INFLUENCE OF TIE POINT DISTRIBUTION ON INTEGRATED SENSOR ORIENTATION

Size: px

Start display at page:

Download "INFLUENCE OF TIE POINT DISTRIBUTION ON INTEGRATED SENSOR ORIENTATION"

Ethel Phelps
5 years ago
Views:

1 IFUEE OF TIE POIT DISTRIUTIO O ITEGRATED SESOR ORIETATIO K.Khoshelham a,b, M. Saadatseresht b,.g. Gorte a a Delft Unversty of Technology, Dept. of Earth Observaton and Space Systems, Kluyverweg 1, 2629 HS, The etherlands. b enter of Excellence n Geomatcs Engneerng and Dsaster Management, Dept. of Surveyng and Geomatcs Engneerng, Unversty of Tehran, Iran. KEY WORDS: Aeral Photogrammetry, GPS, IMU, Drect Sensor Orentaton, Integrated Sensor orentaton, Aeral Trangulaton ASTRAT: Drect measurement of exteror orentaton parameters has been a challenge n photogrammetry for many years. Drect sensor orentaton usng a calbrated GPS/IMU system can potentally elmnate the need for ground control ponts and aeral trangulaton, and consequently, result n a great reducton n the cost and tme of aeral photogrammetry. Prevous studes have shown that, comparng to conventonal aeral trangulaton, drect sensor orentaton yelds larger errors n mage and object space. It has also been shown that ncludng a number of te ponts wthn an ntegrated orentaton approach can result n a reducton of errors n mage space. In ths paper the nfluence of the number and dstrbuton of te ponts on ntegrated orentaton s nvestgated. Experments wth varous numbers of te ponts regularly as well as randomly dstrbuted are presented. Results ndcate that an ncrease n the number of te ponts up to one pont per model results n a consderable reducton of the mean error n mage space. 1. ITRODUTIO Ground control survey and aeral trangulaton are the most costly and tme-consumng stages n most photogrammetrc mappng projects. Drect measurement of exteror orentaton parameters by a thoroughly calbrated GPS/IMU system can potentally elmnate the need for ground control ponts and aeral trangulaton, and consequently, result n a great reducton n the cost and tme of aeral photogrammetry. Wth drect measurement of the poston and atttude of the camera perspectve center at exposure tmes, object space coordnates of mage ponts can be computed usng a least-squares forward ntersecton. Ths method s referred to as drect sensor orentaton (ramer and Stallmann, 21; Yastkl and Jacobsen, 25a). Whle drect sensor orentaton seems to reduce the photogrammetrc mappng process to photography and stereo plottng, n practce the accuracy of atttude parameters drectly measured wth the current technology of IMUs s generally lower than that of conventonal photogrammetry. Prevous experments wth commercally avalable GPS/IMU systems have shown that drect sensor orentaton n the scale of 1:5 reaches accuraces that are two to three tmes lower when compared to the results of conventonal aeral trangulaton (Hepke et al., 22; Khoshelham et al., 27). An alternatve approach to determnng sensor orentaton parameters and transformng mage-space coordnates to object space s ntegrated sensor orentaton (Ip, 25; Jacobsen, 24). In ths approach, te ponts contrbute to the refnement of the exteror orentaton parameters through a bundle adjustment. It has been shown that the ntroducton of te ponts n the computatons leads to a consderable mprovement of the accuracy n mage space (Hepke et al., 22). Snce ntegrated sensor orentaton does not requre ground control nformaton but the mage coordnates of te ponts must be measured, t can be consdered as a trade-off between drect sensor orentaton and conventonal aeral trangulaton n terms of cost and speed. An mportant ssue n ntegrated sensor orentaton s the number and dstrbuton of te ponts. Whle prevous studes have shown the effect of ncludng a certan number of te ponts, t s not known how the accuracy s nfluenced by varatons n the number and dstrbuton of the tes. The Objectve of ths research s to nvestgate the nfluence of the number and dstrbuton of te ponts on the accuracy of ntegrated sensor orentaton. We focus on the orentaton of an arborne frame camera usng a commercal GPS/IMU system. The paper s structured n fve sectons. Secton 2 descrbes the calbraton of ntegrated GPS/IMU system. In secton 3 the transformaton of ponts from mage space to object space through drect and ntegrated sensor orentaton s dscussed. Experments wth varous numbers of te ponts n ntegrated sensor orentaton are presented n secton 4. onclusons appear n the last secton. 2. AIRATIO OF GPS/IMU FOR AIRORE FRAME AMERAS The calbraton of GPS/IMU s bascally a comparson of exteror orentaton parameters measured drectly by GPS/IMU wth those obtaned by usng a reference method (Forlan and Pnto, 22; Honkavaara, 24; Yastkl and Jacobsen, 25b). The dscrepances are modelled by computng calbraton parameters that relate GPS/IMU poston and atttude to the reference exteror orentaton parameters. undle adjustment aeral trangulaton s most often used as the reference method for the computaton of exteror orentaton parameters. Therefore, the determnaton of calbraton parameters requres one or more test flghts over a test feld wth sgnalsed control ponts. There are two man approaches to the computaton of

