geometric in-flight calibration of the stereoscopic line ...directory.umm.ac.id/data...

Ž .ISPRS Journal of Photogrammetry & Remote Sensing 55 2000 59–71www.elsevier.nlrlocaterisprsjprs

Geometric in-flight calibration of the stereoscopic line-CCDscanner MOMS-2Pq

Wolfgang Kornus ), Manfred Lehner, Manfred Schroeder( )Institute of Optoelectronics, Optical Remote Sensing DiÕision, German Aerospace Center DLR , P.O. Box 1116,

D-82230 Wessling, Germany

Received 31 July 1998; accepted 6 December 1999

Abstract

This paper describes the geometric in-flight calibration of the Modular Optoelectronic Multispectral Scanner MOMS-2P,which has collected digital multispectral and threefold along-track stereoscopic imagery of the earth’s surface from thePRIRODA module of the Russian space station MIR from October 1996 to August 1999. The goal is the verification and, ifnecessary, the update of the calibration data, which were estimated from the geometric laboratory calibration. The paper issubdivided into two parts, describing two different procedures of geometric in-flight calibration. The first method is based onDLR matching software and is restricted to nadir looking channels, which are read out simultaneously. From a high numberof individual point matches between the images of the same area taken by the different CCD arrays, the most reliable onesare selected and used to calculate shifts with components in and across flight direction between the CCD arrays. These actualshifts are compared to the nominal shifts, derived from the results of the laboratory calibration, and parameters of the validcamera model are estimated from both data sets by least squares adjustment. A special case of band-to-band registration arethe two optically combined CCD-arrays of the nadir high-resolution channel. They are read out simultaneously with anominal 10 pixel overlap in stereoscopic imaging mode A. The DLR matching software is applied to calculate thedisplacement vector between the two CCD-arrays. The second method is based on combined photogrammetric bundleadjustment using an adapted functional model for the reconstruction of the interior orientation. It requires precise andreliable ground control information as well as navigation data of the navigation-package MOMS-NAV. Nine contiguousimage scenes of MOMS-2P data-take T083C building an about 550-km-long strip over southern Germany and Austria takenin March 1997 were evaluated. From both procedures calibration data are estimated, which are presented and compared tothe lab-calibration results. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: MOMS-2P; geometric calibration; in-flight calibration; band-to-band registration; bundle adjustment; line-CCD sensor; satellite

q Revised version of a paper presented at the ISPRS Commis-sion I Symposium, February 25–27, 1998, Bangalore, India.

) Corresponding author.Ž .E-mail address: [email protected] W. Kornus .

1. Introduction

The Modular Optoelectronic Multispectral Scan-ner MOMS-2P is a push-broom scanner for multi-spectral and along-track stereoscopic imaging in fourdifferent modes. It is built by the German Daimler-

0924-2716r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0924-2716 99 00037-4

( )W. Kornus et al.r ISPRS Journal of Photogrammetry & Remote Sensing 55 2000 59–7160

Chrysler Aerospace company Dasa and mounted onthe PRIRODA module of the Russian space stationMIR since May 1996. It delivers imagery since endof September 1996. MOMS-2P is the refurbishedMOMS-02 camera, which has been flown on thespace shuttle during the D2 mission in AprilrMay

Ž .1993 Seige et al., 1998 .The optical system of MOMS is based on a

modular concept. The multispectral module com-prises two nadir-oriented lenses, containing twoCCD-arrays each for colour image acquisition infour narrow banded spectral channels with 18-mground pixel size. The stereo module consists ofthree lenses, which are oriented in three differentdirections. The forward and aft looking lenses con-tain one CCD array each for panchromatic imageacquisition with 18-m ground pixel size. The thirdlens is nadir looking and contains two CCD-arrays,which are optically combined to one high-resolutionchannel, providing panchromatic imagery with aground pixel size of 6 m. The complexity and also

Ž .the high mass 143 kg of the optical module posedhigh demands on the process of laboratory calibra-tion, which was conducted by Dasa. Experience fromthe D2 mission showed that for this big camera withfive different lenses in-flight geometric calibrationactivities are necessary. In this paper, two differentmethods of in-flight calibration are described. Thefirst method is restricted to channels, which aresimultaneously read out, while nominally looking atnadir. These are channels MS1, MS2, MS3, MS4,

Ž .and HR5A or sub-arrays thereof in certain combi-Žnations in the imaging modes B, C, and D see Table

.3 . Here, DLR matching software has been used tocalculate displacement vectors with components in

Ž .and across flight direction rows, columns . Thesemeasurements are produced with sub-pixel accuracyby local least squares matching techniques using aspecial evaluation strategy for the matching results to

Ž .cope with the generally wanted! dissimilarities be-tween the images of the four multispectral channels.The second method is based on photogrammetricbundle adjustment and therefore is restricted to chan-

Ž .nels of the stereo imaging modes A and D . In thisexample, channels HR5A, HR5B, ST6 and ST7 ofimaging mode A are involved. The approach can beconsidered as the reverse process of photogrammet-ric point determination using precise navigation data

and also a substantial amount of very accurate groundcontrol information in order to estimate the camerageometry. Parameters of the actual camera model areestimated with both methods from in-flight and labo-ratory measurements by least squares adjustment.From the derived camera parameters, new calibrationtables are generated as input for the Levels 1A) and1B processing at DLR Neustrelitz and for pho-togrammetric evaluation of stereoscopic MOMS-2Pimagery.

