Comparison of Very High Resolution Space Images - asprs

COMPARISON OF VERY HIGH RESOLUTION SPACE IMAGES Gurcan Buyuksalih Zonguldak Karaelmas University [email protected] Karsten Jacobsen University of Hannover [email protected]

ABSTRACT In the Zonguldak test area IKONOS, QuickBird and OrbView-3 images are available. Their geometric quality has been analyzed and compared with different mathematical models in relation to precise ground control points allowing sub-pixel accuracy. The highest geometric precision was reached by bias corrected rational polynomial coefficients followed by geometric reconstruction. For 3D-affine transformation and especially the DLT method quite more and three-dimensional distributed control points are required. IKONOS scenes do have the best inner geometry, leading to the full accuracy just by shifting the scene after terrain relief correction. For the other images a higher degree of improvement is required. Because of not the same ground sample distance (GSD), a different imaging system of OrbView-3 and the required permanent change of the view direction during imaging of QuickBird and OrbView-3 it is not so easy to compare the information contents of the sensors just by the GSD. So the information contents were checked by mapping the same area. In addition the effective resolution was determined by edge analysis. Keywords: IKONOS, QuickBird, OrbView-3, accuracy, resolution

INTRODUCTION The comparison of space images mainly has to be done in relation to the geometry and the information contents. The image geometry, that means the orientation, depends upon the direct sensor orientation based on a positioning system like GPS, gyros and star sensors. This has to be improved by means of control points for reaching a sufficient accuracy. The possible scale for topographic mapping is a function of the resolution; that means under usual conditions the ground sampling distance (GSD) – the distance of the centers of neighbored pixels projected to the ground. As a rule of thumb, a GSD of 0.1mm in the map scale is required for topographic mapping corresponding to a map scale 1 : 10 000 for 1m GSD. A topographic map must not have accuracy better than 0.25mm in the map scale or together with the preceding condition 2.5 times the GSD.

IMAGE GEOMETRY The high resolution satellite images, important for mapping, are based on CCD-lines. Across the scan direction – in the CCD-line direction - we do have perspective geometry. In the scan direction the image geometry depends upon the motion of the satellite or satellite view direction. The newest satellites are equipped with reaction or momentum wheels enabling a fast and continuous change of the view direction during imaging. The actual orientation of the sensor is determined by direct sensor orientation with an accuracy not leading to a loss of accuracy even in the case of stronger rotations during imaging. Such a rotation is required for sensors having a sampling rate below the image motion or for very high resolution sensor not equipped with transfer delay and integration; that means they cannot accumulate enough energy with the high image motion corresponding to the speed of the satellite. These satellites have to use a slow-down of the angular motion (figure 1) by permanent rotation. IKONOS does not require a slow down mode, but it is using the permanent rotation during imaging for images taken in the forward mode – that means if the images are scanned against the movement of the satellite in the orbit (figure 2). QuickBird originally was constructed for flying in the same height like IKONOS, but with the allowance to distribute space images also with a smaller GSD, the flying height was reduced to allow a GSD of 0.62m. The ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

sampling rate of 6500 lines/second could not be increased; it corresponds to a speed of 6500*0.62m = 4017m/sec. For the flying height of 450km the footprint speed is 7134m/sec. The relation of 7134m/sec / 4017m/sec = 1.776 has to be used as slow down factor – in relation to the orbit length used for the imaging of a scene with approximately the same view direction, the view direction is continuously changed to reach a 1.776 times longer length in the orbit. OrbView-3 is limited to a sampling rate of 5000 GSD/sec. In the elevation of 470km it has a footprint speed of 7103km/sec requiring a slow down factor of 1.42.

Figure 1. Slow down of imaging by permanent rotation of view direction slow down factor = b / a.

Figure 2. principle of IKONOS image generation - scan direction with orbit and scan direction against orbit.

Original images like QuickBird Basic Imagery and OrbView-3 images are available as well as images projected to a plane with constant height like IKONOS Geo and QuickBird OR Standard. A corresponding mathematical model has to be used. OrbView-3 has an imaging system different to IKONOS and QuickBird. It is not equipped with transfer delay and integration (TDI) sensors which can accumulate the energy reflected from the ground over several pixels. By this reason the original pixel size projected to the ground has a size of 2m, but neighbored pixels are over-sampled by 50% (figure 4). This over-sampling is caused by staggered CCD-lines. OrbView-3 is equipped for the panchromatic spectral range with staggered CCD-lines – there are 2 CCD-lines shifted ½ pixel in the CCD-line direction against each other.

