Directory UMM :Data Elmu:jurnal:P:Photogrametry & Remotesensing:Vol55.Issue1.Feb2000:

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www.elsevier.nlrlocaterisprsjprs

Geometric in-flight calibration of the stereoscopic line-CCD

scanner MOMS-2P

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 the PRIRODA module of the Russian space station MIR from October 1996 to August 1999. The goal is the verification and, if necessary, the update of the calibration data, which were estimated from the geometric laboratory calibration. The paper is subdivided into two parts, describing two different procedures of geometric in-flight calibration. The first method is based on DLR matching software and is restricted to nadir looking channels, which are read out simultaneously. From a high number of individual point matches between the images of the same area taken by the different CCD arrays, the most reliable ones are selected and used to calculate shifts with components in and across flight direction between the CCD arrays. These actual shifts are compared to the nominal shifts, derived from the results of the laboratory calibration, and parameters of the valid camera model are estimated from both data sets by least squares adjustment. A special case of band-to-band registration are the two optically combined CCD-arrays of the nadir high-resolution channel. They are read out simultaneously with a nominal 10 pixel overlap in stereoscopic imaging mode A. The DLR matching software is applied to calculate the displacement vector between the two CCD-arrays. The second method is based on combined photogrammetric bundle adjustment using an adapted functional model for the reconstruction of the interior orientation. It requires precise and reliable ground control information as well as navigation data of the navigation-package MOMS-NAV. Nine contiguous image scenes of MOMS-2P data-take T083C building an about 550-km-long strip over southern Germany and Austria taken in March 1997 were evaluated. From both procedures calibration data are estimated, which are presented and compared to the lab-calibration results.q2000 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

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 scanScan-ner for multi-spectral and along-track stereoscopic imaging in four different modes. It is built by the German

Ž .

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Chrysler Aerospace company Dasa and mounted on the PRIRODA module of the Russian space station MIR since May 1996. It delivers imagery since end of September 1996. MOMS-2P is the refurbished MOMS-02 camera, which has been flown on the

space 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 two CCD-arrays each for colour image acquisition in four narrow banded spectral channels with 18-m ground pixel size. The stereo module consists of three lenses, which are oriented in three different directions. The forward and aft looking lenses con-tain one CCD array each for panchromatic image acquisition with 18-m ground pixel size. The third lens is nadir looking and contains two CCD-arrays, which are optically combined to one high-resolution channel, providing panchromatic imagery with a ground pixel size of 6 m. The complexity and also

Ž .

the high mass 143 kg of the optical module posed high demands on the process of laboratory calibra-tion, which was conducted by Dasa. Experience from the D2 mission showed that for this big camera with five different lenses in-flight geometric calibration activities are necessary. In this paper, two different methods of in-flight calibration are described. The first method is restricted to channels, which are simultaneously read out, while nominally looking at nadir. These are channels MS1, MS2, MS3, MS4,

Ž .

and HR5A or sub-arrays thereof in certain

combi-Ž

nations in the imaging modes B, C, and D see Table

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

Ž .

and across flight direction rows, columns . These measurements are produced with sub-pixel accuracy by local least squares matching techniques using a special 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 photogrammetric bundle adjustment and therefore is restricted to

chan-Ž .

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

and also a substantial amount of very accurate ground control information in order to estimate the camera geometry. Parameters of the actual camera model are estimated with both methods from in-flight and labo-ratory measurements by least squares adjustment. From the derived camera parameters, new calibration tables are generated as input for the Levels 1A) _and

1B processing at DLR Neustrelitz and for pho-togrammetric evaluation of stereoscopic MOMS-2P imagery.

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

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

Ž .

D2 mission 1993 . For MOMS-2P, it has been

refined to provide a full displacement function over

Ž .

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

Ž .

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

2.1. Image matching

The DLR matching software has been developed for the automated measurement of massive numbers of conjugate points in the stereoscopic imagery of

three-line stereo scanners projects MEOSS and

MOMS . More details about this software can be

Ž .

found in Lehner and Gill 1992 , Lehner and Kornus

Ž_{1995 and Kornus et al. 1996 .}. Ž . Ž .

The main features used here are: 1 An interest operator selects well defined patterns suitable for digital image correlation; the principles of the Forstner interest operator are used with slight modi-

¨

fication; a good interest operator point is defined by a surrounding window with multi-directional edge information and a local contrast above a given

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Ž .

threshold. 2 Conjugate points at pixel accuracy

level 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

reliable 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 calculacorrela-tion is based on the val-ues and the distribution of the five largest elements of this matrix — a quality figure 0.6 will belong to a very pronounced peak, quality figures below 0.2

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

points in the neighbourhood normally, an image

pyramid is used for getting these approximate points .