2 calbraton parameters: 1-step approach and 2-step approach (Hepke et al., 22) step calbraton approach In the 1-step calbraton approach, a bundle adjustment of all avalable nformaton n mage and object space s performed. albraton parameters are estmated n such a way that the sum of squared resduals of observatons s mnmzed. The man calbraton parameters nclude the three components of the lever arm dstance between the GPS/IMU and the camera perspectve centre and three msalgnment angles that model the relatve orentaton of the IMU wth respect to the camera. Usually the camera exposure s precsely synchronzed wth GPS and IMU; however, f ths s not the case then a synchronzaton offset can be added to the set of calbraton parameters. Parameters of the nteror orentaton of the camera can also be estmated n the calbraton procedure, provded that the calbraton flghts are desgned n a way that the effects of dfferent parameters can be separated. (2), navgaton angles must be converted to photogrammetrc angles, omega, ph and kappa, whch determne the relatve orentaton of the camera wth respect to a 3D artesan object coordnate system (Fgure 1). Assumng that all the computatons are to be carred out n orthogonal coordnate systems, the converson of navgaton angles to photogrammetrc angles nvolves the followng sequence of rotatons: R R R R R where s a rotaton matrx that contans photogrammetrc angles, omega, ph and kappa, and brngs the camera axes parallel to object coordnate system (local frame); and R s the rotaton from IMU body to navgaton frame and contans navgaton angles, roll, ptch and yaw. As Fgure 1 llustrates, the rotatons from camera to body frame, R, and from navgaton to local frame, R, can be smply descrbed wth the followng matrces: (3) step calbraton approach A more straght forward way to compute the calbraton parameters s to perform the aeral trangulaton frst, and then compare the estmated exteror orentaton parameters wth GPS/IMU measurements. The dscrepances between GPS/IMU measurements and the camera poston and atttude parameters estmated n aeral trangulaton are modelled by a polynomal functon. The general form of the polynomal for poston measurements s expressed as (ramer and Stallmann, 21): 1 R 1 R (4) X Y Z X Y Z n a b. t c (1) and for atttude measurements: ω ϕ κ ω ϕ κ n u v. t w (2) where varables wth GPS/IMU subscrpt denote GPS/IMU measurements, those wth subscrpt denote aeral trangulaton estmate of the exteror orentaton parameters, subscrpts denote the polynomal coeffcents, t s tme and n s the order of the polynomals. The polynomal coeffcents play the role of calbraton parameters. A zero order polynomal ncorporates only three GPS shfts and three msalgnment angles. Ths basc set of sx parameters can properly calbrate the GPS/IMU f a comparson of aeral trangulaton estmate of exteror orentaton parameters and GPS/IMU measurements shows dscrepances that reman wthn a lmted constant range over tme. Otherwse, a large varaton of dscrepances over tme ndcates that addtonal drft parameters must be taken nto account, thus a hgher order of the polynomal should be used. Transformaton between dfferent coordnate systems also requres careful attenton n the calbraton process. GPS/IMU atttude measurements are navgaton angles, roll, ptch and yaw, whch defne the relatve orentaton of the IMU body wth respect to the navgaton frame. In order to be used n Equaton Fgure 1: oordnate systems used n navgaton and photogrammetry. 3. DIRET AD ITEGRATED ORIETATIO Once determned, the calbraton parameters are used to correct the GPS/IMU measurements of the exteror orentaton parameters. In ths drect orentaton approach, object space coordnates of all the mage ponts can be computed usng a least-squares forward ntersecton procedure, wth no need for ground control or te ponts (Khoshelham et al., 27). The exteror orentaton parameters corrected by the calbraton parameters are treated as constants n the forward ntersecton estmaton model. In other words, no further correctons are appled to the poston and atttude of the perspectve centres, and only the postons of the ponts n mage and object space are adjusted. In the ntegrated orentaton approach a further correcton of the exteror orentaton parameters of the camera s permssble. Ths s acheved by a smultaneous adjustment of a number of