Figure 3. Staggered CCD-lines.

Figure 4. Projected pixel size =2m, GSD=1m for OrbView-3.

The staggered CCD-lines are not influencing the geometry. The small offset of the projection centers of neighbored lines is negligible. But the imaging of OrbView-3 is a little different like IKONOS and QuickBird. The scanned lines must not be parallel on the ground (figure 5).

ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

Figure 5. areas covered by an OrbView-3 stereo pair in the test field Zonguldak.

METHODS OF IMAGE ORIENTATION The photogrammetric data acquisition is based on the relation between image and ground position. By the orientation process this relation will be determined. The classical orientation reconstructs the relation between the image and the ground system based on control points. The small field of view and the change of the orientation parameters from line to line do not allow the use of standard methods. The relation of the projection centers from line to line is known by the satellite orbit. The classical satellites did not change the attitude against the orbit during imaging. This is not any more the case for the very high resolution flexible satellites. If the change of the orientation is linear, this can be included into a general solution. In addition some information about the view direction is required if a three-dimensional, well distributed control point field is not available. Based on gyros, star sensors and GPS the full orientation information is available for the high and very high resolution optical satellites. For IKONOS, QuickBird and OrbView-3 the orientation accuracy (direct sensor orientation) has a standard deviation in the range of 10m for the ground coordinates, confirmed by the used scenes. This is sufficient for some applications, but usually it has to be improved based on control points. Following orientation methods are in use: a) Rational Polynomial Coefficients (RPC): The information about the direct sensor orientation is distributed as RPC, describing the image positions as functions of the ground coordinates X, Y and Z (Grodecki 2001).

xij =

Pi1( X , Y , Z ) j Pi 2( X , Y , Z ) j

yij =

Pi3( X , Y , Z ) j Pi 4( X , Y , Z ) j

Formula 1. Rational polynomial coefficients xij, yij =scene coordinates

Pn(X,Y,Z)j = a1 + a2 Y + a3 X +a4 Z + a5 Y X + a6 Y Z + a7 X Z + a8 Y² + a9 X² + a10 Z²+ a11 Y*X*Z + a12 Y³ +a13 Y X² + a14 Y Z² + a15 Y² X + a16 X + a17 X Z² + a18 Y² Z+ a19 X²*Z+ a20 Z³

X,Y,Z = geographic object coordinates

Usually the orientation based on the RPC has to be improved by control points leading to bias corrected RPC. The influence of the terrain height to the horizontal location can be respected with the local height and the RPC, also named terrain relief correction. After terrain relief correction a two-dimensional transformation to the control points is required, this can be made by a simple shift, an affine transformation or also with some additional corrections. b) Reconstruction of imaging geometry: For the scene centre or the first line, the direction to the satellite is available in the image header data of the very high resolution sensors. This direction can be intersected with the orbit of the satellite published with its Keppler elements. For the location of a point in the image the time interval to the imaging of the scene centre can be computed, using also information of the header data. With this time interval the actual projection centre for each point can be computed and together with this the ground position also the actual view direction. This method requires the same number of control points like the sensor oriented RPC-solution, that means, it can be used also without control points if the direct sensor orientation is accepted as accurate enough or it requires the same additional transformation of the computed object points to the control points like the sensor oriented RPCs. ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

c)

Three-dimensional affinity transformation: it is not using available sensor orientation information. The 8 unknowns for the transformation (see formula 2) of the object point coordinates to the image coordinates have to be computed based on control points located not in the same plane. At least 4 well distributed control points are required. The computed unknowns should be checked for high correlation values between the unknowns – large values are indicating numerical problems which cannot be seen at the residuals of the control points, but they may cause large geometric problems for extrapolations outside the three-dimensional area of the control points. Three dimensional means also the height, so problems with the location of a mountain top may be caused if the control points are only located in the valleys. A simple significance check of the parameters, e.g. by a Student test, is not sufficient. The 3D-affinity transformation is based on a parallel projection which is approximately given in the orbit direction but not in the direction of the CCD-line. The transformation can be improved by a correction term for the correct geometric relation of the satellite images having only a limited influence (Hanley et al 2002). xij = a1 + a2 X + a3 Y + a4 Z yij = a5 + a6 X + a7 Y + a8 Z Formula 2. 3D-affinity transformation d) Direct Linear Transformation (DLT): Like the 3D-affinity transformation the DLT is not using any preinformation. The 11 unknowns for the transformation of the object point coordinates to the image coordinates have to be determined with at least 6 control points. The small field of view for high resolution satellite images together with the limited object height distribution in relation to the satellite flying height is causing quite more numerical problems like for the 3D-affinity transformation. The DLT is based on a perspective image geometry which is available only in the direction of the CCD-line. There is no justification for the use of this method for the orientation of satellite images having more unknowns as required for the solution.