Ž ._{3 Local least squares matching LLSQM is finally}Ž .

used for refinement of the conjugate points to sub-pixel accuracy; in this step, it is also possible to match images of different resolutions like MOMS high and low resolution channels.

2.2. EÕaluation strategy

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

Ž ._{1 Interest operator points are generated for one}

channel; the interest operator will avoid areas with low contrast and patterns with ambiguous matching

results; typical operator window size used is 7=7

pixels.

Ž .2 Run the matching software for the channel

combination under investigation: a search area size of 19=19 pixel is used for matching at pixel accu-racy; for search area selection it is sufficient to use an estimated mean shift between the channels which was determined beforehand during the lab-calibra-tion and is valid for all data-takes; local least squares matching is run twice using two different window

Ž .

sizes 15=15 and 17=17 pixels have been used

for sub-pixel registration.

Ž ._{3 Consider both resulting point files selecting}

only points, which satisfy the following conditions:

Ž ._{a Maximum of correlation coefficient and}

qual-Ž

ity figure from areal correlation with pixel

accu-.

racy are beyond given thresholds to guarantee

well defined objects 0.9 and 0.23, respectively, have been used for image pairs involving channels 1–3; 0.8 and 0.23 for channel pairs containing

Ž .

channel 4 because channel 4 near infrared shows less 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 coordinates}

for the two window sizes are below a given

threshold 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 pairs

Ž . 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 the local shifts between the channels. In order to even more reduce the impact of natural channel differ-ences, these shifts are averaged over the whole scene

length 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 column intervals.

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

1996 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

valid calibration tables and camera parameters see

Section 2.6 .

2.3. Example

Ž .

Fig. 1 shows the image of channel MS3 red of

Ž .

scene 3 part of Ethiopia of data-take T081A

im-Ž

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

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

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pat-Fig. 1. MOMS-2P Ethiopia: data-take T081A, scene 3, channel MS3, about 104=106 km; the window shows the marked sub-scene of 600=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 by the image matching software. The window in Fig. 1 shows a small part of the scene in full resolution with the interest operator points drawn on it.

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

Table 2 shows the shifts between channels MS2 and MS3 as the results of the evaluation for 29

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Table 1

T081A, scene 3, mean correlation coefficient and quality figures of all matched points

Channel pair MS3rMS1 MS3rMS2 MS3rMS4 Mean correl. coeff. 0.92 0.93 0.89 Mean quality figure 0.28 0.27 0.25

column intervals. The graphical representation is given in Fig. 2.

2.4. Particularities of the different imaging modes

For an exact definition of the imaging modes of

Ž .

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 active pixels are given in Table 3.

Table 2

T081A, 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

sx sy

1 2939 100 1.40 6.31 0.14 0.16

2 3126 300 1.42 6.31 0.12 0.16

3 3195 500 1.46 6.37 0.11 0.16

4 3369 700 1.49 6.48 0.10 0.13

5 3659 900 1.51 6.59 0.11 0.14

6 3579 1100 1.53 6.71 0.11 0.14

7 3328 1300 1.55 6.84 0.11 0.12

8 3426 1500 1.60 6.98 0.10 0.13

9 3419 1700 1.63 7.13 0.10 0.14

10 3504 1900 1.66 7.29 0.13 0.15

11 3573 2100 1.68 7.41 0.12 0.15

12 3495 2300 1.71 7.54 0.11 0.14

13 3944 2500 1.75 7.65 0.12 0.13

14 4257 2700 1.79 7.74 0.12 0.13

15 4648 2900 1.85 7.80 0.12 0.14

16 5174 3100 1.94 7.88 0.12 0.13

17 5031 3300 2.06 7.97 0.12 0.13

18 5580 3500 2.21 8.07 0.11 0.12

19 5368 3700 2.32 8.16 0.11 0.13

20 3842 3900 2.42 8.24 0.11 0.14

21 3115 4100 2.56 8.31 0.11 0.14

22 3490 4300 2.70 8.39 0.10 0.12

23 4048 4500 2.82 8.47 0.10 0.12

24 4155 4700 2.97 8.54 0.12 0.12

25 4550 4900 3.16 8.61 0.12 0.10

26 3835 5100 3.33 8.65 0.13 0.10

27 3720 5300 3.51 8.72 0.12 0.11

28 4780 5500 3.68 8.77 0.12 0.11

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Table 3

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

w x

Imaging MS1 MS2 MS3 MS4 HR5A HR5B ST6 ST7 Swath width km

Ž . 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 HRr54 ST

B 5800 5800 5800 5800 – – – – 105

Ž . Ž .

