Integration of Ikonos and QuickBird imagery for geopositioning accuracy analysis

Abstract

This research investigated the accuracy in three-dimensional (3D) geopositioning achieved by integrating Ikonos and QuickBird images using the vendor-provided rational polynomial coefficients (RPCs). One pair of stereo Ikonos images and one pair of stereo QuickBird images were collected for the same region of Tampa Bay, Florida, and used in this study. Results of 3D geopositioning from different combinations of Ikonos and QuickBird stereo images were generated by using an improved rational function model (RFM). The relationship between the satellite-borne pointing geometry and the attainable ground accuracy is examined. This research demonstrates that the integration of Ikonos and QuickBird images is feasible and can improve the 3D geopositioning accuracy using a proper combination of images.

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PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2007 1067
Photogrammetric Engineering & Remote Sensing
Vol. 73, No. 9, September 2007, pp. 1067–1074.
0099-1112/07/7309–1067/$3.00/0
© 2007 American Society for Photogrammetry
and Remote Sensing
Abstract
This research investigated the accuracy in three-dimensional
(3D) geopositioning achieved by integrating Ikonos and
QuickBird images using the vendor-provided rational
polynomial coefficients (RPCs). One pair of stereo Ikonos
images and one pair of stereo QuickBird images were
collected for the same region of Tampa Bay, Florida, and
used in this study. Results of 3Dgeopositioning from different
combinations of Ikonos and QuickBird stereo images were
generated by using an improved rational function model
(RFM). The relationship between the satellite-borne pointing
geometry and the attainable ground accuracy is examined.
This research demonstrates that the integration of Ikonos
and QuickBird images is feasible and can improve the
3Dgeopositioning accuracy using a proper combination
of images.
Introduction
Since the launch of GeoEye’s Ikonos Earth imaging satellite
in September 1999, commercial high-resolution satellite
imaging systems have initiated a new era of Earth observa-
tion and digital mapping (Li, 1998). With such advantages
as high resolution, short revisit time, and adaptable stereo
imaging capability, high-resolution satellite imagery (HRSI)
is very attractive due to its ability to provide accurate
3Dmapping products. During the past five years, HRSI has
become widely used in digital topographic mapping and
surveying. Table 1 lists the associated accuracies of different
Ikonos and QuickBird image products (GeoEye, 2006;
DigitalGlobe, 2005). Generally, the cost is proportional to the
accuracy required.
The high cost of high-accuracy products makes it very
attractive to find practical methods that are capable of using
low-cost products to generate highly accurate mapping
products (Wang et al., 2005). One of the major barriers to
deriving such an approach is the lack of access to the
appropriate rigorous sensor model that is normally
unavailable with Ikonos and QuickBird products. Instead,
the vendors provide a rational function model (RFM), in the
form of rational polynomial coefficients (RPCs), to describe
the orientation information for these high-resolution imaging
systems (Tao and Hu, 2001; Di et al., 2003a). The advantages
of the RFM include its high fitting capability, its simplicity,
and its independency of sensors. Furthermore, the fact that
the rigorous sensor model cannot be derived directly from
the RPCs makes the RFM very popular among satellite
imagery vendors (Fraser, 1999; Tao et al., 2004).
Integration of Ikonos and QuickBird Imagery
for Geopositioning Accuracy Analysis
Rongxing Li, Feng Zhou, Xutong Niu, and Kaichang Di
As a generalized sensor model, the RFM represents
the relationship between the image coordinates and the
object coordinates with ratios of polynomials, as shown
in Equation 1:
(1)
The polynomial P
i
(i1, 2, 3, and 4) has the following
general form:
(2)
where (x, y) are the column and row of each image point
and (X, Y, Z) are, for example, the longitude and latitude
(in degrees, WGS84) and ellipsoidal height (in meters, WGS84)
of the corresponding ground point. All the image and
ground coordinates are normalized to the range [–1, 1] by
using offset and scale parameters provided by the vendor.
For each image, eighty RPCs (including two that are always 1)
are also provided.
The RPCs are usually computed by satellite image
providers without using ground control points (GCPs). Instead,
the object space is sliced in the vertical direction to generate
virtual control points for calculating the RPCs (Tao and Hu,
2001; Di et al., 2003a). The ground coordinates derived from
such RPCs, for example for the Ikonos “Geo” product, typi-
cally have an RMSE of about 25 m. If quality GCPs are avail-
able, there is a potential to use the GCPs for enhancing the
ground accuracy. Li et al. (2003) found a systematic error of
16 meters between RPC-derived coordinates and the ground
truth. A similar result was reported in Fraser and Hanley
(2003). It is desirable that such errors in the image products
be reduced or eliminated by employing relatively simple
methods so that the improved products can be used for
applications that require a higher mapping accuracy.
Before actual Ikonos images were available, Li (1998)
discussed the potential accuracy of high-resolution imagery
using basic photogrammetry principles. Zhou and Li (2000)
simulated 1 m resolution Ikonos imagery based on pushb-
room sensor imaging geometry to estimate the potential
 a18X2Z  a19Y2Z  a20Z3
 a13XY2  a14XZ 2  a15X2Y  a16Y3  a17YZ 2
 a8X2  a9Y2  a10Z2  a11XYZ  a12X3
P(X,Y,Z)a1  a2X  a3Y  a4Z  a5XY  a6XZ  a7YZ

