOP wll vary from one scan lne to the other. Hence, the eppolar lnes should be clearly defned n such scenes before studyng ther geometry. Fgure shows a schematc drawng of

4 v two lnear array scanner scenes. For a D mage n the left scene wth O as ts perspectve centre, pont p can correspond to many eppolar planes (unlke the case of frame mages - compare Fgures and. In ths case, there are as many eppolar planes as the perspectve centres n the rght scene. Therefore, the eppolar lne cannot be defned as the ntersecton of planes. Instead, the second defnton used n frame mages s adopted, where the eppolar lne s defned as the locus of all possble conugate ponts of p on the other scene based on the orentaton parameters. ( X, Y, s the constant velocty vector of the scanner whle capturng the left scene; (X, Y, s the poston of the frst exposure staton n the rght scene; ( X, Y, s the constant velocty vector of the scanner whle capturng the rght scene; (ω, ϕ, κ are the rotaton angles of the left scanner; and (ω, ϕ, κ are the rotaton angles of the rght scanner. For a pont (, y on the left scene, the collnearty equatons can be wrtten as: O B v O O k X A. + A Y A. + A ( p Eppolar lne where A to A are functons of the IOP and EOP of the left scene. Equaton represents two planes parallel to Y and X axes, respectvely. Ther ntersecton s a straght-lne (a lght ray n space. On the other hand, for the rght scene, the collnearty equatons are: v x' x y' y c λ ' R' T ( ω ', ϕ ', κ ' X X ' Y Y ' ' ( Fgure. Eppolar lne n lnear array scanner scenes In order to determne the eppolar lne, EOP of the scan lnes together wth the IOP of the scanner must be avalable. The eppolar lne can be determned n a smlar way as dscussed n Secton.. by repeatng the procedure for each scan lne snce each scan lne has dfferent EOP. The change n EOP from one scan lne to the next s one of the factors that determne the shape of the eppolar lne.. UTILIING CONSTANT VELOCITY AND CONSTANT ATTITUDE MODEL The motvaton of nvestgatng the constant-velocty-constantatttude model s that many space scenes are acqured n very short tme (e.g., about one second for IKONOS scene. In addton, smlar assumptons were made for EOP when dervng the SDLT model for lnear array scanners (Wang, 999. The scanner, therefore, can be assumed to travel wth constant velocty and constant atttude durng the scene capture, Equatons. X X + X X ' X ' + X ' Y Y + Y Y ' Y ' + Y ' + + ( ' ' ', κ κ κ ' κ ' ω ω ω' ω' ϕ ϕ ϕ ' ϕ ' where: s the scan lne number on the left scene; s the scan lne number on the rght scene; (X, Y, s the poston of the frst exposure staton n the left scene; Usng EOP from Equatons, and substtutng for X and Y from Equaton, Equatons can be wrtten as: y '. E y'.. E. E + + E (6 where E to E are functons of the IOP and EOP of the scanner. Detaled dervaton of the above equaton can be found n (Morgan,.. ANALYSIS OF EPIPOLAR LINES Equaton 6 represents the locus of potental conugate ponts n the rght scene (.e., the equaton of the eppolar lne n the rght scene. It s mportant to note that y s unknown (at mage number. The eppolar curve s a straght lne f E, hence y s a lnear functon of. Therefore, the term E has to be analyzed. Settng E to, the condton for havng the eppolar curve as a straght lne can be expressed as trple product of three vectors v, v and v, Fgure, as: ( v v v o (7 Equaton 7 ndcates that these three vectors, shown n Fgure, must be coplanar n order to have the eppolar curve as a straght lne. In realty, t s hard to fnd the above condton vald and equals to absolute zero. In order to quantfy the straghtness of the eppolar curve, the value of E has to be compared to the value of E. The smaller the rato of (E /E, the eppolar curve wll become closer to beng straght. ( v v o v ( v B o v E (8 E where B s the arbase vector, connectng the perspectve pont of the pont under consderaton n the left scene and the perspectve centre of the frst mage n the rght scene. Recall that eppolar lnes n frame mages are straght lnes n both the