C – 3220 3220 3220 6000 – – – 58 MSr36 HR

D 5800 – – 5800 – – 5800 5800 105

Ž .1 Mode A: the panchromatic channels HR5,

ST6, and ST7 look in different directions at every time instant, thus, the method mentioned above is not applicable; there is only a very small overlap of the high-resolution channels HR5A and HR5B of nominally 10 pixels which can help in the

composi-Ž

tion of a really continuous channel HR5 array there is an obvious shift between the two channels of about 1 pixel along and 2 pixels across flight

direc-.

tion . The values of important camera parameters for these stereo channels can only be estimated by pho-togrammetric adjustment, if very good knowledge of the 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 MS4 over the full length of the 5800 active pixels can be measured.

Ž .3 Mode C: the pairwise shifts between the

multispectral channels MS2, MS3, and MS4 over 3220 active pixels can be measured; the shifts to channel HR5A can be measured for a sub-array of 2000 pixels of these 3220 pixels; the latter measure-ment is done in two steps:

Ž .a a first matching is carried out between the

multispectral 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 the second step, a least squares matching between channel HR5A and the multispectral channels, whereby the known resolution ratio between these channels was used as approximation for the scale parameters determined in the least squares match-ing.

Ž ._{4 Mode D: the shifts between the multispectral}

channels MS1 and MS4 can be measured over the full length of the 5800 active pixels; the stereo channels 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 coupled to form the high-resolution channel HR5. These two channels are read out with a nominal overlap of 10 pixel. Via image matching, shifts in and across flight

direction of 1.2 andy1.9 pixels were measured. For

these measurements, the overlap area was 8=

en-larged by bilinear interpolation to get meaningful window sizes for LLSQM. The latter was performed for a regular set of initial approximations. Two

window sizes, 37=37 and 41=41 pixel, have been

used. These window sizes appear to be large, but in

reality they refer to 8= enlarged image areas. Only

these conjugate points entered into the calculation of shifts for which the following two conditions ap-plied:

1. LLSQM converged to nearly identical results for the two window sizes.

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

The means and standard deviations of the differ-ences between the coordinates of channels HR5A and HR5B for these conjugate points can be seen in Table 4 for several sub-scenes. The standard devia-tions are larger as those listed in Table 2, because of

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Table 4

Ž .

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

sx sy

T0700rpart 1 115 1.18 y1.89 0.26 0.26

T0700rpart 2 135 1.12 y1.90 0.24 0.29

T07FBrpart 1 57 1.16 y1.79 0.19 0.19

T07FBrpart 2 58 1.20 y1.79 0.21 0.23

All 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 the

laboratory calibration to such an extent partly

sev-.

eral pixels that makes it necessary to change the calibration tables for the systematic processing of the MOMS images. As an example Fig. 3 shows a comparison of the shifts between channels MS2 and

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

MS3 derived from laboratory calibration versus the results of image matching. Here, the differences of about 1.8 pixel in the along-track shifts, e.g., indicate that the along-track components of the camera

pa-rameters in channel MS2 andror channel MS3 have

changed 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

real imaging condition in space non-zero gravity,

non-vacuum, controlled temperature, etc. . The dif-ferent angles between the y-axis and the curves representing the along scan-line shifts indicate changes in the image scale, which correspond to changes in the focal lengths of channel MS2 andror channel MS3.

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

Ž .

channel see Table 5 . For that purpose, the differ-ences xdiff and ydiff between the shifts derived from lab-calibration and from image matching were fed into a least squares adjustment, estimating parame-ters of an adjusting parabola in case of the along-track shifts or a line in case of the along scan-line shifts. The correction equations read:

ˆ

Õ sx y A qB yqC y

x diff x x x

ˆ

Õ sy y A qB y

y diff y y

Ž .

with y denoting the y-coordinate along scan-line of the respective centre of column interval with respect to the centre of the CCD-array.

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

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Table 5

Adjusted camera parameters x, their standard deviationˆ sˆx and the deviations from the lab-calibration Dx for five MOMS-2P

channels

xˆ sˆx Dx

MS1 w x

c mm 220.139 0.003 y0.021

w x

x0 pixel y1.3 0.057 y0.6

w x

y0 pixel 7.4 0.078 2.4

w x

K pixel 0.3 0.012 y0.1

w x

k mdeg 2.1 1.783 y3.5

MS2 w x

c mm 220.076 0.003 y0.019

w x

x0 pixel y1.0 0.044 y1.4

w x

y0 pixel 7.2 0.048 0.2

w x

K pixel y0.6 0.014 0.3

w x

k mdeg 2.7 1.763 y6.5

MS3 w x

c mm 219.964 0.002 y0.151

w x

x0 pixel 1.3 0.048 0.0

w x

y0 pixel 15.1 0.027 y0.8

w xŽ .