xP1(X, Y, Z)
P2(X,Y, Z)
yP3(X, Y, Z)
P4(X, Y, Z)
.
Mapping and GIS Laboratory, Department of Civil &
Environmental Engineering and Geodetic Science, The Ohio
State University, 470 Hitchcock Hall, 2070 Neil Avenue,
Columbus, OH 43210 (li.282@osu.edu).
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T
ABLE
2. P
ARAMETERS OF
P
ANCHROMATIC
S
TEREO
I
MAGERY
QuickBird Ikonos
Forward Backward Forward Backward
Acquisition date & time (GMT) 2003-09-12 15:58:08 2003-09-12 15:59:17 2004-07-08 16:17:17 2004-07-08 16:18:08
Image resolution 0.767 m 0.751 m 1 m 1 m
Image size (row *column) 25776 *27552 24620 *27552 8484 *12160 8484 *12160
Image corner coordinates
Upper Left 27.726611° 27.724392° 27.682928° 27.682909°
Latitude
Upper Left 82.624066° 82.623689° 82.595190° 82.596768°
Longitude
Lower Right 27.536944° 27.539502° 27.574130° 27.574144°
Latitude
Lower Right 82.427541° 82.427908° 82.510763° 82.509266°
Longitude
Collection azimuth (

) 17.7° 184.5° 40.7986° 120.1049°
Collection elevation (

) 58.7° 59.2° 60.75331° 74.14089°
accuracy of ground point determination, and an accuracy
of 2 to 3 meters was achieved. Dial (2000) estimated the
stereo mapping accuracy of Ikonos products with GCPs as
1.32 m (RMSE) in the horizontal direction and 1.82 m
(RMSE) in the vertical direction, respectively. Grodecki and
Dial (2003) demonstrated that, for Ikonos satellite imagery,
an RPC block adjustment with one ground control point can
reduce average errors in longitude, latitude, and height
from 5.0, 6.2, and 1.6 meters to 2.4, 0.5, and 1.1
meters, respectively. Robertson (2003) achieved an accu-
racy level better than 3 m (RMSE) in both the Xand Y
directions for QuickBird Basic images with limited ground
control. Di et al. (2003b) used a 3Daffine transformation
model to refine the RPC-derived ground coordinates for
Ikonos images and achieved accuracies of better than 1.5 m
in planimetry and 1.6 m in height. Noguchi et al. (2004)
investigated the geopositioning accuracy of QuickBird
stereo imagery and obtained an accuracy of 0.6 m in
planimetry and 0.5 m in height. Eisenbeiss et al. (2004)
analyzed the accuracies of Ikonos and QuickBird imagery
in the same region for 3Dpositioning, orthoimage, and DSM
generation and concluded that, with sufficient modeling,
the planimetric accuracy can reach 0.4 to 0.5 meters even
with very few GCPs. Wang et al. (2005) compared the
results from using different methods in both image space
and object space including translation, translation and
scale, affine, and second-order polynomial transformation
models with different GCP distributions, to improve the
Ikonos stereo geopositioning accuracy. It was found that
the affine transformation can produce better accuracies
with four to six evenly distributed GCPs. Similar results
were found in the research on geopositioning accuracy
using QuickBird stereo images (Niu et al., 2004).
For many applications, it is necessary to integrate data
acquired by sensors from various spatial positions of
different platforms (satellites, aircraft, ships, vehicles, and