2. In-flight calibration of channels MS1, MS2,MS3, MS4 and HR5A

The image based band-to-band registration methodused here has already been applied to MOMS-02 on

Ž .D2 mission 1993 . For MOMS-2P, it has beenrefined to provide a full displacement function over

Ž .the applicable range of image pixels columns of theCCD sensor arrays, which is different for the indi-vidual imaging modes. Because natural displace-ments may occur between different bands of a sensorfor objects with distinctively different reflection inthe respective wavelength intervals a strategy has tobe found to exclude such object areas from thisevaluation. Of course, all images used have been

Ž .radiometrically corrected Level 1A products . Mea-surement tools and evaluation strategy are explainedin the following subsections.

2.1. Image matching

The DLR matching software has been developedfor the automated measurement of massive numbersof conjugate points in the stereoscopic imagery of

Žthree-line stereo scanners projects MEOSS and.MOMS . More details about this software can be

Ž .found in Lehner and Gill 1992 , Lehner and KornusŽ . Ž .1995 and Kornus et al. 1996 .

Ž .The main features used here are: 1 An interestoperator selects well defined patterns suitable fordigital image correlation; the principles of theForstner interest operator are used with slight modi-¨fication; a good interest operator point is defined bya surrounding window with multi-directional edgeinformation and a local contrast above a given

( )W. Kornus et al.r ISPRS Journal of Photogrammetry & Remote Sensing 55 2000 59–71 61

Ž .threshold. 2 Conjugate points at pixel accuracylevel are generated using the maximum of the nor-malised correlation coefficient; the latter and a qual-ity figure are stored for further selection of the most

Žreliable conjugate points the quality figure as de-Ž .fined in Lehner 1986 should assess the steepness

and uniqueness of the peak in the matrix of correla-tion coefficients; its calculation is based on the val-ues and the distribution of the five largest elementsof this matrix — a quality figure 0.6 will belong to avery pronounced peak, quality figures below 0.2

.indicate dangerous side peaks ; the positioning of thesearch areas is done via an affine transformation,which is calculated using already known conjugate

Žpoints in the neighbourhood normally, an image.pyramid is used for getting these approximate points .

Ž . Ž .3 Local least squares matching LLSQM is finallyused for refinement of the conjugate points to sub-pixel accuracy; in this step, it is also possible tomatch images of different resolutions like MOMShigh and low resolution channels.

2.2. EÕaluation strategy

The steps for the extraction of the shifts betweenthe MOMS-2P channels are found below.

Ž .1 Interest operator points are generated for onechannel; the interest operator will avoid areas withlow contrast and patterns with ambiguous matchingresults; typical operator window size used is 7=7pixels.

Ž .2 Run the matching software for the channelcombination under investigation: a search area sizeof 19=19 pixel is used for matching at pixel accu-racy; for search area selection it is sufficient to usean estimated mean shift between the channels whichwas determined beforehand during the lab-calibra-tion and is valid for all data-takes; local least squaresmatching is run twice using two different window

Ž .sizes 15=15 and 17=17 pixels have been usedfor sub-pixel registration.

Ž .3 Consider both resulting point files selectingonly points, which satisfy the following conditions:

Ž .a Maximum of correlation coefficient and qual-Žity figure from areal correlation with pixel accu-

.racy are beyond given thresholds to guaranteeŽwell defined objects 0.9 and 0.23, respectively,

have been used for image pairs involving channels1–3; 0.8 and 0.23 for channel pairs containing

Ž .channel 4 because channel 4 near infrared showsless correlation with the other channels, particu-

.larly in vegetated areas .Ž .b Local least squares matching converged for

Ž .both window sizes take well defined objects only .Ž .c Differences between the resulting coordinatesfor the two window sizes are below a given

Žthreshold exclusion of objects with different pat-terns in the different spectral bands; 0.25 pixel has

.been used throughout the investigation .

