EXPERIMENTAL STUDY ON GROUND POINT ... - Semantic Scholar

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ensor. Camera lens. B. B. Flight direction. Orbit height. Focal length κ ω. ϕ. Z. X. Y ..... from Mr. Alex Gonzalez of OSU, Mr. David Albrecht of Ohio Department of ...
EXPERIMENTAL STUDY ON GROUND POINT DETERMINATION FROM HIGH RESOLUTION AIRBORNE AND SATELLITE IMAGERY Ron Li and Guoqing Zhou Department of Civil and Environmental Engineering and Geodetic Science The Ohio State University 470 Hitchcock Hall, 2070 Neil Avenue, Columbus, OH 43210-1275 Tel (614) 292-6946, Fax (614) 292-2957, Email: [email protected]

Abstract In this paper we introduced the principle of stereo imaging using linear arrays and its implementation in several imaging systems. A simulation study was conducted in which simulated IKONOS-I fore-, nadir- and aft-looking images were produced using airborne AIMS images, IKONOS-I technical data, and a DEM. The attainable accuracy of ground points determined by the imagery is reported, considering various conditions such as number of GCPs, distribution of GCPs, errors in image and ground coordinates and others. It is concluded that the accuracy of ground points can reach about 2-3m with GCPs and 12m without GCPs. The experimental results of HRSC and MOMS-02P data validated the bundle adjustment software system designed and implemented for processing high-resolution satellite imagery.

1. INTRODUCTION The new generation of commercial one-meter resolution satellite imagery will open a new era for digital mapping (Fritz 1996, Li 1998). Several US companies scheduled launches of such high-resolution imaging satellites in 1999. For example, IKONOS-I of SpaceImaging is expected to provide a ground point accuracy of 12m horizontal and 8m vertical without ground control points (GCPs) and 2m to 3m with GCPs (Li 1998, Li et al. 1998). This level of accuracy is considered sufficient to support most national mapping products. A key technical component in the high-resolution space-borne sensors is stereo imaging from linear array sensors, which is formed by aiming an object on the ground from more than one linear array sensor from different sight of views. Three-line stereo imaging technique was pioneered by Hofmann et al. (1982). It was implemented by DLR (German Aerospace Research Establishment) as MOMS system series first on board of a space shuttle and then on space station MIR (Kornus and Lehner 1998). Results of simulation, calibration, and data processing have been reported by Ebner and Strunz (1988), Ebner et al. (1991, 1992), Fraser and Shao (1996), and Fritsch et al. (1998). The very same concept was used by DLR to develop HRSC (High Resolution Stereo Cameras) to map the Mars terrain surface (Albertz et al. 1996, Wewel 1996). After the failure of its launch, HRSC has been used for mapping applications on the Earth. A modified version of three-line imaging is, for example, implemented in satellite-borne IKONOS-I of SpaceImaging to be launched in June 1999. This paper briefly reviews the principle of stereo imaging using linear array sensors. It also reports our recent experiences in processing of simulated IKONOS-I data, HRSC and MOMS-02P data.

2. STEREO IMAGING FROM LINEAR ARRAY SENSORS Three-line Stereo Imaging Traditionally, stereo imaging is realized by taking pictures of an object by one or more frame cameras from different locations. In contrast, a linear array can be used in a so-called push-broom system that produces a strip of image. The images are usually rectified using a simplified model such as a polynomial function. A three-line stereo imaging system has three linear arrays (fore-, nadir- and aft-looking) mounted separately across the flight direction with three different looking angles (Figure 1). The imaging system produces three strips overlapping the same

ground area. Such an imaging system preserves all advantages of linear array based remote sensing imaging systems, including multispectral sensing and continuous scanning along the track. Flight direction