K pixel reference 0.2 – –

w x

k mdeg y21.9 1.763 y7.6

MS4 w x

c mm 219.951 0.003 y0.140

w x

x0 pixel 0.7 0.052 1.3

w x

y0 pixel 14.5 0.056 y0.8

w x

K pixel 0.5 0.016 0.0

w x

k mdeg y22.8 1.796 y6.1

( )

HR5A reference w x

c mm 660.256 – –

w x

x0 pixel 0.1 – –

w x

y0 pixel y0.4 – –

w x

K pixel y0.3 – –

w x

k mdeg I2.9 – –

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

ˆ

parameters A , B , A , B , and C_x _x _y _y _x were trans-formed into the five following parameters dc, dx ,₀

dy , dK, d0 k, describing deviations of camera pa-rameter differences between the two selected chan-nels, which obviously occurred since the time of lab-calibration:

1. the calibrated focal length c, 2. the along-track displacement x ,0 3. the along scan-line displacement y ,0

4. 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 channel combination are obtained as follows:

ˆ

dcscBy

ˆ

dx0sAx

ˆ

dy0sAy

ˆ

dKsC_x

ˆ

dks

_ˆ

₂Bx,Bx

1qBx

For the first equation the nominal focal length value cs220.0 mm is used with sufficient accuracy. The 20 investigated channel combinations resulted in 20 camera parameter differences, which correspond to camera parameter changes of altogether five

chan-Ž .

nels four multispectral and HR5A . By least squares adjustment a final set of camera parameters for each channel was estimated from these differences, while the lab-calibrated parameters of one selected channel were taken as reference. Due to the small swath width of imaging mode C, the sensor curvature K

could 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

ˆ

x resulting from the adjustment of the camera parameter

differ-ences. The column Dx reflects the deviations from

the lab-calibrated results. K represents the

along-track effect caused by sensor curvature at ys3000

pixel i.e., at the end points of the 6000 pixel long CCD-arrays. The along-track effect caused by a

sen-sor rotation of ks10 mdeg is about 0.5 pixel at

ys3000 pixel. The deviations from the lab-calibra-tion values in Table 5 show that the effect of K and

k 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 exceed 2 pixels. For comparison, the camera parameters estimated from the lab-calibration evaluation are listed in Table 6. In both Table 5 and 6, four focal lengths were used for the multispectral channels,

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Table 6

Lab-calibrated camera parameters of multispectral channels

MS1 MS2 MS3 MS4 HR5A

w x

c mm 220.160 220.095 220.115 220.091 660.256

w x

x0 pixel y0.7 0.4 1.3 y0.6 0.1

w x

y0 pixel 5.0 7.0 15.9 15.3 y0.4

w x

K pixel 0.4 y0.9 0.2 0.5 y0.3

w x

k mdeg 5.6 9.2 y14.3 y16.7 y2.9

although only two lenses are used for them, in order to 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 conducted

in 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 ground control points should have been derived in an

auto-Ž .

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

3.1. Input data

Due to high cloud coverage in the western part of the strip, the evaluation starts with image scenea_25,

approximately 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 scenea_33.

Thus, the control and checkpoints all located in

Germany are also imaged by the backward looking channel ST7. The total length of the strip is about 415 km corresponding to 23310 image lines for the ST6 and ST7 channels. The ground pixel sizes of the imagery at 390-km orbit altitude are 5.9 m and 17.7 m.

3.1.1. Image coordinates of tie points

From 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 using the correlation coefficient and the quality figure as

Ž .

selection criteria best point within each grid mesh .

3.1.2. Ground control points

As 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 in medium-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 were

manually measured in the nadir looking channel at the 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 the strip, since for those so-called 3-ray-points the

im-Ž

age 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 tie points and the ground control points. The identifica-tion accuracy was adversely affected by defocusing effects in the high-resolution channel, which oc-curred during the warming-up phase of the scanner and are documented in the temperature measure-ments of the housekeeping data. Nevertheless, it was preferred to conduct the measurements in the defo-cused high-resolution imagery rather than in the 3= decreased resolution of the oblique viewing stereo channels. Therefore, the a priori standard deviations of the object coordinates were set to 6 m in the bundle adjustment, corresponding to 1 pixel identifi-cation accuracy. After identifiidentifi-cation, the image points

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Ž . Ž .