5 X(m Rght Scanlnes Footprnt X(m Rght Scanlnes Footprnt Rght Scanlnes Footprnt X(m Rght Scanlnes Footprnt 6 8 X(m Rght Scanlnes Footprnt 6 8 Rght Scanlnes Footprnt x 6 X(m Rght Scanlnes Footprnt 6 X(m Rght Scanlnes Footprnt Rght Scanlnes Footprnt 6 raw and normalzed mages. Therefore, no dstortons are ntroduced n such a process. On the other hand, n lnear array scenes, eppolar lnes may not be straght, but t s desrable to have them as straght lnes n the normalzed scenes. Therefore, the evaluaton of ther non-straghtness n the raw scenes wll gve an dea about the errors ntroduced n the normalzed scenes.. EXPERIMENTS In order to study the eppolar geometry, two scenes are needed. Nne experments are performed. Experments, and are smulated to obtan stereo coverage for a three-lne camera, at dfferent alttudes. On the other hand, Experments, and 6 are smulated to obtan stereo coverage by changng the ptch angles along track smlar to that of IKONOS, at dfferent alttudes. Fnally, Experments 7, 8 and 9 are smulated to obtan stereo coverage by changng roll angles across track smlar to that of SPOT at dfferent alttudes. The summary of the experments s lsted n Table. Fgure 6 shows the footprnts of the scan lnes of the scenes. Alttude m 68 km 8 km Stereo Three-lne scanner Exp. Exp. Exp. coverage Changng ptch angle Exp. Exp. Exp. 6 method Changng roll angle Exp. 7 Exp. 8 Exp. 9 Table. Summary of Experments to 9 In each of these experments, fve ponts are selected n the left scene. Fgure 7 shows the correspondng eppolar lnes of the experments. The eppolar lnes are drawn wthn the extent of the rght scenes. Dotted straght lnes are added between the begnnng and endng ponts to vsually examne the straghtness of these eppolar lnes. It has been found that E does not equal zero. Therefore, for general lnear array scanner (even wth the constant-velocty-constant-atttude traectory model, the eppolar lnes are not straght. In order to quantfy the straghtness of eppolar lnes, Table lsts the values of E /E for the experments. Examnng the standard devaton of E /E of the selected ponts n each experment, t s notceable that E /E values do not change from pont to pont n the scene n Experments to 6. Ths means that these eppolar lnes, even f they are not straght lnes, are changng n a smlar fashon. On the other hand, the standard devatons of E /E values n Experments 7 to 9 are relatvely large, whch consequently means that there s a hgh varaton of the shapes of the eppolar lnes. Ths s confrmed by extreme example, Experment 7 n Fgure 7. Therefore, t can be concluded that stereo coverage smlar to that of three-lne camera or IKONOS are superor, n terms of shape varaton of eppolar lnes, to that of SPOT. Examnng the average values of E /E, t s notceable that E /E decreases as the alttude ncreases, for the same stereo coverage type. Moreover, stereo coverage smlar to IKONOS or three-lne cameras gves smaller average values than that of SPOT at the same alttude (Compare the average values of Experments, and 7; those of Experment, and 8, and fnally those of Experments, 6 and 9. Fgure 6. Scan lnes footprnts of Experments to 9 Fgure 7. Eppolar lnes of Experments to 9 Pont# Mean ±Std......± ± ± ± ± ± ± ± ±. Table. E /E values for varous ponts n Experments to 9 Experment Experment Experment Experment CONCLUSIONS AND RECOMMENDATIONS It has been concluded that for constant-velocty-constantatttude EOP model, the eppolar lne s found to be a nonstraght lne n general and a quanttatve analyss of ts nonstraghtness was ntroduced. Analyss of alternatve stereocoverage possbltes revealed that along track stereo observaton usng ptch angles as well as three-lne scanners are Experment Experment Experment x Experment Experment Experment Experment Experment Experment Experment 7 Experment 8 Experment 9 - x x x x