3 te ponts wthn a bundle adjustment model wth addtonal constrants for refnng the exteror orentaton parameters. Snce every te pont appears n at least two mages, ntegratng a number of te ponts n the estmaton model results n a redundancy of observatons that allows for the correcton of exteror orentaton parameters. The ntroducton of te ponts n the ntegrated orentaton approach allows one to explot the strength of the bundles for the refnement of exteror orentaton parameters. Snce n the estmaton model sum of the squared resduals of the mage coordnates are mnmzed, one can expect that ntegrated orentaton results n mproved accuracy n mage space, and consequently, reduced Y parallax n the stereo model. For the experments wth drect and ntegrated orentaton the data of the 1:5 flght were used. A bundle adjustment aeral trangulaton of these data was performed so that the results can serve as reference for the evaluaton of drect and ntegrated orentaton approaches. The data of the bundle adjustment ncluded the ground coordnates of 13 control ponts evenly dstrbuted n the block. o control ponts were ntroduced n the computatons of drect and ntegrated orentaton. omputed ground coordnates for 18 check ponts were used to evaluate the accuracy of bundle adjustment as well as drect and ntegrated orentaton approaches n object space. Fgure 2 depcts the perspectve centres of a total of 181 photographs taken at the scale 1:5 along wth the control and check ponts. x 1 6 The Assgnment of sutable weghts to the exteror orentaton parameters s a determnant factor n the refnement of the calbrated poston and atttude parameters of the camera. If the exteror orentaton parameters are assgned very large weghts, as compared to mage coordnates, then the result of the estmaton model would be very smlar to that of drect orentaton. In other words, the correctons to exteror orentaton parameters would be very small, and the object space coordnates of the te ponts would be smlar to those obtaned from drect orentaton. On the other hand, f the exteror orentaton parameters are assgned weghts that are too small, then large correctons would be estmated for these parameters, whch may result n a greater error n the coordnates of the ponts n object space. 4. EXPERIMETS AD RESUTS Perspectve enter heck pont ontrol pont To experment wth the ntegrated orentaton approach and the nfluence of the te ponts a test dataset acqured by Applanx ntegrated GPS/IMU system was used. The dataset s one of the two datasets that were dstrbuted to the partcpants of the OEEPE test on ntegrated sensor orentaton (See lsen, 22). The data acquston comprsed of a calbraton flght at an mage scale of 1:1, and a test flght at 1:5 over a test feld wth 49 sgnalsed control ponts located n orway. The dataset conssts of the followng data: Poston and atttude measurements made by GPS/IMU; Ground coordnates of the control ponts n EUREF89/UTM system wth heghts over the reference ellpsod; Image coordnates of control ponts and a number of te ponts. The calbraton of the system was carred out usng the data of the 1:1 flght. A bundle adjustment aeral trangulaton of the mage coordnates and control ponts was performed usng PAT- aeral trangulaton software. o GPS/IMU data were ntroduced at ths step and the exteror orentaton parameters computed wthn the bundle adjustment were used as reference n the calbraton procedure. The 2-step approach was mplemented for the estmaton of calbraton parameters. A comparson of the camera poston and atttude parameters from bundle adjustment wth GPS/IMU measurements showed dscrepances that dd not largely vary over tme; therefore, the basc set of sx calbraton parameters consstng of three GPS shfts and three msalgnment angles was adopted for the calbraton x 1 5 Fgure 2. Perspectve centers of the mages of 1:5 flght along wth the control and check ponts. Arrows ndcate the drecton of the flghts. To nvestgate the nfluence of te ponts, ground coordnates of the check ponts were computed usng dfferent methods wth varous numbers of te ponts. Obvously, all te ponts contrbute n the bundle adjustment aeral trangulaton, and no te ponts are ntroduced n the drect orentaton approach. In the ntegrated orentaton approach seven schemes for the selecton of the te ponts were desgned. Table 1 summarses the te pont selecton schemes. In addton, for each selecton scheme two dstrbuton schemes were taken nto account. In the regular dstrbuton scheme an even dstrbuton of the te ponts across the block was desred; whereas, n the random dstrbuton scheme, a number of te ponts equal to the correspondng regular dstrbuton scheme but randomly dstrbuted wthn the block was selected. For example, n the selecton scheme S-1 wth regular dstrbuton a te pont at the centre of the overlappng area of every par of consecutve mages was selected, whch resulted n 19 te ponts evenly dstrbuted across the block. Thus, n the selecton scheme S-1 wth random dstrbuton, 19 te ponts at random postons wthn the block were selected. In the selecton schemes S-2 and S-4 wth regular dstrbuton te ponts n symmetrc von Gruber postons were chosen. The accuracy n object space was evaluated by the RMSE of the dscrepances between measured and computed ground