Ž .4 Averaging: the image matching results in ir-regularly distributed sets of conjugate point pairsŽ . Ž X X .l,c and l ,c for the two channels. The differences

Ž . X Ž .l–l’ along-track and c–c across-track define thelocal shifts between the channels. In order to evenmore reduce the impact of natural channel differ-ences, these shifts are averaged over the whole scene

Žlength for 29 equidistant column intervals one col-.umn imaged by one CCD-array element of 200

pixels. The mean values and their standard devia-tions are then assigned to the centers of the columnintervals.

Thus, displacement functions have been derivedfor all channel pairs for five data-takes acquired in

Ž1996 unfortunately, there was a large gap in imag-.ing in 1997 because of the MIR accident . These

functions enter an adjustment process combining lab-oratory calibration and matching results to give final

Žvalid calibration tables and camera parameters see.Section 2.6 .

2.3. Example

Ž .Fig. 1 shows the image of channel MS3 red ofŽ .scene 3 part of Ethiopia of data-take T081A im-

Žaged on December 18, 1996 in imaging mode B 4multispectral channels, 5800 pixel per channel, 5920

.image lines per scene . This is a good scene for themeasurements discussed in this paper. The interest

Žoperator found about 173,000 points centers of pat-


Fig. 1. MOMS-2P Ethiopia: data-take T081A, scene 3, channel MS3, about 104=106 km; the window shows the marked sub-scene of600=800 pixel in full resolution with the interest operator points drawn on it.

.tern areas in the image of channel MS3, about 83%of which could be located in the other channels bythe image matching software. The window in Fig. 1shows a small part of the scene in full resolutionwith the interest operator points drawn on it.

The mean values of the maximum of the correla-tion coefficients and the quality figure are shown inTable 1.

Table 2 shows the shifts between channels MS2and MS3 as the results of the evaluation for 29


Table 1T081A, scene 3, mean correlation coefficient and quality figuresof all matched points

Channel pair MS3rMS1 MS3rMS2 MS3rMS4

Mean correl. coeff. 0.92 0.93 0.89Mean quality figure 0.28 0.27 0.25

column intervals. The graphical representation isgiven in Fig. 2.

2.4. Particularities of the different imaging modes

For an exact definition of the imaging modes ofŽ .the MOMS-2P camera see Dasa 1996 . The channel

Fig. 2. T081A, scene 3: shifts between channels MS2 and MS3.

selection and the corresponding numbers of activepixels are given in Table 3.

Table 2T081A, scene 3: shifts channel MS2 — channel MS3; the points for each column interval stem from an image sub-area of 200=5920

Ž . Ž .pixel; x is along track image rows , y is along scan-line image columns

Ž . Ž .Interval number No. of points Centre column Mean x Shift y Standard deviation

s sx y

1 2939 100 1.40 6.31 0.14 0.162 3126 300 1.42 6.31 0.12 0.163 3195 500 1.46 6.37 0.11 0.164 3369 700 1.49 6.48 0.10 0.135 3659 900 1.51 6.59 0.11 0.146 3579 1100 1.53 6.71 0.11 0.147 3328 1300 1.55 6.84 0.11 0.128 3426 1500 1.60 6.98 0.10 0.139 3419 1700 1.63 7.13 0.10 0.14

10 3504 1900 1.66 7.29 0.13 0.1511 3573 2100 1.68 7.41 0.12 0.1512 3495 2300 1.71 7.54 0.11 0.1413 3944 2500 1.75 7.65 0.12 0.1314 4257 2700 1.79 7.74 0.12 0.1315 4648 2900 1.85 7.80 0.12 0.1416 5174 3100 1.94 7.88 0.12 0.1317 5031 3300 2.06 7.97 0.12 0.1318 5580 3500 2.21 8.07 0.11 0.1219 5368 3700 2.32 8.16 0.11 0.1320 3842 3900 2.42 8.24 0.11 0.1421 3115 4100 2.56 8.31 0.11 0.1422 3490 4300 2.70 8.39 0.10 0.1223 4048 4500 2.82 8.47 0.10 0.1224 4155 4700 2.97 8.54 0.12 0.1225 4550 4900 3.16 8.61 0.12 0.1026 3835 5100 3.33 8.65 0.13 0.1027 3720 5300 3.51 8.72 0.12 0.1128 4780 5500 3.68 8.77 0.12 0.1129 4519 5700 3.85 8.80 0.12 0.11


Table 3MOMS-2PrPRIRODA imaging modes and corresponding numbers of active pixels per channel

w xImaging MS1 MS2 MS3 MS4 HR5A HR5B ST6 ST7 Swath width kmŽ . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .mode blue green red NIR pan pan pan pan at 400 km altitude

Ž . Ž .A – – – – 4152 4152 2976 2976 50 HR r54 STB 5800 5800 5800 5800 – – – – 105

Ž . Ž .C – 3220 3220 3220 6000 – – – 58 MS r36 HRD 5800 – – 5800 – – 5800 5800 105

Ž .1 Mode A: the panchromatic channels HR5,ST6, and ST7 look in different directions at everytime instant, thus, the method mentioned above isnot applicable; there is only a very small overlap ofthe high-resolution channels HR5A and HR5B ofnominally 10 pixels which can help in the composi-