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Figure 1. Three-line stereo imaging (Seige 1998) Fore-looking (t) Nadir-looking (t+ ∆ t) Aft-looking (t+∆t1)

x yc ϕt

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xc ωt B

X St = XSo + a1t + a2t 2 + a3t 3

YSt = Y So + b1t + b2t 2 + b3t 3 Z St = Z So + c1t + c2 t 2 + c3t 3

ϕ t = ϕ 0 + d1t + d 2 t 2 + d3t 3

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Figure 2. Coordinate systems defined in the three-line imaging system

Figure 3. Image reference coordinate system

Figure 2 shows the established image, camera and ground coordinate systems. Each of the fore-, nadir- and aftlooking array has its own camera coordinate system (xc, yc and zc) that is used to define array related parameters such as interior orientation parameters. An image reference coordinate system (xR, yR zR) is defined to unify the camera coordinate systems and to define platform related parameters such as navigation data and exterior orientation parameters (see Figure 3). The transformation from a camera coordinate system to the image reference coordinate system is expressed as

 xR   xc      R  y R  = Rc  y c  + z  z   R  c

dx    dy  dz   

(1)

with a translation and a rotation. The nadir looking camera coordinate system may be chosen as the image reference system. For any image point within a CCD array, we have its image reference coordinates (xR, yR, zR). The

coordinates of the exposure center of the array in the ground coordinate system at epoch t are (Xs(t), Ys(t), Zs(t)). The corresponding ground point coordinates are (XG, YG, ZG). These points should satisfy the collinearity condition:

xR = z R

r11 ( X G − X S (t )) + r12 (YG − Y S (t )) + r13 ( Z G − Z S (t )) r31 ( X G − X S (t )) + r32 (YG − Y S (t )) + r33 ( Z G − Z S (t ))

y R = zR

r21 ( X G − X S (t )) + r22 (YG − YS (t )) + r23 (Z G − Z S (t )) r31 ( X G − X S (t )) + r32 (YG − YS (t )) + r33 (Z G − Z S (t ))

(2)

where RGR is a rotation matrix from the ground coordinate system to the image reference coordinate system. Depending on types of observations, coordinates and parameters in Equation (2) may be treated as knowns and unknowns differently in various situations. Each line in an image strip has its own exterior orientation parameters (Xs, Ys, Zs) and attitudes (ω,φ,κ). If treated as unknowns they would practically make a photogrammetric bundle adjustment unsolvable. Assume that the platform moves in a relatively smooth track segment (at least true for satellite cases). The exterior orientation parameters can be approached as a function of time or image line number, for example, a third order polynomial

X (t ) = a0 + a1t + a2 t 2 + a3t 3

(3)

The same applies to other exterior orientation parameters (Ys, Zs, ω,φ,κ). When calibrated, navigation equipment such as GPS, star trackers and INS provide exterior orientation parameters at certain image lines, called Orientation Lines (OL). Such orientation lines are then used to determine the polynomial parameters in Equation (3) that is further applied for exterior orientation parameters of image lines between OLs. Suppose that we have N1 OLs with GPS and INS derived exterior orientation parameters, N2 GCPs, and N3 unknown points with measured image coordinates. If we consider one pair of stereo image strips, observation equations are: Navigation data

=

VGPS

Vω ,φ,κ = 3 N1×1

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VGCP 4 N 2 ×1

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3 N1 ×1

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4 N 2 ×1

P2INS 3N1 ×3N1

P3GCP 4 N 2 ×4 N 2

P4M

(4)

4 N 3 ×4 N 3

Implementation of three-line stereo imaging MOMS system series directly implemented the three-line stereo imaging principle by placing linear arrays in the focal planes of more than one lens. The sensors are oriented perpendicularly to the direction of flight. During flight the sensors continuously scan the terrain with a constant frequency, recording three images. As a consequence, three push-broom image strips cover the terrain surface. MOMS-2P provides 4 data collection modes (Kornus 1997). Mode A uses PAN channels 5, 6 and 7 only, which provide 3-fold along track stereo scanning with different ground resolutions. The nadir looking HR channel has a ground pixel size of 6m, and the other two channels have a ground pixel size of 18m. Mode B delivers all 4 multispectral channels simultaneously (1, 2, 3 and 4). Mode C offers high resolution multispectral imaging (5A PAN, 2,3,4). Mode D provides simultaneous stereo and multispectral capability. In general, each object point is projected into three along track stereo images. If blocks with 20% or 60% side-lap is used, object points are projected into as many as six to nine images.