Table 2 summarses the accuraces obtaned by ncludng varous numbers of te ponts wth regular dstrbuton n ntegrated orentaton. Results of usng the random dstrbuton scheme are presented n Table 3.

4 coordnates of the check ponts. Fgure 3 shows these dscrepances for S-1, S-2 and S-4 te pont selecton schemes wth both regular and random dstrbuton. In mage space, the mean resdual of the mage coordnates of the te ponts was used as an ndcator of the accuracy. Table 2 summarses the accuraces obtaned by ncludng varous numbers of te ponts wth regular dstrbuton n ntegrated orentaton. Results of usng the random dstrbuton scheme are presented n Table 3. Results of bundle adjustment aeral trangulaton and drect orentaton are also ncluded n Table 2 and Table 3 for the sake of comparson. Table 1: Te pont selecton schemes Selecton Scheme Descrpton S-1/1 1 te pont n every 1 th model S-1/5 1 te pont n every 5 th model S-1/3 1 te pont n every 3 rd model S-1/2 1 te pont n every 2 nd model S-1 1 te pont n every model S-2 2 te ponts n every model S-4 4 te ponts n every model A comparson of the results of drect orentaton and ntegrated orentaton n Table 2 as well as Table 3 reveals that ntroducng a mnmum number of te ponts has a mnor mpact on the accuracy n object space. Whle the RMSE values n X and Y drecton obtaned by ntegrated orentaton are smlar to (even worse than) those obtaned by drect orentaton, a slght mprovement of the RMSE n the Z drecton can be observed. A consderable mprovement, however, can be seen n the accuracy n mage space as ndcated by the mean resduals. These results confrm prevous fndngs of the OEEPE test on ntegrated sensor orentaton (Hepke et al., 22). A close examnaton of the results n Table 2 and Table 3 also shows that the accuraces n mage space exhbt a further mprovement as a consequence of ncreasng the number of te ponts; whereas, the accuraces n object space reman more or less n the same range, and are not affected by the ncrease n the number of te ponts. The changes n the mean resdual values obtaned by ntegrated orentaton ndcates that by ncludng a suffcent number of te ponts n the computatons the Y parallax n mage space can be reduced to values that are two to three tmes lower than those obtaned by drect orentaton. Fgure 4 demonstrates the nfluence of the number and dstrbuton of te ponts on the accuracy of ntegrated orentaton n mage space. As can be seen, by ncreasng the number of te ponts up to one pont per model (scheme S-1) the mean resdual values decrease almost lnearly. The selecton schemes S-2 and S-4 result n only a slght mprovement of the accuracy n mage space. It s nterestng to note that regular and random dstrbutons of the te ponts yeld very smlar results. Ths means that the accuracy n mage space s not nfluenced by the dstrbuton of the te ponts. One excepton to ths concluson s the scheme S- 4, where the mean resdual assocated wth random dstrbuton s notceably smaller than that of regular dstrbuton. A possble explanaton for ths could be that the accdental proxmty of the te ponts n random dstrbuton can bas the mean resdual to a smaller value. Fgure 3. Vectors of error n check ponts obtaned by usng varous te pont selecton and dstrbuton schemes n ntegrated orentaton. Top row: regular dstrbuton; button row: random dstrbuton; from left to rght: selecton schemes S-1, S-2 and S-3.