6 superor to across track stereo coverage usng roll angles as they ntroduce straghter eppolar lnes. Moreover, as the flyng heght ncreases, eppolar lnes become straghter. Such conclusons motvate the nvestgaton of eppolar resamplng of space scenes such as IKONOS. As the derved quanttatve measure examnes the straghtness of eppolar lnes wthout restrcton to the scene extent, dfferent measure has to be ntroduced to examne ther qualty wthn the scenes. On the other hand, as the general EOP model does not result n straght eppolar lnes, dfferent models have to be sought for the purpose of eppolar resamplng of lnear array scanner scenes. REFERENCES Abdel-Azz, Y., and H. Karara, 97. Drect Lnear Transformaton from Comparator Coordnates nto Obect Space Coordnates n Close-Range Photogrammetry, Proceedngs of ASP/UI Symposum on CloseRange Photogrammetry, Unversty of Illnos at Urbana Champagn, Urbana, Illnos, pp. -8. Cho, W., T. Schenk, and M. Madan, 99. Resamplng Dgtal Imagery to Eppolar Geometry, IAPRS Internatonal Archves of Photogrammetry and Remote Sensng, 9(B: -8. Ethrdge, M., 977. Geometrc Analyss of Sngle and Multply Scanned Arcraft Dgtal Data Array, PhD Thess, Purdue Unversty, West Lafayette, Indana, p. Fraser, C., H. Hanley, and T. Yamakawa,. Sub-Metre Geopostonng wth IKONOS GEO Imagery, ISPRS Jont Workshop on Hgh Resoluton Mappng from Space, Hanover, Germany,. Lee, C., H. Thess, J. Bethel, and E. Mkhal,. Rgorous Mathematcal Modelng of Arborne Pushbroom Imagng Systems, Journal of Photogrammetrc Engneerng & Remote Sensng, 66(: 8-9. McGlone, C., and E. Mkhal, 98. Photogrammetrc Analyss of Arcraft Multspectral Scanner Data, School of Cvl Engneerng, Purdue Unversty, West Lafayette, Indana, 78p. Morgan, M.,. Eppolar Resamplng of Lnear Array Scanner Scenes, PhD Dssertaton, Department of Geomatcs Engneerng, Unversty of Calgary, Canada. Ono, T., Y. Honmach, and S. Ku, 999. Eppolar Resamplng of Hgh Resoluton Satellte Imagery, Jont Workshop of ISPRS WG I/, I/ and IV/ Sensors and Mappng from Space. Orun, A., and K. Nataraan, 99. A Modfed Bundle Adustment Software for SPOT Imagery and Photography: Tradeoff, Journal of Photogrammetrc Engneerng & Remote Sensng, 6(: -7. Sandau, R., B. Braunecker, H. Drescher, A. Eckardt, S. Hlbert, J. Hutton, W. Krchhofer, E. Lthopoulos, R. Reulke, and S. Wck,. Desgn Prncples of the LH Systems ADS Arborne Dgtal Sensor, Internatonal Archves of Photogrammetry and Remote Sensng, Amsterdam, (B: 8-6. Tao, V. and Y. Hu,. A Comprehensve Study for Ratonal Functon Model for Photogrammetrc Processng, Journal of Photogrammetrc Engneerng & Remote Sensng, 67(:7-7. Wang, Y., 999. Automated Trangulaton of Lnear Scanner Imagery, Jont Workshop of ISPRS WG I/, I/ and IV/ on Sensors and Mappng from Space, Hanover, 999. Frtz, L., 99. Recent Developments for Optcal Earth Observaton n the Unted States, Photogrammetrc Week, pp7-8, Stuttgart, 99. Habb, A. and B. Beshah, 998. Mult Sensor Aeral Trangulaton, ISPRS Commsson III Symposum, Columbus, Oho, 6 July, 998. Habb, A., Y. Lee, and M. Morgan,. Bundle Adustment wth Self-Calbraton of Lne Cameras usng Straght Lnes, Jont Workshop of ISPRS WG I/, I/ and IV/7: Hgh Resoluton Mappng from Space, Unversty of Hanover, 9- September,. Hepke, C., W. Kornus, and A. Pfannensten, 996. The Evaluaton of MEOSS Arborne Three-Lne Scanner Imagery: Processng Chan and Results, Journal of Photogrammetrc Engneerng & Remote Sensng, 6(: Km, T.,. A Study on the Eppolarty of Lnear Pushbroom Images, Journal of Photogrammetrc Engneerng & Remote Sensng, 66(8: Kraus, K. 99. Photogrammetry, Dümmler Verlag, Bonn., Volume, 97p. Lee, Y., and A. Habb,. Pose Estmaton of Lne Cameras Usng Lnear Features, ISPRS Symposum of PCV' Photogrammetrc Computer Vson, Graz, Austra.