Fig. 5. Distribution of tie points dots and ground control points triangles in the image scenesa25 toa33.

were automatically transferred to the other image

Ž .

strips by least squares matching Kornus et al., 1996 .

3.1.3. NaÕigation data

MOMS-2P has its own navigation system

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

The processing of the gyro data including the absolute referencing with INS data of the MIR sta-tion or — if available — star camera measurements using the star sensor on MIR module Kvant 2 takes place at the German Space Operations Center

ŽGSOC of DLR. This also includes the time syn-.

chronisation of navigation data and image frames. For the data-take T083C discussed here a standard

deviation of the angular measurements of 15.3Y is

indicated, corresponding to about 1.6 pixel

ST-.

channel . Star camera measurements were available. Since the MOMS camera was mounted by an

extra-Ž

vehicular activity onto the module PRIRODA May

1996 , it was impossible to conduct exact calibration

measurements for MOMS-2P orientation on

PRIRODA. Because of the uncertainties in the over-all arrangement of the modules of the MIR station there remains an unknown rotation matrix to be estimated via bundle adjustment.

Ž .

At the GeoForschungsZentrum GFZ Potsdam

the GPS raw data were analyzed and differential GPS computations were performed using the geode-tic ground station network and geodegeode-tic high-preci-sion orbit models, resulting in orbit position with an absolute 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 to WGS-84 coordinate system

3.1.4. Calibration data

The camera parameters in Table 7 again are taken from the lab-calibration evaluation. Here, they solely serve as initial information:

3.2. Bundle adjustment

The functional model for the reconstruction of the exterior orientation is based on the principle of

orien-Ž .

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

Table 7

Lab-calibrated camera parameters of high-resolution and stereo channels

HR5A HR5B ST6 ST7

w x

c mm 660.256 660.224 237.241 237.246

w x

x0 pixel 0.1 0.2 y7.2 y0.5

w x

y0 pixel y0.4 0.1 8.0 19.2

w x

K pixel y0.3 y0.4 y1.1 1.7

w x

(11)

Table 8

Observations introduced into the bundle adjustment

Observations Type A prioris

2880 tie points image coordinates 0.2 Pixel 252 control points image coordinates 0.2 Pixel 252 control points object coordinates 6.0 m

8=3 attitude angles exterior orientation 15.3 8=3 positions exterior orientation 3 m Three 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 funcorienta-tion. The attitude and position information of the naviga-tion data are treated as uncorrelated observanaviga-tions. In this evaluation, they are introduced only at the times of the orientation images. Systematic errors in these data like biases and linear drifts are treated as addi-tional unknowns and estimated simultaneously with the other unknowns in the adjustment.

The model of the interior orientation is charac-terised by a separate image coordinate system for each CCD-array, which is related to the camera fixed coordinate system by a six-parameter transformation, employing three-dimensional displacements and rota-tions around three axes. The rotation around the

z-axis of the image coordinate system already

ex-presses the sensor rotation k as one of the five

parameters described in Section 2.6. Together with the remaining four parameters, the deviation of the focal length dc, the two-dimensional displacement

Ž .T

vector x , y0 0 of the CCD-array in the respective

focal plane and the parameter K modelling the sen-sor curvature, they form a set of 10 parameters per CCD-array. With this model, the geometry of both one-lens- and also multi-lens-cameras like MOMS-2P can be described rigorously. In this evaluation, five of these 10 parameters per CCD-array are simultane-ously estimated in the adjustment, while the nominal values of the other five parameters are treated as constants. A detailed description of the functional model of the bundle adjustment is given in Kornus

Ž_{1997 .}.

Table 8 gives an overview of all observations and their 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. An interval of 3330 image lines for the ST6 and ST7 channels, corresponding to 8.2 s flight time, led to eight orientation images, which proved to be suffi-cient for modelling the temporal variation of the exterior orientation.