Žtion of a really continuous channel HR5 array thereis an obvious shift between the two channels ofabout 1 pixel along and 2 pixels across flight direc-

.tion . The values of important camera parameters forthese stereo channels can only be estimated by pho-togrammetric adjustment, if very good knowledge ofthe terrain and precise orbit and attitude data are

Ž .available see Section 3 .Ž .2 Mode B: the pairwise shifts between the

multispectral channels MS1, MS2, MS3, and MS4over the full length of the 5800 active pixels can bemeasured.

Ž .3 Mode C: the pairwise shifts between themultispectral channels MS2, MS3, and MS4 over3220 active pixels can be measured; the shifts tochannel HR5A can be measured for a sub-array of2000 pixels of these 3220 pixels; the latter measure-ment is done in two steps:

Ž .a a first matching is carried out between themultispectral channels and a corresponding re-duced-resolution image of the high-resolution

Ž .channel factor 3 reduction in both dimensions ;Ž .b this results in initial approximations for thesecond step, a least squares matching betweenchannel HR5A and the multispectral channels,whereby the known resolution ratio between thesechannels was used as approximation for the scaleparameters determined in the least squares match-ing.

Ž .4 Mode D: the shifts between the multispectralchannels MS1 and MS4 can be measured over thefull length of the 5800 active pixels; the stereochannels ST6 and ST7 are not simultaneously look-ing onto the same terrain.

2.5. Registration between channels HR5A and HR5B

Channels HR5A and HR5B are optically coupledto form the high-resolution channel HR5. These twochannels are read out with a nominal overlap of 10pixel. Via image matching, shifts in and across flightdirection of 1.2 and y1.9 pixels were measured. Forthese measurements, the overlap area was 8= en-larged by bilinear interpolation to get meaningfulwindow sizes for LLSQM. The latter was performedfor a regular set of initial approximations. Twowindow sizes, 37=37 and 41=41 pixel, have beenused. These window sizes appear to be large, but inreality they refer to 8= enlarged image areas. Onlythese conjugate points entered into the calculation ofshifts for which the following two conditions ap-plied:

1. LLSQM converged to nearly identical results forthe two window sizes.

2. The normalised cross correlation coefficient ofthe image chips at the end of the LLSQM waslarger than 0.9.

The means and standard deviations of the differ-ences between the coordinates of channels HR5Aand HR5B for these conjugate points can be seen inTable 4 for several sub-scenes. The standard devia-tions are larger as those listed in Table 2, because of


Table 4Ž .Result of matching in overlap area of channels HR5A and HR5B imaging mode A ; parts 1 and 2 are the upper and lower half of each

Ž . Ž .scene; this separation was made for checking the reliability of the matching scheme; x is along track rows , y is along scan-line columns

Ž . Ž .Data-take No. of points Mean x Shift y Standard deviation

s sx y

T0700rpart 1 115 1.18 y1.89 0.26 0.26T0700rpart 2 135 1.12 y1.90 0.24 0.29T07FBrpart 1 57 1.16 y1.79 0.19 0.19T07FBrpart 2 58 1.20 y1.79 0.21 0.23All 365 1.16 y1.86 0.23 0.26

the small overlap region, which necessitated extrac-tion of image chips with lower contrast for LLSQM.

2.6. Generation of calibration tables

The matching results differ from the values of theŽlaboratory calibration to such an extent partly sev-

.eral pixels that makes it necessary to change thecalibration tables for the systematic processing of theMOMS images. As an example Fig. 3 shows acomparison of the shifts between channels MS2 and

Fig. 3. Shifts between channels MS2 and MS3: in-flight versuslaboratory calibration results.

MS3 derived from laboratory calibration versus theresults of image matching. Here, the differences ofabout 1.8 pixel in the along-track shifts, e.g., indicatethat the along-track components of the camera pa-rameters in channel MS2 andror channel MS3 havechanged to that extent since the time of lab-calibra-tion. The reason is attributed to the different environ-mental situation in the laboratory compared to the

Žreal imaging condition in space non-zero gravity,.non-vacuum, controlled temperature, etc. . The dif-

ferent angles between the y-axis and the curvesrepresenting the along scan-line shifts indicatechanges in the image scale, which correspond tochanges in the focal lengths of channel MS2 androrchannel MS3.