HRSC (High Resolution Stereo Camera) system has nine CCD linear arrays. It uses five high resolution linear arrays to provide along-track stereo and photometric viewing capability, in addition to its high-resolution hyperspectral linear arrays (Albertz et al. 1996). It uses three focal planes to form one high-resolution panchromatic nadir channel, two panchromatic stereo channels with convergence angles of ±19°, four color channels at ± 3°and ± 6°and two additional channels at ± 13°for photometric purposes. HRSC is designed as a compact single-optic pushbroom instrument that can be mounted on orbital platforms for planetary exploration and on airborne platforms for earth mapping. Compared to other imaging systems, a miniaturization by a factor of 5 to 10 has been achieved. A raw HRSC image consists of 9 image strips (1 strip per sensor). Different image strips may have different pixel resolution depending on the commanded pixel binning which is constant during one imaging sequence. IKONOS-I implements the three-line stereo imaging in a very unique way. It uses only one linear array to form stereo images by pointing to the mapping area with a fore-looking angle when approaching to the area to produce the fore-looking image. It changes the looking angle to 0o when above the area and to an aft-looking angle when leaving the area (Parker 1997). The system is equipped with a camera of a very long focal length (10m), which is folded to two meters through the use of a mirror system. This allows it to achieve a ground resolution of 0.8m from an orbit of 680km. It was designed to capture both panchromatic images with around one-meter resolution and multispectral images with a four-meter resolution. In addition to along-track stereo capability, the satellite is able to pivot in orbit to collect cross-track images at distance of 725km on either side of the ground track. The system is equipped with GPS antennas and three digital star trackers to maintain precise camera position and attitude.

3. OUR EXPERIENCES Simulation of IKONOS-I images In this section we report some of our results in simulating IKONOS-I images and estimating attainable accuracies of ground points triangulated from the simulated images. The test site was chosen as the High Altitude Test Range located in Madison County in Central Ohio. A ground control network consisting of 21 ground target points placed in a flat area approximately 16x11 km. The target points are spaced at least 1km apart and distributed in a generally east-west direction. All target points are painted with concentric circles, a one-meter flat white circle and a threemeter flat black circle as background, centered on a monument (see Figure 4). The 21 control points, 23 checkpoints and 5 feature points were GPS-surveyed for the simulation study and experiments with future real IKONOS-I imagery (Gonzalez 1998). Geographic coordinates in WGS-84 and 3D coordinates in UTM were obtained. The standard deviations of ground coordinates are 0.02m, 0.02m and 0.10m in X, Y and Z, respectively.

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DEM

Figure 4. Control network and ground targets at Madison County Figure 5. Simulation of satellite images from aerial images

Some technical specifications of IKONOS-I important to this simulation study are listed in Table 1. A DEM of the test range was computed from hypsographic features (contour lines) in DLG files from 7.5’ USGS quad sheets. ARC/INFO was used to compute the DEM with 1m by 1m spacing. Additionally, the OSU Center for Mapping provided georeferenced aerial images acquired by AIMS (Airborne Integrated Mapping System) with dimension of 4,096 by 4,096 pixels taken in 1997. Figure 6 shows a frame of AIMS image. Parameter Value Parameter Value Parameter Altitude (km) 680 Convergence angle (deg) 45 Ground resolution (m) Inclination (deg) 98.1 12 Swath width (km) Pixel size (µm) Table 1. Some technical specifications of IKONOS-I