e) L1 ∗ X + L 2 ∗ Y + L3 ∗ Z + L 4 L9 ∗ X + L10 ∗ Y + L11 ∗ Z + 1 L5 ∗ X + L6 ∗ Y + L 7 ∗ Z + L8 yij = L9 ∗ X + L10 ∗ Y + L11 ∗ Z + 1 xij =

e)

Formula 3. DLT transformation

Terrain dependent RPCs: The relation scene to object coordinates can be approximated by a limited number of the polynomial coefficients shown in formula 1 and can be computed based on control points. The number of possible unknowns is quite depending upon the number and three-dimensional distribution of the control points. Just by the residuals of the control points the effect of this method cannot be controlled. Some commercial programs offering this method, do not use any statistical checks for high correlations of the unknowns, making the correct handling very dangerous. A selection of the unknowns may lead also to the three dimensional affinity transformation. Some tests with commercial software were leading to not acceptable results. At the control points no problems have been indicated, but at independent check points errors up to 50m have been seen in the case of not optimal control point distribution. Under operational conditions the control point distribution usually is not optimal, so a strong warning for the use of this method has to be given. This method should never be used for commercial projects, the quality of the result cannot be guaranteed.

EXPERIENCES The different orientation methods have been used for image orientation in the test field of Zonguldak for IKONOS, QuickBird and OrbView-3 images. The same control points, determined by GPS survey, have been used for all image types. Based on different number of control points the orientation accuracy has been analysed. The not used control points have been used as independent check points. The image orientation and analysis has been done with programs of the University of Hannover.

IKONOS The bias corrected RPC-solution, as well as the geometric reconstruction, were leading to sufficient results just based on one control point. Of course under operational conditions at least 2 control points are required for reliability reason. It does not matter, where the control points are located in the scene. For the 3D-affine ASPRS 2006 Annual Conference Reno, Nevada May 1-5, 2006

transformation at least 4 three-dimensional well distributed control points are required, for DLT 6 control points. For both methods at least 2 more control points have to be used for reaching stable results. With less than 6 or 8 control points the used program TRAN3D has warned for not acceptable correlation between the unknowns.

Figure 6. IKONOS Zonguldak Results at independent check points for the different orientation methods as a function of the number of control points - only the case of 32 reference points shows the residuals at control points. After terrain relief correction a transformation to the control points is required. The used Hannover programs CORIKON for the geometric reconstruction and RAPORI for the bias corrected RPC solution are checking the used transformation parameters by statistical tests. The not justified parameters can be removed.

Figure 7. Influence of shift and affinity transformation after terrain relief correction For the IKONOS scenes after terrain relief correction there was no advantage of an affine transformation to the control points. The inner accuracy of the IKONOS scenes is sufficient for a simple shift to the ground control.

QuickBird QuickBird has a smaller GSD of 0.62m and a swath of 16 km. This of course makes the scene orientation more sensitive.


Figure 8. QuickBird Zonguldak Results at independent check points for the different orientation methods as a function of the number of control points - only the case of 40 reference points shows the residuals at control points

For QuickBird the approximations 3D-affine transformation and DLT have not reached the same accuracy like the bias corrected RPC solution and the geometric reconstruction. This may be caused the required slow down mode by the factor 1.776 (figure 1). By this reason the 3D-affine transformation can been extended in the Hannover program TRAN3D by 4 additional unknowns describing the change of the scene orientation. xij = a1 + a2 *X + a3 *Y + a4 *Z + a9*X*Z + a10*Y*Z yij = a5 + a6 *X + a7 *Y + a8 * Z+ a11*X*Z + a12*Y*Z

Formula 4. Extended 3D-affinity transformation

Based on 40 control points the 3D-affine transformation reached only root mean square discrepancies at control points of 1.06m for X and for Y. With the extended affinity transformation (formula 4) it has been improved to 0.42m, similar like the geometric reconstruction and the bias corrected RPC.