3.3. Results

Table 9 contains the estimated camera parameters

x and the theoretical standard deviations

ˆ

x as

re-sults of the bundle adjustment. The column Dx

reflects the deviations from the lab-calibrated results

Žsee Table 7 . Statistically significant deviations are.

marked by boldfaced characters. All these deviations have also a significant effect with the exception of the focal length deviation for ST6; this and all other nonsignificant deviations have each an effect of less than about 0.4 pixel in the worst case, i.e., for the

Table 9

Results of bundle adjustment

xˆ sˆx Dx

HR5A w x

c mm 660.198 0.024 y0.058

Ž .w x

x0 ref. pixel 0.10 – –

Ž .w x

y0 ref. pixel y0.40 – –

w x

K pixel y0.38 0.19 y0.07

Ž .w x

k ref. mdeg y2.92 – –

HR5B w x

c mm 660.224 0.024 0.000

w x

x0 pixel 0.61 0.14 0.41

w x

y0 pixel y0.09 0.06 y0.19

w x

K pixel y0.32 0.22 0.05

w x

k mdeg 4.40 6.57 y1.02

ST6 w x

c mm 237.180 0.008 y0.061

w x

x0 pixel I4.83 0.16 2.37

w x

y0 pixel 10.55 0.73 2.55

w x

K pixel y1.15 0.41 y0.07

w x

k mdeg 7.65 4.51 9.12

ST7 w x

c mm 237.234 0.007 y0.012

w x

x0 pixel 1.27 0.15 1.77

w x

y0 pixel 18.86 0.71 y0.34

w x

K pixel 1.42 0.37 y0.25

w x

(12)

Table 10

Estimated bias and drift parameters

ˆ ˆ ˆ

X0 sˆ Y0 sˆ Z0 sˆ

w x

Bias m 0.2 5.5 y0.3 5.5 0.6 5.5

wˆ sˆ vˆ sˆ kˆ sˆ

w x

Bias 8 0.073 0.003 I0.164 0.003 0.035 0.006

w x

Drift 8rmin 0.051 0.005 I0.065 0.005 0.053 0.007

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

devia-Ž

tions 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 a common lens, in order to account for errors in the optical 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-NAV navigation data were simultaneously estimated. The estimated bias parameters of the positions are small compared to their standard deviation and therefore not significantly determined. The estimated attitude biases are also small values, considering, that the MOMS camera axes were not precisely adjusted to the MIR coordinate system, where the absolute atti-tude data of the ASTRO-1 star sensor are referenced to. An attitude bias of 0.18, however, is equivalent to a position bias on the ground of approximately 700 m for the given flying height. The drift parameters are, like the attitude biases, all significantly deter-mined. The estimated bias and drift parameters and their standard deviations are summarised in Table 10. Statistically significant values are again marked by boldfaced characters.

4. Conclusions

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

as 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 stereo channels are involved, photogrammetric bundle ad-justment is required to consider the movement and the attitude behavior of the camera carrier. Here, the parameters of the interior orientation can simultane-ously be estimated by self-calibration methods, if navigation data and ground control points are avail-able.

Both methods led to significant deviations of the camera parameters from the results achieved during the geometric calibration in the laboratory, which was conducted prior to the mission. The need for a regular geometric in-flight calibration is also empha-sised by deviations, which occurred between the same channels for different data-takes. After the problems on-board the MIR space station in 1997, MOMS-2P was operating again since January 1998. However, further photogrammetric evaluations to verify the results achieved was unfortunately not possible 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 making available the control data and also Timm Ohlhof,

Elmar Putz and Harald Froba from the Chair for

¨

Photogrammetry and Remote Sensing, TU Munich for organising and conducting the control point mea-surements. The work presented in this paper was funded by grant 50EE9529 of the former German Space 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 .

(13)

Kornus, W., 1997. Dreidimensionale Objektrekonstruktion mit digitalen 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 digital elevation 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-2P mission on the MIR station. Int. Arch. Photogramm. Remote

Ž .

(1)

Table 5

Adjusted camera parameters x, their standard deviationˆ sˆx and the deviations from the lab-calibration Dx for five MOMS-2P

channels

xˆ sˆx Dx

MS1

w x

c mm 220.139 0.003 y0.021

w x

x0 pixel y1.3 0.057 y0.6

w x

y0 pixel 7.4 0.078 2.4

w x

K pixel 0.3 0.012 y0.1

w x

k mdeg 2.1 1.783 y3.5

MS2

w x

c mm 220.076 0.003 y0.019

w x

x0 pixel y1.0 0.044 y1.4

w x

y0 pixel 7.2 0.048 0.2

w x

K pixel y0.6 0.014 0.3

w x

k mdeg 2.7 1.763 y6.5

MS3

w x

c mm 219.964 0.002 y0.151

w x

x0 pixel 1.3 0.048 0.0

w x

y0 pixel 15.1 0.027 y0.8

w xŽ .