Value 0.82 11

The simulated satellite images are generated based on the IKONOS-I technical specifications, the AIMS images and the terrain model. The fore-, nadir- and aft-looking satellite images are defined according to the IKONOS-I specification. For each point in an image, it is projected to the terrain using the specified exterior orientation parameters (Figure 5). The corresponding point on the terrain is then back projected to a corresponding AIMS image. The gray value interpolated at the back projected image point is then assigned to the simulated satellite image point. The key steps for generating the images include •Determining the segment of the track that covers the established geodetic network where aerial photographs and DEM are also available and orientation parameters of AIMS images are known. •Specifying the number of orientation lines (OLs), exterior orientation parameters of OLs, interpolation parameters, and fore-, nadir-, and aft-looking angles. Table 2 shows simulated exterior orientation parameters at the initial time and after 5 seconds. •For each pixel of the simulated line, say ( x1 , y1 ) in the satellite image, its corresponding ground coordinates ( X 1 ,Y1 , Z1 ) are determined by projection from the satellite image to the DEM. Furthermore, the corresponding coordinates ( x'1 , y '1 ) in the aerial image are determined by a back projection from ( X1 ,Y1 , Z1 ) to the aerial image. Finally, the gray value at ( x '1 , y '1 ) of the aerial image is assigned to that at ( x1 , y1 ) of the satellite image. This process is repeated for all pixels of the satellite image, so that a simulated satellite image can be produced. In this way, we produced simulated nadir-, fore-, and aft-looking satellite images (Figures 7, 8 and 9). Parameter Xs (m) Ys (m) Zs (m) Omega (arc sec) Phi (arc sec) Kappa (arc sec)

Fore-look Nadir-look Aft-look Initial Initial Initial In 5″ In 5″ In 5″ 3.0 330459.91 365125.34 284315.71 318981.13 238171.49 272830.637 3.0 4096476.85 4091613.07 4424815.01 4419951.12 4753153.21 4748289.39 3.0 679996.87 679996.63 679996.87 679999.67 679996.87 679998.90 2.0 0.000020 -0.000157 0.000020 -0.006215 0.000010 -0.000633 2.0 0.000020 0.000022 0.000020 -0.000931 0.000010 0.00001 2.0 0.139636 0.139560 0.139647 0.139749 0.139647 0.144059 Table 2. Exterior orientation parameters of a segment of orbit

Sigma

Using the IKONOS-I technical data, GCPs, check points and simulated images, we assessed the attainable accuracy of ground points determined from the satellite images. Accuracy versus number of GCPs: A bundle adjustment simulation system uses equations derived from Equation (2) for GCPs and checkpoints. We added random errors (1 sigma) to the exterior orientation parameters at OLs (Table 2). Measured image coordinates of GCPs and checkpoints were given a random error of 0.5 pixel. Ground coordinates of 14 checkpoints were computed. Differences between the computed and known ground coordinates of the checkpoints are depicted in Figure 10, with a variation of the number of GCPs used. The average planimetric and vertical errors are 11 to 12m without GCPs, and around 2.8m with 24 GCPs. When 4 GCPs are used, the accuracy is largely improved. However, more than 4 GCPs do not contribute significantly. Accuracy versus distributions of GCPs: Figure 12 shows the GPS distribution. We chose 6 groups of GCPs to form 6 distributions in order to examine the impact of GCP distribution on accuracy. The 6 distributions are:

Distribution 1: a triangle consisting of points MAD-1, BLTZ-0 and H-34; Distribution 2: a trapezoid formed by points H-34, BLTZ-0, H-105 and H-106; Distribution 3: approximately a straight line (cross track) formed by points H-105, M-1 and H-106; Distribution 4: Points S-20, H-5, S-34, MAD-1, S-41, S-57, S-63, H-6, H-7 and H-11 spreading in the area; Distribution 5: Points H-34, H-14, H-13, H-12 and BLT-0 approximately on a straight line (cross track); and Distribution 6: Points S-20, S-34, S41 and S-57 approximately on a straight line (cross track).