fixed locations) and at various times. This becomes essential
either for achieving a higher geometric accuracy, or better
object detection capability, or improved temporal coverage.
For instance, the availability of appropriate HRSI data for a
specific area may be limited because of a busy satellite data
acquisition task schedule, data costs, weather condition, and
the urgency of data needs. It is often desirable, if technically
feasible, to integrate data from different high-resolution
imaging satellites (e.g., Ikonos and QuickBird) at different
times for achieving an improved accuracy using cross-
satellite stereo capabilities. This is especially important for
applications that need timely 3Dinformation and needs to
be investigated.
This study investigated the integration of Ikonos and
QuickBird images with different imaging geometry based on
the RFM. A pair of Ikonos stereo “Reference” product images
and a pair of QuickBird stereo “Basic” product images were
used in the study. During geometric processing, GCPs and affine
transformation were applied to refine the outcomes from the
RPCs. The ground accuracies of various integration schemes of
Ikonos and QuickBird images are analyzed and discussed.
Data Set
The QuickBird stereo pair was taken in September 2003 in
south Tampa Bay, Florida. The center of the scene was near
lat. 27.63°N, long. 82.52°W. The Ikonos stereo pair was taken
in July 2004 in the same region. Additional information
about the scene locations can be found in Table 2. The
coverage of the Ikonos stereo pair is within the coverage of
the QuickBird pair. The elevation range in this area is
between 29.7 and 31.9 meters. Corresponding RPCs were
provided in metadata files supplied by both vendors, Digital-
Globe, Inc. and GeoEye. Figure 1 illustrates the orbital
geometry of the QuickBird and Ikonos satellites.
Nominal collection azimuth and nominal elevation
angles of both satellites as viewed from the scene centers
were included in the metadata files. With these parameters
(see Table 2), the convergent angles of both stereo pairs were
calculated. The convergent angle is calculated by the
intersection of two lines: a line from the first position of
T
ABLE
1. A
CCURACIES OF
I
KONOS AND
Q
UICK
B
IRD
I
MAGE
P
RODUCTS
Ikonos QuickBird
Products CE90 RMSE Products CE90 RMSE
Geo 15 m NA Basic 23 m 14.0 m
Reference 25.4 m 11.8 m Standard 23 m 14.0 m
Pro 10.2 m 4.8 m Orthorectified 25.4 m 15.4 m
(1:50 000)
Precision 4.1 m 1.9 m Orthorectified 10.2 m 6.2 m
(1:12 000)
Precision 2.0 m 0.9 m Orthorectified 4.23 m 2.6 m
Plus (1:5 000)
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PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2007 1069
Figure 3. Distribution of GCPs (triangles) and CKPs
(circles).
Figure 2. Relationships between azimuth, elevation,
and convergent angles.
Figure 1. Illustration of the orbital geometry of
QuickBird and Ikonos satellites.
the satellite to the center of the scene and another line from
the second position of the satellite to the center. Equation 3
shows the relationship among these three angles:
(3)
where