OrbView-3 The use of staggered CCD-lines caused a small loss of image quality against IKONOS having the same GSD of 1m. It was a little more difficult to identify the control points. The scene length of approximately 19km caused together with the slow down factor 1.42 problems for the approximate solutions. In addition it seems that the CCDline was rotating against the scan direction (figure 5). Such a motion is included in the RPC-information, but it causes problems for the 3D-affine transformation and the DLT which are not using any given scene orientation information. Table 1. root mean square errors at 34 control points [m] test area Zonguldak, RPC absolute is showing the mean difference of the direct sensor orientation

OrbView-3 3D affine 3D affine improved DLT RPC absolute RPC shift RPC affine RPC affine, relative

scene 471890 RMSX RMSY 6.71 11.95 3.28 1.90 4.98 7.80 8.37 8.56 1.55 1.57 1.54 1.26 1.17 0.53

scene 443940 RMSX RMSY 8.06 21.16 3.15 2.88 7.69 11.79 3.58 -13.61 2.21 2.09 1.68 1.89 1.33 1.47


The results of the 3D-affine transformation and also the DLT cannot be accepted. With the extended 3D-affine transformation, taking care also about the change of the view direction in the scene (formula 4), the achieved accuracy is quite better but also not sufficient. The bias corrected RPC solution is usable, but with the same control points like for IKONOS and QuickBird no sub-pixel accuracy has been reached. With an affine transformation to the control points after terrain relief correction the result is slightly better than with a simple shift.

Figure 9. OrbView-3 discrepancies at control points, bias corrected RPC, affine.

Figure 10. Relative standard deviation, RPC affine, horizontal = distance between points.

As mentioned before, the image measurement of the control points for OrbView-3 is more difficult like with IKONOS. A separation of the pointing accuracy from the geometric scene problems is possible by covariance analysis. Directly neighbored control points are influenced in a similar manner by long periodic geometric problems (figure 9), that means, they are correlated. This is causing also a trend function for the relative standard deviation (figure 10) – neighbored points are more accurate to each other than to points having a larger distance. The relative standard deviation (figure 10) shows an accuracy of directly neighbored points of approximately 1m. This corresponds to the pointing accuracy. So the standard deviations exceeding 1m are caused by the image geometry not included in the RPC.

CONCLUSION With strict orientation solutions with IKONOS and QuickBird images sub-pixel accuracy has been reached without problems just based on few control points. The small field of view of IKONOS images allows also the use of an orientation with the approximate methods 3D-affine transformation and DLT with at least 6 to 8 well distributed control points. Of course this is not an economic solution and should be avoided. The inner accuracy of QuickBird scenes is not so stable like for IKONOS, so after terrain relief correction affine transformation to the control points is required. That means, for QuickBird at least 3, better 4 control points are necessary while IKONOS can be oriented just with 1 or better 2 control points. Even with a higher number of control points the 3D-affine transformation and DLT have not reached sub-pixel accuracy. The geometry of the original OrbView-3 images does not allow a simplified orientation with the approximate solutions of the 3D-affine transformation and DLT. Even with an extended 3D-affine transformation with 12 parameters, it is not possible to reach the same accuracy like with the bias corrected rational polynomial coefficients. But also with the RPCs sub-pixel accuracy has not been reached. This is caused by the image quality, slightly lower than for IKONOS, resulted by the over-sampling of the staggered CCD lines and not so good image accuracy. A GSD of 1m allows usually a topographic mapping up to a map scale of 1 : 10 000. For this scale a mapping accuracy of 2.5m is sufficient. This requirement is fulfilled also with the used OrbView-3 images. For all very high resolution optical space sensors the bias corrected RPCs are leading to optimal orientation results. The geometric reconstruction is very close to this and has the same advantages in relation to the control points. The approximate orientation solutions do require more and well distributed control points and do not lead to the optimal accuracy. Especially for OrbView-3 images they cannot be used.


ACKNOWLEGMENTS Thanks are going to the Jülich Research Centre, Germany, and TUBITAK, Turkey, for the financial support of the investigation in this area.

REFERENCES Grodecki, J. (2001): IKONOS Stereo Feature Extraction – RPC Approach, ASPRS annual conference St. Louis 2001, on CD. Hanley, H.B., Yamakawa. T., Fraser, C.S. (2002): Sensor Orientation for High Resolution Imagery, Pecora 15 / Land Satellite Information IV / ISPRS Com. I, Denver. Jacobsen. K., Büyüksalih, G., Topan, H., 2005: Geometric Models fort the Orientation of High Resolution Optical Satellite Sensors, ISPRS Hannover Workshop 2005, http:/www.ipi.uni-hannover.de