Figure 6. AIMS image (0.4m)

Figure 8. Simulated fore-looking image (0.82m)

Figure 7. Simulated nadir-looking image (0.82m)

Figure 9. Simulated aft-looking image (0.82m)

The GCPs of the 6 distributions are used in bundle adjustment to calculate the ground coordinates of 14 checkpoints. The accuracy versus various distributions of GCPs is depicted in Figure 11. We find that the strength of GCP distributions affects the planimetric and vertical accuracy significantly. For example, Distributions 1 and 3 have the same number of GCPs, but not distributions. The accuracy for Distribution 1 achieves 1.84m and 3.43m in X and Y, 3.21 in Z, while Distribution 3 has 53.4m and 8.11m in X and Y, and 5.88m in Z. Distribution 2 and 6 present a similar situation. It is to note that GCPs distributed on a straight line across the track constitutes a weak geometric configuration (Distributions 3, 5 and 6). Thus GCP distribution is a critical key to achieve high accuracy.

Accuracy varity with various number of GCPs

Geometric Accuracy and Distribution of GCPs 60.00

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Figure 10. Accuracy vs. number of GCPs

Figure 11. Accuracy vs. GCP distribution

Accuracy versus image measuring errors of checkpoints: When measuring image coordinates in a stereo pair, errors are unavoidable. The impact of these errors on determined ground coordinates should be assessed. Suppose that image coordinate measurement errors of the checkpoints range from 6µm (0.5pixel) to 24µm (2pixel), and all other parameters are error-free. The ground coordinate accuracy of 14 checkpoint points versus errors in image coordinates is depicted in Figure 13. The result demonstrates that large measurement errors in image coordinates of the checkpoints affect the accuracy of ground coordinates if a small number of GCPs (less than 6) is used. 4430000

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Figure 12. GCPs at Madison Test Range 8.0

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Figure 13. Accuracy versus errors in image coordinates Accuracy versus errors of image coordinates of GCPs: Under the same conditions as above, we examine the impact of image coordinate errors of GCPs on ground coordinate accuracy. The errors of ground coordinates for 14 checkpoints are shown in Figure 14. In general, the errors of ground points increase as the image measurement errors increase. When image errors are 5 pixels, the Z coordinate error reaches 7.7m and X and Y errors are around

4m even though all of 24 GCPs are taken into account. Obviously accurately locating and measuring GCPs in images is important in improving the accuracy.

Figure 14. Accuracy versus errors of image coordinates of GCPs

Test with Airborne HRSC data The airborne HRSC images cover a trip over an area in western Germany with a flying height of 2,500m. The images are recorded in VICAR format of JPL/NASA. Image coordinates and ground coordinates of GCPs and exterior orientation parameters of each image line are provided by DLR. Table 3 indicates the calculated accuracy of 49 checkpoints versus the number of GCPs ranging from 0 to 49. The experimental results demonstrate that increasing the number of GCPs does not improve the accuracy. The standard deviation (interior accuracy measure) and RMS (exterior accuracy measure) appear to be close. An explanation is that the exterior orientation parameters of each CCD line and the image coordinates of GCPs and checkpoints are provided by DLR, and they are bundle adjustment results already. A further adjustment does not improve the accuracy. GCP 0 1 2 3 4 5 49

σ 0 [µm]

6.990 6.952 6.914 6.877 6.840 6.805 5.628

σ x [cm]

σ y [cm]

σ z [cm]

RMS x [cm]

RMS x [cm]

RMS x

[cm]

15.140 7.324 18.010 15.144 8.276 18.758 16.025 8.230 18.654 15.140 7.324 18.010 15.939 8.186 18.553 15.140 7.324 18.010 15.853 8.142 18.454 15.140 7.324 18.010 15.769 8.099 18.355 15.140 7.324 18.010 15.686 8.059 18.259 15.140 7.324 18.010 12.973 6.663 15.101 15.140 7.324 18.009 Table 3. Accuracy of ground points versus number of GCPs

Another experiment reported no significant impact of the order of polynomial function of exterior orientation parameters and the number of OLs on the accuracy improvement. This may be because the flight path of this mission is relatively straight (Li et al. 1998).