is the convergent angle, and

i
and

i
, (i1, 2), are
the nominal collection azimuth and nominal elevation
angles, respectively, as shown in Figure 2. Also included in
Table 2 are coverage ranges, collection dates, image resolu-
tion, and image sizes for both satellites.
The four GCPs and sixteen checkpoints (CKPs) used in
this study were obtained from triangulated aerial photo-
graphs. Figure 3 shows the distribution of these points:
triangles show the positions of the four GCPs and circles the
positions of the sixteen CKPs. The background image is the
Ikonos forward-looking image. The RMSEs of the aerial
cos dsin a1sin a2  cos a1 cos a2cos(u2u1)
triangulation are 0.153 m, 0.195 m, and 0.067 m in the X, Y,
and Zdirections, respectively (Xis east, Yis north, and Zis
elevation).
Geometric Integration of Ikonos and QuickBird Images
For each GCP, an affine transformation in the image space is
used to correct the systematic errors and to improve the
image coordinates (Wang et al., 2005). This is shown in
Equation 4:
(4)
where Iand Jare the image coordinates calculated from
the ground coordinates and RPCs using Equation 1, and Iand
Jare the image coordinates manually measured at each GCP
on the satellite image. The coefficients a
i
and b
i
, (i0,1,2),
were calculated by using (I, J) and (I, J) for four GCPs
through a least-squares adjustment. By using Equation 4 and
the calculated affine transformation parameters, the adjusted
(I, J) of the CKPs can be calculated. Through the RFM, the
refined object coordinates of the CKPs can be obtained, as
can the RMSEs that are computed through differences
between the known and calculated ground coordinates of
the CKPs.
Based on our prior work (Di et al., 2003a and 2003b;
Li et al., 2003; Niu et al., 2004; Wang et al., 2005), a
Jb0  b1I  b2J
Ia0  a1I  a2J
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T
ABLE
3. C
OMBINATIONS OF
I
KONOS AND
Q
UICK
B
IRD
I
MAGES
Combination
Combination Ikonos Ikonos QuickBird QuickBird Geometry
ID Forward Backward Forward Backward Illustration
1 X X Figure 5a
2 X X Figure 5b
3 X X Figure 5c
4 X X Figure 5d
5 X X Figure 5e
6 X X Figure 5f
7 X X X Figure 5g
8 X X X Figure 5h
9 X X X Figure 5i
10 X X X Figure 5j
11 X X X X N/A
program system used to calculate the ground coordinates
and perform adjustment has been specifically developed for
this research. As shown in Figure 4, input information for
the program includes the coordinates of GCPs and CKPs in
both the image and object spaces, as well as RPCs corre-
sponding to the various combinations. The coordinates of
GCPs in both the image and object spaces were used to
calculate the affine transformation coefficients as shown in
Equation 4. These coefficients were then used to refine the
image coordinates of CKPs. The refined image coordinates
of CKPs from two or more satellite images were applied to
Equation 1 along with the corresponding RPCs. The refined
ground coordinates of these CKPs were computed through a
least-squares triangulation method (Di et al., 2003a).
Finally, the RMSEs of these CKPs were calculated by com-
paring their refined ground coordinates and known ground
coordinates. The study considered three types of integra-
tion schemes involving the four Ikonos and QuickBird
images: (a) a stereo of two images, (b) stereo of three
images, and (c) stereo of all four images. All combinations
are listed in Table 3.
The GCPs and CKPs are generally very clear image
features, such as building corners and road intersection
corners. Their locations in the first image are identified
manually by zooming in and taking careful measurements
considering the image feature patterns at sub-pixel level
(typically 0.1 pixels or better). The corresponding points on
the other image(s) are determined in the same way.
The satellite imaging geometry of each combination
can be illustrated by nominal azimuth angles, nominal
elevation angles, and convergent angles. In Figure 5,
illustrations 5a through 5j display the imaging geometry
for each combination. The nominal azimuth and elevation
angles, and the convergent angles of the combined stereo
images are illustrated.