5 Table 2: Results of usng varous numbers of te ponts wth regular dstrbuton n ntegrated orentaton Method Scheme r. of te ponts RMSE_X RMSE_Y RMSE_Z Mean Resdual (µm) undle AT Drect Orentaton S-1/1-Reg S-1/5-Reg S-1/3-Reg Integrated S-1/2-Reg Orentaton S-1-Reg S-2-Reg S-4-Reg Table 3: Results of usng varous numbers of te ponts wth random dstrbuton n ntegrated orentaton Method Scheme r. of te ponts RMSE_X RMSE_Y RMSE_Z Mean Resdual (µm) 5. OUSIOS In ths paper the nfluence of the number and dstrbuton of te ponts on ntegrated orentaton of an aeral frame camera was nvestgated. The ntegrated orentaton approach was mplemented through a bundle adjustment of a number of te ponts wth addtonal constrants for refnng the exteror orentaton parameters. The number of te ponts vared across experments from 17 (one pont n every 1 th model, selecton scheme S-1/1) to 516 (one pont n each model, selecton scheme S-4). Experments were also conducted wth regularly dstrbuted te ponts as well as randomly dstrbuted ones. It was found that ncludng te ponts n ntegrated orentaton approach, regardless of ther number and dstrbuton, does not substantally mprove the accuracy n object space, and the results are smlar to those obtaned by drect orentaton approach. In mage space, however, t was shown that an ncrease n the number of te ponts up to one pont per model results n a consderable reducton of the mean resdual of the mage coordnates. Ths suggests that ncludng a mnmum of one te pont per model can be recommended for practcal applcatons snce t leads to a consderable reducton of Y parallax n mage space. Also, t was shown that regular and random dstrbutons of the te ponts result n a smlar range of errors n mage space. Therefore, t can be concluded that the dstrbuton of the te ponts does not have an nfluence on the accuracy of ntegrated orentaton approach n mage space. AKOWEDGEMET undle AT Drect Orentaton Integrated Orentaton Mean error n mage space S-1/1-Rand S-1/5-Rand S-1/3-Rand S-1/2-Rand S-1-Rand S-2-Rand S-4-Rand /1 1/5 1/3 1/ Regularly Dstrbuted Dstrbuton scheme Randomly Dstrbuted Fgure 4. Mean error values n mage space obtaned for varous selecton and dstrbuton schemes. The authors would lke to thank Prof. Karsten Jacobsen of the Unversty of Hanover for provdng the dataset that was used n the experments. REFEREES ramer, M. and Stallmann, D., 21. On the use of GPS/nertal exteror orentaton parameters n arborne photogrammetry, ISPRS Workshop "Hgh Resoluton Mappng from Space 21", Hannover, Germany, pp Forlan, G. and Pnto,., 22. Integrated IS/DGPS systems: calbraton and combned block adjustment, Proceedngs of the OEEPE Workshop: Integrated Sensor Orentaton, Insttute for Photogrammetry and Geonformaton, Unversty of Hannover, Hannover, Germany, pp Hepke,., Jacobsen, K. and Wegmann, H., 22. Analyss of the results of the OEEPE test "Integrated Sensor Orentaton", Proceedngs of the OEEPE Workshop: Integrated Sensor Orentaton, Insttute for Photogrammetry and Geonformaton, Unversty of Hannover, Hannover, Germany, pp Honkavaara, E., 24. albraton n drect georeferencng: Theoretcal consderatons and practcal results. Photogrammetrc Engneerng and Remote Sensng, 7(11): Ip, A.W.., 25. Analyss of ntegrated sensor orentaton for aeral mappng. MSc Thess, Unversty of algary, algary, 181 pp. Jacobsen, K., 24. Drect/ntegrated sensor orentaton - pros and cons, XX ISPRS ongress, ommsson III, Istanbul, Turkey, pp

6 Khoshelham, K., Saadatseresht, M. and Mlan, A., 27. albraton of ntegrated GPS/IS system and drect sensor orentaton, Geomatc '86 annual conference, atonal artographc entre, Tehran, Iran. Yastkl,. and Jacobsen, K., 25a. Drect sensor orentaton for large scale mappng - potental, problems, solutons. Photogrammetrc Record, 2(111): Yastkl,. and Jacobsen, K., 25b. Influence of system calbraton on drect sensor orentaton. Photogrammetrc Engneerng and Remote Sensng, 71(5):

Proper Choice of Data Used for the Estimation of Datum Transformation Parameters

Proper Choice of Data Used for the Estimation of Datum Transformation Parameters Proper Choce of Data Used for the Estmaton of Datum Transformaton Parameters Hakan S. KUTOGLU, Turkey Key words: Coordnate systems; transformaton; estmaton, relablty. SUMMARY Advances n technologes and