Test with MOMS-2P data The data set is comprised of 4 scenes covering an area of about 178 km long and 50 km wide from southeast Germany to about 160 km beyond the Austrian border (Fritsch et al. 1998, Kornus and Lehner 1998). Its navigation system, MOMS-NAV, consists of a Motorola GPS receiver with dual antennas and a LITEF gyro system. There are 8 OLs for the strip covered. The interval between two OLs is 3330 image lines, corresponding to 8.2 seconds flight time. 10 GCPs and 24 checkpoints within the test field are provided. The ground coordinates of GCPs and checkpoints were obtained from topographic maps of scale 1:50,000 with an accuracy of 1.5 m in X, Y and Z (Fritsch et al. 1998). They are in the 4th zone of Gauss-Krueger coordinate system.

The provided navigation data of OLs are in the geocentric WGS-84 coordinate system. However, the coordinates of GCPs and checkpoints are in Gauss-Krueger coordinate system. We performed a coordinate transformation from Gauss-Krueger coordinate system to WGS-84. Geoid undulations were considered in transforming the height above the geoid to the ellipsoidal height with respect to WGS-84. Table 4 gives an overview of all observations and their a priori standard deviations. These were fed into the bundle adjustment. Observations Type Priori σ 24 checkpoints Image coord. 0.5 pixel 10 GCPs Image coord. 0.5 pixel 3 x 8 OL positions Ext. orient. 6.0 m 3 x 8 OL angles Ext. orient. 0.11e-2° Table 4. Observations and a priori standard deviations In the bundle adjustment the exterior orientation parameters are estimated only at OLs, while these between OLs are modeled by third order polynomials. The parameters and navigation data are treated as uncorrected. With 10 GCPs, RMS of 10.4m, 9.8m and 13.8m in X, Y and Z respectively were achieved using 24 checkpoints. It is to note that the above result was achieved by adding an additional 3-D offset to fore- and aft-looking exposure center respectively. This is our first result of handling the data set. Further study is needed to investigate reasons that cause the offsets.

4. CONCLUSIONS Space-borne stereo imaging using high-resolution linear arrays will provide a new tool for digital mapping in the future. The presented simulation study examines the geometric potential of the one-meter resolution satellite imagery, especially IKONOS-I. Under the conditions studied, four or slightly more GCPs are recommended for digital mapping purposes. In addition, the distribution of GCPs is very important. For example, a distribution of GCPs along a straight line across the track should be avoided. The accuracy of ground points determined from the imagery can reach about 2-3m with GCPs and 12m without GCPs. The experimental results of HRSC and MOMS02P data processing verified the bundle adjustment software system designed and implemented for processing high resolution satellite imagery. In addition, higher precision navigation data is very helpful for enhancing the accuracy of ground points in the case of weak distributions of GCPs and/or few or no GCPs.

ACKNOWLEDGEMENTS We appreciate the funding from Sea Grant–NOAA National Partnership Program. Funding from and partnership with CSC, OCS, and NGS of NOAA are appreciated. We would like to acknowledge the assistance in GPS survey from Mr. Alex Gonzalez of OSU, Mr. David Albrecht of Ohio Department of Transportation (ODOT) and Dr. Dorota Grejner-Brezezinska of Center for Mapping. Discussion with Mr. David Conner, NOAA geodetic advisor to Ohio, on geodetic datum issues was very helpful. Our thanks also go to Dr. Charles Toth and Mr. Panny Zafiropoulos of Center for Mapping, Dr. Franz Wewel and Dr. Yun Zhang of Institute of Planetary Exploration/DLR, and Dr. Dieter Fritsch and Mr. Michael Kiefner of University of Stuttgart for providing data and assistance in handling AIMS, HRSC and MOMS-02P data, respectively.

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