When performing computations, each image is treated
equally in using Equation 4 and the subsequent image-to-
ground photogrammetric triangulation. The 3Dgeoposition-
ing accuracies, computed from each combination using the
same set of GCPs and CKPs, are listed in Tables 4, 5, and 6
corresponding to the three types of combinations. The RMSEs
in these tables are derived from the differences between the
RPC-triangulated ground coordinates of the CKPs and their
known ground coordinates.
Table 4 shows the geopositioning accuracies of stereo
pairs of any two Ikonos and QuickBird images. Rows 1
and 4 represent the results of the QuickBird and Ikonos
stereo pairs, respectively. It can be observed according to
the results that:
•Accuracies of the QuickBird stereo pair in the X, Y,
and Zdirections are the best (sub-meter) among all
configurations; and
•The planimetric accuracy of the Ikonos stereo pair is better
than the ground resolution and the elevation accuracy is
slightly lower than that.
Table 4 also shows the results of combinations containing
one Ikonos image and one QuickBird image. RMSEs of most
of the combinations are about one meter or less. However,
the combination of both forward images has the worst
accuracy; RMSEs in the Yand Zdirections reach 2.011 m
and 3.339 m, respectively. To facilitate the comparison, the
rows in the table are sorted in the descending order of the
convergent angles.
Table 5 shows the geopositioning accuracies of combi-
nations of three images. The first two rows represent the
combinations of the Ikonos stereo pair with one QuickBird
image. These two combinations provide better accuracies
than the Ikonos stereo pair alone (Table 4). In particular,
when the Ikonos stereo pair is combined with the QuickBird
backward-looking image, the improvement in accuracy is
significant because of both the higher resolution of the
additional QuickBird image and the larger convergent
angles. The remaining two rows in Table 5 show combina-
tions of the QuickBird stereo pair with one Ikonos image.
Compared with accuracies of just the QuickBird stereo pair,
the accuracies of these two combinations show a slight
improvement in the Zdirection, but a slight decrease in the
Xand Ydirections (several centimeters).
Table 6 shows the geopositioning accuracies of the
combination of all four images. These lie between the
accuracies of the Ikonos stereo pair and those of the Quick-
Bird stereo pair.
To summarize, from Table 4 we can observe that there
is an approximate linear relationship between the accuracies
in the Y(along-track) and Z(elevation) directions and the
convergent angles. The greater the convergent angle, the
better the accuracies. However, this relationship does not
apply so well in the X(cross-track) direction. Essentially,
Figures 5a through 5d have a combination of forward-
looking and backward-looking images; Figures 5e and 5f are
combinations of two backward-looking images and two
forward-looking images, respectively. The convergent angles
of Figures 5e and 5f are, therefore, smaller than those of
Figures 5a through 5d, and their accuracies are lower,
accordingly. In Table 5 there are three convergent angles for
each combination of three images. For each two rows
involving the Ikonos (first and second rows) or the Quick-
Bird (third and fourth rows) stereo pair, the first convergent
Figure 4. The workflow of the developed multi-satellite
3D geopositioning program system.
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PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2007 1071
Figure 5. Imaging geometries of different Ikonos and QuickBird combinations:
(a) forward and backward QuickBird, (b) forward Ikonos and backward QuickBird,
(c) forward QuickBird and backward Ikonos, (d) forward and backward Ikonos,
(e) backward Ikonos and backward QuickBird, (f) forward Ikonos and forward
QuickBird.
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PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
T
ABLE
4. G
EOPOSITIONING
A
CCURACIES OF
S
TEREO
P
AIRS
3D Geopositioning Accuracy
Combination
(RMSE: meter)
Image Combination ID