If the relative shifts are determined for a varietyof possible channel combinations, camera parametersfor all investigated channels can be derived withrespect to the parameters of a selected reference

Ž .channel see Table 5 . For that purpose, the differ-ences x and y between the shifts derived fromdiff diff

lab-calibration and from image matching were fedinto a least squares adjustment, estimating parame-ters of an adjusting parabola in case of the along-trackshifts or a line in case of the along scan-line shifts.The correction equations read:

2ˆ ˆ ˆÕ sx y A qB yqC yx diff x x x

ˆ ˆÕ sy y A qB yy diff y y

Ž .with y denoting the y-coordinate along scan-lineof the respective centre of column interval withrespect to the centre of the CCD-array.

This was done for 20 different channel combina-tions in imaging modes B and C involving the fourmultispectral channels and also the high-resolution


Table 5Adjusted camera parameters x, their standard deviation s andˆ ˆx

the deviations from the lab-calibration D x for five MOMS-2Pchannels

x s D xˆ ˆx

MS1w xc mm 220.139 0.003 y0.021

w xx pixel y1.3 0.057 y0.60w xy pixel 7.4 0.078 2.40w xK pixel 0.3 0.012 y0.1w xk mdeg 2.1 1.783 y3.5

MS2w xc mm 220.076 0.003 y0.019

w xx pixel y1.0 0.044 y1.40w xy pixel 7.2 0.048 0.20w xK pixel y0.6 0.014 0.3w xk mdeg 2.7 1.763 y6.5

MS3w xc mm 219.964 0.002 y0.151

w xx pixel 1.3 0.048 0.00w xy pixel 15.1 0.027 y0.80w x Ž .K pixel reference 0.2 – –w xk mdeg y21.9 1.763 y7.6

MS4w xc mm 219.951 0.003 y0.140

w xx pixel 0.7 0.052 1.30w xy pixel 14.5 0.056 y0.80w xK pixel 0.5 0.016 0.0w xk mdeg y22.8 1.796 y6.1

( )HR5A referencew xc mm 660.256 – –

w xx pixel 0.1 – –0w xy pixel y0.4 – –0w xK pixel y0.3 – –w xk mdeg I2.9 – –

channel HR5A. For channel HR5A the image coordi-nates were reduced by a factor of 3 to enable thefurther processing in a common image scale. The

ˆ ˆ ˆ ˆ ˆparameters A , B , A , B , and C were trans-x x y y x

formed into the five following parameters dc, dx ,0

dy , dK , dk , describing deviations of camera pa-0

rameter differences between the two selected chan-nels, which obviously occurred since the time oflab-calibration:

1. the calibrated focal length c,2. the along-track displacement x ,0

3. the along scan-line displacement y ,0

Ž4. the sensor curvature K multiplied with the.squared pixel position along the scan-line and

5. the sensor rotation k within the image plane.

The mentioned deviations for the respective channelcombination are obtained as follows:

ˆdcscBy

ˆdx sA0 x

ˆdy sA0 y

ˆdKsCx

1ˆ ˆdks B ,Bx x2ˆ1qBx

For the first equation the nominal focal lengthvalue cs220.0 mm is used with sufficient accuracy.The 20 investigated channel combinations resulted in20 camera parameter differences, which correspondto camera parameter changes of altogether five chan-

Ž .nels four multispectral and HR5A . By least squaresadjustment a final set of camera parameters for eachchannel was estimated from these differences, whilethe lab-calibrated parameters of one selected channelwere taken as reference. Due to the small swathwidth of imaging mode C, the sensor curvature K

Žcould not be estimated in this case it was deter-mined only for the four multispectral channels of

.imaging mode B .Table 5 contains the estimated camera parameters

x and the theoretical standard deviations s resultingˆ ˆx

from the adjustment of the camera parameter differ-ences. The column D x reflects the deviations fromthe lab-calibrated results. K represents the along-track effect caused by sensor curvature at ys3000pixel i.e., at the end points of the 6000 pixel longCCD-arrays. The along-track effect caused by a sen-sor rotation of ks10 mdeg is about 0.5 pixel atys3000 pixel. The deviations from the lab-calibra-tion values in Table 5 show that the effect of K and

Žk are each less than 0.4 pixel in the worst case end.points of CCD-line , while the effect of the devia-

tions for the remaining three parameters can exceed2 pixels. For comparison, the camera parametersestimated from the lab-calibration evaluation arelisted in Table 6. In both Table 5 and 6, four focallengths were used for the multispectral channels,


Table 6Lab-calibrated camera parameters of multispectral channels

MS1 MS2 MS3 MS4 HR5A

w xc mm 220.160 220.095 220.115 220.091 660.256w xx pixel y0.7 0.4 1.3 y0.6 0.10w xy pixel 5.0 7.0 15.9 15.3 y0.40w xK pixel 0.4 y0.9 0.2 0.5 y0.3w xk mdeg 5.6 9.2 y14.3 y16.7 y2.9

although only two lenses are used for them, in orderto better model differences between the two CCD-lines of each lens.