K pixel reference 0.2 – –

w x

k mdeg y21.9 1.763 y7.6

MS4

w x

c mm 219.951 0.003 y0.140

w x

x0 pixel 0.7 0.052 1.3

w x

y0 pixel 14.5 0.056 y0.8

w x

K pixel 0.5 0.016 0.0

w x

k mdeg y22.8 1.796 y6.1

( )

HR5A reference

w x

c mm 660.256 – –

w x

x0 pixel 0.1 – –

w x

y0 pixel y0.4 – –

w x

K pixel y0.3 – –

w x

k mdeg I2.9 – –

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

ˆ

parameters A , B , A , B , and C_x _x _y _y _x were trans-formed into the five following parameters dc, dx ,₀

dy , dK, d0 k, describing deviations of camera pa-rameter differences between the two selected chan-nels, which obviously occurred since the time of lab-calibration:

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

3. the along scan-line displacement y ,0

4. 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 channel combination are obtained as follows:

ˆ

dcscBy

ˆ

dx0sAx

ˆ

dy0sAy

ˆ

dKsC_x

ˆ

dks

_ˆ

₂Bx,Bx 1qBx

chan-Ž .

could 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

ˆ

x resulting from the adjustment of the camera parameter differ-ences. The column Dx reflects the deviations from

the lab-calibrated results. K represents the along-track effect caused by sensor curvature at ys3000 pixel i.e., at the end points of the 6000 pixel long CCD-arrays. The along-track effect caused by a sen-sor rotation of ks10 mdeg is about 0.5 pixel at

ys3000 pixel. The deviations from the lab-calibra-tion values in Table 5 show that the effect of K and

Ž k are each less than 0.4 pixel in the worst case end

(2)

MS1 MS2 MS3 MS4 HR5A w x

c mm 220.160 220.095 220.115 220.091 660.256

w x

x0 pixel y0.7 0.4 1.3 y0.6 0.1

w x

y0 pixel 5.0 7.0 15.9 15.3 y0.4

w x

K pixel 0.4 y0.9 0.2 0.5 y0.3

w x

k mdeg 5.6 9.2 y14.3 y16.7 y2.9

although only two lenses are used for them, in order to 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 conducted in cooperation with the Institut Cartografic de

`

Ž .

auto-Ž .

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

3.1. Input data

Due to high cloud coverage in the western part of the strip, the evaluation starts with image scenea_25,

approximately 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 scenea_33.

Thus, the control and checkpoints all located in

3.1.1. Image coordinates of tie points

From 350,000 homologous points found by local least squares image matching in all three image

the correlation coefficient and the quality figure as

Ž .

selection criteria best point within each grid mesh .

3.1.2. Ground control points

As ground control information, navigation points

Ž .

of the AMilGeo Amt fur militarisches Geowesen

¨

Y and Z. More than 250 navigation points were

manually measured in the nadir looking channel at the 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 the strip, since for those so-called 3-ray-points the

im-Ž

age coordinates of all three viewing directions fore,

decreased resolution of the oblique viewing stereo channels. Therefore, the a priori standard deviations of the object coordinates were set to 6 m in the bundle adjustment, corresponding to 1 pixel identifi-cation accuracy. After identifiidentifi-cation, the image points

(3)

Ž . Ž .

Fig. 5. Distribution of tie points dots and ground control points triangles in the image scenesa25 toa33.

were automatically transferred to the other image

Ž .

strips by least squares matching Kornus et al., 1996 .

3.1.3. NaÕigation data

MOMS-2P has its own navigation system MOMS-NAV consisting of a Motorola Viceroy GPS receiver with dual antennas and LITEF gyro systems. The raw GPS and gyro data are recorded along with the MOMS image frames. Additionally, time infor-mation for later exact synchronisation of MOMS-NAV data and image frames is written into these auxiliary housekeeping data.

ŽGSOC of DLR. This also includes the time syn-.

chronisation of navigation data and image frames. For the data-take T083C discussed here a standard deviation of the angular measurements of 15.3Y is

indicated, corresponding to about 1.6 pixel

ST-.

channel . Star camera measurements were available. Since the MOMS camera was mounted by an

extra-Ž

vehicular activity onto the module PRIRODA May

1996 , it was impossible to conduct exact calibration measurements for MOMS-2P orientation on PRIRODA. Because of the uncertainties in the over-all arrangement of the modules of the MIR station there remains an unknown rotation matrix to be estimated via bundle adjustment.

Ž .

At the GeoForschungsZentrum GFZ Potsdam the GPS raw data were analyzed and differential GPS computations were performed using the geode-tic ground station network and geodegeode-tic high-preci-sion orbit models, resulting in orbit position with an absolute 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 to WGS-84 coordinate system

3.1.4. Calibration data

The camera parameters in Table 7 again are taken from the lab-calibration evaluation. Here, they solely serve as initial information:

3.2. Bundle adjustment

The functional model for the reconstruction of the exterior orientation is based on the principle of

orien-Ž .