x

y

z
Convergent Angle (

i
)
QuickBird (F) – QuickBird (B) 1 0.546 0.339 0.623 61.64337°
Ikonos (F) – QuickBird (B) 2 0.421 0.476 0.648 56.76096°
Ikonos (B) – QuickBird (F) 3 0.846 0.661 1.100 37.67997°
Ikonos (F) – Ikonos (B) 4 0.877 0.791 1.091 30.22133°
Ikonos (B) – QuickBird (B) 5 0.437 1.002 1.308 27.53404°
Ikonos (F) – QuickBird (F) 6 1.143 2.011 3.339 11.76017°
Note: F – forward and B – backward. The RMSEs are derived from the checkpoints.
Figure 5. (Continued) Imaging geometries of different Ikonos and QuickBird
combinations: (g) Ikonos stereo and forward QuickBird, (h) Ikonos stereo and
backward QuickBird, (i) forward Ikonos and QuickBird stereo, and (j) backward
Ikonos and QuickBird stereo.
angles formed by the same satellite imaging system are
always same. The remaining two convergent angles have a
combined impact on the accuracies, which is similar to the
relationship of convergent angle versus accuracy found in
Table 4. Moreover, in this case, the accuracy in the X(cross-
track) direction is also affected by the convergent angles.
Conclusions and Future Work
In this research, one QuickBird stereo pair and one Ikonos
stereo pair were collected in the same region. We compared
three-dimensional geopositioning accuracies of different
combinations from these four images. According to the results
in Tables 4 through 6, the following conclusions can be made.
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PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
September 2007 1073
•First, the integration of a higher resolution QuickBird image
with Ikonos images (a pair or a single image) achieved a
ground point accuracy that is generally better than that of
the Ikonos pair (Tables 4 and 5).
•Second, the satellite imaging geometry plays a significant
role in improving ground point accuracies. When forming
stereo pairs or three-image triangulation cases involving both
satellite systems, the ground point accuracy improves as the
convergent angle(s) increases (Tables 4 and 5), which should
be a quality indicator for such integration.
•Third, as shown in Figure 6, the relationship between the
ground point accuracy and the convergent angle is direction
dependent if only one stereo pair is considered. The conver-
gent angle has more significant impact on Y(along-track) and
Z(elevation) coordinates than on the X(cross-track) coordi-
nate. However, if three images are involved (Table 5), the
combined convergent angles impact the accuracy of all three
coordinates.
•Finally, the integration of all four images does not produce
a better result than that of the QuickBird stereo pair. In fact,
it can be seen that the achieved accuracy (Table 6) is
between those of the QuickBird and the Ikonos stereo pairs
(Table 4). Therefore, an analysis of various factors as
mentioned above should be performed before an integration
of images from multiple high-resolution satellite imaging
systems is carried out.
The above results were generated from our Ikonos and
QuickBird stereo images in the area including the GCPs and
CKPs, which were designed to have an appropriate distribu-
tion and to form a strong configuration, based on our
successful prior experiments in this and other sites. The
conclusions should be at least representative for non-
mountainous regions.
It is generally true that image matching is less challeng-
ing if the two images of a stereo pair are close, or the stereo
base is short. For achieving a higher accuracy, we want to
have a larger convergent angle, i.e., wider stereo base. This
issue may be significant for close-range photogrammetry.
However, for the satellite image integration case of this
study, objects on the ground are relatively far away from the
sensors and the wider stereo bases do not pose a significant
challenge for matching.
In this research, the higher resolution QuickBird stereo
pair happens to have the greatest convergent angle among
the tested stereo pairs, and it also has the best accuracies in
all directions. We would like to have a stereo pair of Ikonos
(F/B) and QuickBird (B/F) that would have a convergent
angle greater than that of the QuickBird stereo pair. Such a
combination would help us distinguish between the effects
of the convergent angle on the geopositioning accuracies and
those of image resolution.
Acknowledgments
This research has been funded by the National Science
Foundation Digital Government Program and the National
Geospatial-Intelligence Agency. We appreciate reviewers’
constructive comments.
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T
ABLE
5. G
EOPOSITIONING
A
CCURACIES OF
T
HREE
I
MAGES
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Comb.
(RMSE: meter)
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Image Combination ID

x

y

z
(

i
)
Ikonos (S) – QuickBird (F) 7 0.818 0.752 1.021 30.22133° 11.76017° 37.67997°
Ikonos (S) – QuickBird (B) 8 0.468 0.639 0.626 30.22133° 56.76096° 27.53404°
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Figure 6. The relationships between geopositioning
accuracies and convergent angles of stereo pairs.
T
ABLE
6. G
EOPOSITIONING
A
CCURACIES OF
A
LL
F
OUR
I
MAGES
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Accuracy (RMSE: meter)
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
x

y

z
Ikonos – QuickBird 11 0.568 0.456 0.508
Note: The RMSEs are derived from the check points.
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(Received 31 January 2006; accepted 14 February 2006; revised
21 February 2006)
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