3. In-flight calibration of channels HR5A, HR5B,ST6 and ST7

Originally, this task was planned to be conductedin cooperation with the Institut Cartografic de`

Ž .Catalunya ICC using MOMS-2P imagery of Cat-alonia. From the ICC database, containing a country-wide digital terrain model and also digital orthoim-ages in scale 1: 25 000, a large number of groundcontrol points should have been derived in an auto-

Ž .mated way Kornus et al., 1996 . Since a suitabledata-take of Catalonia has not been registered so far,imagery of southern Germany and Austria, taken inApril 1997, was processed instead.

3.1. Input data

Due to high cloud coverage in the western part ofthe strip, the evaluation starts with image scene a25,

Žapproximately at the longitude of Stuttgart see Fig..4 . The end of the strip has been selected about 160

km beyond the Austrian border in image scene a33.ŽThus, the control and checkpoints all located in

.Germany are also imaged by the backward lookingchannel ST7. The total length of the strip is about415 km corresponding to 23310 image lines for theST6 and ST7 channels. The ground pixel sizes of theimagery at 390-km orbit altitude are 5.9 m and 17.7m.

3.1.1. Image coordinates of tie pointsFrom 350,000 homologous points found by local

least squares image matching in all three image

strips, a subset of 2880 tie points distributed regu-larly within the meshes of a grid was selected usingthe correlation coefficient and the quality figure as

Ž .selection criteria best point within each grid mesh .

3.1.2. Ground control pointsAs ground control information, navigation points

Ž .of the AMilGeo Amt fur militarisches Geowesen¨ ¨were used, representing street crossings or junctions,which normally can be well identified also inmedium-resolution satellite imagery. Their object co-ordinates are known with an accuracy of 1.5 m in X,Y and Z. More than 250 navigation points weremanually measured in the nadir looking channel atthe Chair for Photogrammetry and Remote Sensing

Ž .of the Technical University TU Munich. The ma-jority of them was identified in the central part of thestrip, since for those so-called 3-ray-points the im-

Žage coordinates of all three viewing directions fore,.nadir, aft can be considered in the bundle adjust-

ment. Fig. 5 shows the distribution of both the tiepoints and the ground control points. The identifica-tion accuracy was adversely affected by defocusingeffects in the high-resolution channel, which oc-curred during the warming-up phase of the scannerand are documented in the temperature measure-ments of the housekeeping data. Nevertheless, it waspreferred to conduct the measurements in the defo-cused high-resolution imagery rather than in the 3=

decreased resolution of the oblique viewing stereochannels. Therefore, the a priori standard deviationsof the object coordinates were set to 6 m in thebundle adjustment, corresponding to 1 pixel identifi-cation accuracy. After identification, the image points

Fig. 4. Geographic location of the test area.


Ž . Ž .Fig. 5. Distribution of tie points dots and ground control points triangles in the image scenes a25 to a33.

were automatically transferred to the other imageŽ .strips by least squares matching Kornus et al., 1996 .

3.1.3. NaÕigation dataMOMS-2P has its own navigation system

MOMS-NAV consisting of a Motorola Viceroy GPSreceiver with dual antennas and LITEF gyro systems.The raw GPS and gyro data are recorded along withthe MOMS image frames. Additionally, time infor-mation for later exact synchronisation of MOMS-NAV data and image frames is written into theseauxiliary housekeeping data.

The processing of the gyro data including theabsolute referencing with INS data of the MIR sta-tion or — if available — star camera measurementsusing the star sensor on MIR module Kvant 2 takesplace at the German Space Operations CenterŽ .GSOC of DLR. This also includes the time syn-chronisation of navigation data and image frames.For the data-take T083C discussed here a standarddeviation of the angular measurements of 15.3Y is

Žindicated, corresponding to about 1.6 pixel ST-.channel . Star camera measurements were available.

Since the MOMS camera was mounted by an extra-Žvehicular activity onto the module PRIRODA May

.1996 , it was impossible to conduct exact calibrationmeasurements for MOMS-2P orientation onPRIRODA. Because of the uncertainties in the over-all arrangement of the modules of the MIR stationthere remains an unknown rotation matrix to beestimated via bundle adjustment.

Ž .At the GeoForschungsZentrum GFZ Potsdamthe GPS raw data were analyzed and differentialGPS computations were performed using the geode-tic ground station network and geodetic high-preci-sion orbit models, resulting in orbit position with anabsolute accuracy of better than 5 m and a relative

Ž .accuracy of 3 m Fockersperger et al., 1997 . All¨navigation data were provided with reference toWGS-84 coordinate system

3.1.4. Calibration dataThe camera parameters in Table 7 again are taken

from the lab-calibration evaluation. Here, they solelyserve as initial information:

3.2. Bundle adjustment

The functional model for the reconstruction of theexterior orientation is based on the principle of orien-

Ž .tation images, as proposed by Hofmann et al. 1982 .