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

Table 7

Lab-calibrated camera parameters of high-resolution and stereo channels

HR5A HR5B ST6 ST7

w x

c mm 660.256 660.224 237.241 237.246

w x

x0 pixel 0.1 0.2 y7.2 y0.5

w x

y0 pixel y0.4 0.1 8.0 19.2

w x

K pixel y0.3 y0.4 y1.1 1.7

w x

(4)

Observations Type A prioris

2880 tie points image coordinates 0.2 Pixel 252 control points image coordinates 0.2 Pixel 252 control points object coordinates 6.0 m

8=3 attitude angles exterior orientation 15.3 8=3 positions exterior orientation 3 m Three position biases exterior orientation 5 m

z-axis of the image coordinate system already

ex-presses the sensor rotation k as one of the five parameters described in Section 2.6. Together with the remaining four parameters, the deviation of the focal length dc, the two-dimensional displacement

Ž .T

vector x , y0 0 of the CCD-array in the respective focal plane and the parameter K modelling the sen-sor curvature, they form a set of 10 parameters per CCD-array. With this model, the geometry of both one-lens- and also multi-lens-cameras like MOMS-2P can be described rigorously. In this evaluation, five of these 10 parameters per CCD-array are simultane-ously estimated in the adjustment, while the nominal values of the other five parameters are treated as constants. A detailed description of the functional model of the bundle adjustment is given in Kornus

Ž_{1997 .}.

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

interval of 3330 image lines for the ST6 and ST7 channels, corresponding to 8.2 s flight time, led to eight orientation images, which proved to be suffi-cient for modelling the temporal variation of the exterior orientation.

3.3. Results

Table 9 contains the estimated camera parameters

x and the theoretical standard deviations

ˆ

x as re-sults of the bundle adjustment. The column Dx

reflects the deviations from the lab-calibrated results

Žsee Table 7 . Statistically significant deviations are.

Table 9

Results of bundle adjustment

xˆ sˆx Dx

HR5A

w x

c mm 660.198 0.024 y0.058

Ž .w x

x0 ref. pixel 0.10 – –

Ž .w x

y0 ref. pixel y0.40 – –

w x

K pixel y0.38 0.19 y0.07

Ž .w x

k ref. mdeg y2.92 – –

HR5B

w x

c mm 660.224 0.024 0.000

w x

x0 pixel 0.61 0.14 0.41

w x

y0 pixel y0.09 0.06 y0.19

w x

K pixel y0.32 0.22 0.05

w x

k mdeg 4.40 6.57 y1.02

ST6

w x

c mm 237.180 0.008 y0.061

w x

x0 pixel I4.83 0.16 2.37

w x

y0 pixel 10.55 0.73 2.55

w x

K pixel y1.15 0.41 y0.07

w x

k mdeg 7.65 4.51 9.12

ST7

w x

c mm 237.234 0.007 y0.012

w x

x0 pixel 1.27 0.15 1.77

w x

y0 pixel 18.86 0.71 y0.34

w x

K pixel 1.42 0.37 y0.25

w x

(5)

Table 10

Estimated bias and drift parameters

ˆ ˆ ˆ

X0 sˆ Y0 sˆ Z0 sˆ w x

Bias m 0.2 5.5 y0.3 5.5 0.6 5.5

wˆ sˆ vˆ sˆ kˆ sˆ w x

Bias 8 0.073 0.003 I0.164 0.003 0.035 0.006

w x

Drift 8rmin 0.051 0.005 I0.065 0.005 0.053 0.007

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

devia-Ž

tions found for band-to-band registration see Table

4. Conclusions

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

as the nadir looking high-resolution and

multispec-.

tral channels are concerned, the geometry can be

Acknowledgements

We wish to thank AMilGeo for kindly making available the control data and also Timm Ohlhof, Elmar Putz and Harald Froba from the Chair for

¨

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 .

(6)

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., 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-2P mission on the MIR station. Int. Arch. Photogramm. Remote

Ž .

Directory UMM :Data Elmu:jurnal:P:Photogrametry & Remotesensing:Vol55.Issue1.Feb2000:

Geometric in-flight calibration of the stereoscopic line-CCD

scanner MOMS-2P

Wolfgang Kornus

, Manfred Lehner, Manfred Schroeder

¨

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ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

`

¨

¨

¨

ˆ

ˆ

¨

ˆ

ˆ

ˆ

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