International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Specifications
IKONOS H
Satellite
QuickBird II
Satellite
First Launch
September 24, 1999
October 18, 2001
Date
Orbit 98.1 degree, 97.2 degree,
sun synchronous sun synchronous
Speed en 7.5 km / second 7.1 km / second
Orbit
Orbit Time 98 minutes 93.5 minutes
Altitude 681 kilometers 450 kilometers
Nadir: Nadir:
0.82 meters 0.61 meters
panchromatic panchromatic
3.2 meters 2.44 meters
Pixel multispectral multispectral
Resolution 26° Off-Nadir: 25° Off-Nadir:
1.0 meter 0.72 meters
panchromatic panchromatic
4.0 meters 2.88 meters
multispectral multispectral
Image Swath
11.3 km at nadir
13.8 km at 26° off-
nadir
16.5 kilometers at
nadir
Équator | wominally 10:30 10:30 a.m.
Crossing
a.m. solar time (descending node)
Time
Approximately 3 1-3.5 days
Revisit Time days at 1-meter depending on
resolution, latitude
40° latitude (30° off nadir)
Dynamic m Je :
Range 11 bits per pixel 11 bits per pixel
Image Bands
Panchromatic, blue,
green, red, near
infrared
Panchromatic, blue,
green, red, near
infrared
Table 2. Technical specifications of IKONOS and QuickBird
satellites (Space Imaging, 2002; Digital Globe, 2002)
RATIONAL FUNCTIONS
Both IKONOS and QuickBird stereo images are provided with
Rational Function Coefficients (RFCs). As an alternative to a
physical camera model, the rational function (RF) describes the
transformation between the image and object spaces. The rational
function transforms a point in the object space (X, Y, Z) into its
corresponding image point (i, j) through a ratio of the two
polynomials shown in Equation (1),
. PAX. YX. 2)
|
P.(X.Y.Z)
. P0 Y.Z)
“en Phe YZ) (1)
where the polynomial P; (i=1, 2, 3, and 4) has the following
general form:
690
P(X,Y,Z)=a, +a,X+a,Y+a,Z+a,XY+a,XZ +a,YZ+a,X"
2’ +a, XYZ+a,X' +a, XY’ +a, XZ’
Ya YZ ra X Zee MW Z ra ZY (2)
2
+a,Ÿ +a,
+a, X’Y +a,
This is a third-order rational function with a 20-term polynomial
that transforms a point from the object space to the image space.
Substituting P;s in Equation (1) with the polynomials in Equation
(2) and eliminating the first coefficient in the denominator, we
have a total of 39 RF coefficients in each equation: 20 in the
numerator and 19 in the denominator. Since each GCP produces
two equations, at least 39 GCPs are required to solve for the 78
coefficients.
Although they do not describe sensor parameters explicitly, RFs
are simple to implement and perform transformations very rapidly.
They can be used effectively for feature extraction, terrain model
generation, and orthorectification. Generally, RF coefficients are
estimated without the aid of ground control (Tao and Hu, 2001;
Di et al., 2001). Thus, some biases inherent in RFs may not be
corrected, and may be reflected in the geopositioning accuracy. Li
et al. (2003) found a systematic error of 6 meters between RF-
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 users
employing relatively simple methods that can be used for many
different applications that require higher mapping accuracy.
In this research, a pair of IKONOS stereo Geo product images
and a pair of QuickBird basic product stereo images were used to
evaluate methods for the improvement of geopositioning accuracy
based on RF models. Three-dimensional shorelines were also
extracted from both stereo pairs for coastal modeling.
DATA
The IKONOS stereo images used in this experiment were taken in
May 2002 in a Lake Erie coastal area. RFCs of each image were
supplied by Space Imaging Corp. The QuickBird stereo images
(Panchromatic and Multispectral) used in this experiment were
taken in September 2003 in southern Tampa Bay, Florida. RFCs
of the imagery were supplied by DigitalGlobe, Inc. The GCPs
(ground control points) used in this experiment were obtained
from GPS surveys conducted in Ohio in March 2000 and in
Florida in November 2002, respectively. Check points (CKPs) are
those points obtained from high quality aerial photogrammetric
triangulations of overlapped aerial images taken in the same areas.
The accuracy of these GCPs is 6 cm in the horizontal and 9 cm in
the vertical directions. The accuracy of the CKPs is estimated as
0.5 m. Figure 1 gives the distribution of GCP and CKP points in
the forward-looking images of both stereo pairs.
The image coordinates of the GCP and CKP points were
measured manually. Ground coordinates of the measured points
were calculated using the RFCs supplied with the data. After
registering both sets of ground coordinates within the same
reference system (for example, the QuickBird images are based
on State Plane, NAD 83, Florida West), differences between the
RFC-derived coordinates of the control points and their GPS-
surveyed coordinates were calculated. Figure 2 shows such
differences in the QuickBird image measurements. The display in
Interne
Figure
Figure
and exi
both Q
in Tabl
al. (20€