Table 7Lab-calibrated camera parameters of high-resolution and stereochannels

HR5A HR5B ST6 ST7

w xc mm 660.256 660.224 237.241 237.246w xx pixel 0.1 0.2 y7.2 y0.50w xy pixel y0.4 0.1 8.0 19.20w xK pixel y0.3 y0.4 y1.1 1.7w xk mdeg y2.9 5.4 y1.5 y1.4


Table 8Observations introduced into the bundle adjustment

Observations Type A priori s

2880 tie points image coordinates 0.2 Pixel252 control points image coordinates 0.2 Pixel252 control points object coordinates 6.0 m

Y8=3 attitude angles exterior orientation 15.38=3 positions exterior orientation 3 mThree position biases exterior orientation 5 m

Here, the exterior orientation parameters are esti-mated only at certain time intervals, while in be-tween the temporal variation of the exterior orienta-tion is modeled by a third order polynomial function.The attitude and position information of the naviga-tion data are treated as uncorrelated observations. Inthis evaluation, they are introduced only at the timesof the orientation images. Systematic errors in thesedata like biases and linear drifts are treated as addi-tional unknowns and estimated simultaneously withthe other unknowns in the adjustment.

The model of the interior orientation is charac-terised by a separate image coordinate system foreach CCD-array, which is related to the camera fixedcoordinate system by a six-parameter transformation,employing three-dimensional displacements and rota-tions around three axes. The rotation around thez-axis of the image coordinate system already ex-presses the sensor rotation k as one of the fiveparameters described in Section 2.6. Together withthe remaining four parameters, the deviation of thefocal length dc, the two-dimensional displacement

Ž .Tvector x , y of the CCD-array in the respective0 0

focal plane and the parameter K modelling the sen-sor curvature, they form a set of 10 parameters perCCD-array. With this model, the geometry of bothone-lens- and also multi-lens-cameras like MOMS-2Pcan be described rigorously. In this evaluation, fiveof these 10 parameters per CCD-array are simultane-ously estimated in the adjustment, while the nominalvalues of the other five parameters are treated asconstants. A detailed description of the functionalmodel of the bundle adjustment is given in KornusŽ .1997 .

Table 8 gives an overview of all observations andtheir a priori standard deviations, which were intro-duced into the bundle adjustment. The observations

of the exterior orientation parameters were interpo-lated at the times of the orientation images. Aninterval of 3330 image lines for the ST6 and ST7channels, corresponding to 8.2 s flight time, led toeight orientation images, which proved to be suffi-cient for modelling the temporal variation of theexterior orientation.

3.3. Results

Table 9 contains the estimated camera parametersx and the theoretical standard deviations s as re-ˆ ˆx

sults of the bundle adjustment. The column D xreflects the deviations from the lab-calibrated resultsŽ .see Table 7 . Statistically significant deviations aremarked by boldfaced characters. All these deviationshave also a significant effect with the exception ofthe focal length deviation for ST6; this and all othernonsignificant deviations have each an effect of lessthan about 0.4 pixel in the worst case, i.e., for the

Table 9Results of bundle adjustment

x s D xˆ ˆx

HR5Aw xc mm 660.198 0.024 y0.058Ž . w xx ref. pixel 0.10 – –0Ž . w xy ref. pixel y0.40 – –0w xK pixel y0.38 0.19 y0.07Ž . w xk ref. mdeg y2.92 – –

HR5Bw xc mm 660.224 0.024 0.000

w xx pixel 0.61 0.14 0.410w xy pixel y0.09 0.06 y0.190w xK pixel y0.32 0.22 0.05w xk mdeg 4.40 6.57 y1.02

ST6w xc mm 237.180 0.008 y0.061

w xx pixel I4.83 0.16 2.370w xy pixel 10.55 0.73 2.550w xK pixel y1.15 0.41 y0.07w xk mdeg 7.65 4.51 9.12

ST7w xc mm 237.234 0.007 y0.012

w xx pixel 1.27 0.15 1.770w xy pixel 18.86 0.71 y0.340w xK pixel 1.42 0.37 y0.25w xk mdeg y10.24 4.76 y8.82


Table 10Estimated bias and drift parameters

ˆ ˆ ˆX s Y s Z sˆ ˆ ˆ0 0 0

w xBias m 0.2 5.5 y0.3 5.5 0.6 5.5

w s v s k sˆ ˆ ˆ ˆ ˆ ˆw xBias 8 0.073 0.003 I0.164 0.003 0.035 0.006w xDrift 8rmin 0.051 0.005 I0.065 0.005 0.053 0.007

.CCD-line end points . The results demonstrate, thatchanges of the camera geometry since the time oflab-calibration occurred also for the stereo module.The order of magnitude is comparable to the devia-

Žtions found for band-to-band registration see Table.5 . Two different sets of parameters were used for

HR5A and HR5B, although both CCD-lines use acommon lens, in order to account for errors in theoptical mounting of the CCDs and differences be-tween them, e.g., in scale.

Besides the parameters of the interior orientation,also bias and drift parameters of the MOMS-NAVnavigation data were simultaneously estimated. Theestimated bias parameters of the positions are smallcompared to their standard deviation and thereforenot significantly determined. The estimated attitudebiases are also small values, considering, that theMOMS camera axes were not precisely adjusted tothe MIR coordinate system, where the absolute atti-tude data of the ASTRO-1 star sensor are referencedto. An attitude bias of 0.18, however, is equivalent toa position bias on the ground of approximately 700m for the given flying height. The drift parametersare, like the attitude biases, all significantly deter-mined. The estimated bias and drift parameters andtheir standard deviations are summarised in Table10. Statistically significant values are again markedby boldfaced characters.

4. Conclusions

The presented material demonstrates that the geo-metric in-flight calibration of both the multispectraland stereo modules of MOMS-2P is possible. As far

Žas the nadir looking high-resolution and multispec-.tral channels are concerned, the geometry can be

determined in the framework of band-to-band regis-tration with sufficient accuracy. If off-nadir stereochannels are involved, photogrammetric bundle ad-justment is required to consider the movement andthe attitude behavior of the camera carrier. Here, theparameters of the interior orientation can simultane-ously be estimated by self-calibration methods, ifnavigation data and ground control points are avail-able.

Both methods led to significant deviations of thecamera parameters from the results achieved duringthe geometric calibration in the laboratory, whichwas conducted prior to the mission. The need for aregular geometric in-flight calibration is also empha-sised by deviations, which occurred between thesame channels for different data-takes. After theproblems on-board the MIR space station in 1997,MOMS-2P was operating again since January 1998.However, further photogrammetric evaluations toverify the results achieved was unfortunately notpossible due to lack of other MOMS-2P stereo im-agery with suitable orbit and control point data.

Acknowledgements

We wish to thank AMilGeo for kindly makingavailable the control data and also Timm Ohlhof,Elmar Putz and Harald Froba from the Chair for¨Photogrammetry and Remote Sensing, TU Munichfor organising and conducting the control point mea-surements. The work presented in this paper wasfunded by grant 50EE9529 of the former GermanSpace Agency DARA.

References

Dasa, 1996. MOMS-2P: Re-design performance and system re-quirements specification. Company Document No. M2P-DAS-200-RS-001, 1st February.

Fockersperger, S., Hollmann, R., Dick, G., Reigber, C., 1997. On¨Board MIR: orienting remote images with MOMSNAV. GPS

Ž .World 8 10 , 32–39.Hofmann, O., Nave, P., Ebner, H., 1982. DPS — a digital´

photogrammetric system for producing digital elevation mod-els and orthophotos by means of linear array scanner imagery.

Ž .Int. Arch. Photogramm. Remote Sens. 24 3 , 216–227.


Kornus, W., 1997. Dreidimensionale Objektrekonstruktion mitdigitalen Dreizeilenscannerdaten des Weltraumprojekts

Ž .MOMS-02rD2. Forschungsbericht 97-54 Dissertation , DLR,Institute of Optoelectronics.

Kornus, W., Lehner, M., Blechinger, F., Putz, E., 1996. Geomet-ric calibration of the stereoscopic CCD-line-scanner MOMS-

Ž .2P. Int. Archiv. Photogramm. Remote Sens. 31 B1 , 90–98.Lehner, M., 1986. Triple stereoscopic imagery simulation and

digital image correlation for MEOSS project. Int. Arch. Pho-Ž .togram. Remote Sens. 27 1 , 477–484.

Lehner, M., Gill, R.S., 1992. Semi-automatic derivation of digitalelevation models from stereoscopic 3-line scanner data. Int.

Ž .Arch. Photogramm. Remote Sens. 29 B4 , 68–75.Lehner, M., Kornus, W., 1995. The photogrammetric evaluation

Ž .of MOMS-02rD2 mode 3 data Mexico, Ethiopia . Proceed-ings of SPIE Conference on Remote Sensing and Reconstruc-tion for 3-D Objects and Scenes 2572, 102–114.

Seige, P., Reinartz, P., Schroeder, M., 1998. The MOMS-2Pmission on the MIR station. Int. Arch. Photogramm. Remote

Ž .Sens. 32 1 , 204–210.

geometric in-flight calibration of the stereoscopic line ...directory.umm.ac.id/data...

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