ORTHORECTIFICATION OF SATELLITE IMAGES USING EXTERNAL DEMS FROM IFSAR

J. Bryan Mercer, Jeremy Allan, Natalie Glass, Johnathon Rasmussen, Michael Wollersheim

Intermap Technologies Corp., #1000, 736 – 8th Ave. S.W., Calgary, Canada, T2P 1H4

bmercer@intermap.ca

Commission II, Working Group II/2 KEY WORDS: Mapping, Orthorectification, SAR, Interferometer, DTM/DEM, IKONOS, Quickbird ABSTRACT: Images from high-resolution satellites are now in relatively wide use for a variety of applications. For use in most medium and large-scale mapping applications, it is desirable that the imagery be orthorectified. While this may be accomplished by utilizing stereo pairs acquired from these agile-pointing systems, the price and delivery schedule may be significantly impacted by this requirement. On the other hand, savings of time, resources and cost may be realized through use of an external Digital Elevation Model (DEM) of appropriate quality to perform the orthorectification on single, non-stereo, images. The quality of the DEM is a key factor in the ultimate accuracy and robustness of the orthorectification. DEM quality in this sense is equated to vertical accuracy and to sample spacing (posting). It has been shown that as the off-nadir viewing angle increases, the vertical accuracy required must improve for any given horizontal accuracy requirement. DEMs created by the STAR-3i IFSAR system have been used to test and demonstrate orthorectification of IKONOS, QuickBird and EROS-A1 images in addition to aerial photography. Several methodologies have been used including that of a simple Rational Functions approach. Together with input of GCPs (Ground Control Points) taken from the STAR-3i Orthorectified Radar Images (ORIs) that accompany the DEMs, mapping scale accuracies suitable for 1:4800 and larger have been achieved. In this presentation we demonstrate several examples of orthorectification performed with single images from IKONOS and QuickBird. Quantitative and visual results are presented.

1. INTRODUCTION

In order for imagery to be utilised in GIS and other applications for which pixels must be correctly geo-located, image orthorectification is a necessity. The particular application determines the factors required – specifically the image resolution and horizontal accuracy. These are often defined in terms of desired mapping scale. Orthorectification implies that both sensor system and terrain-related errors are reduced to some specified level and that the image pixels are resampled to a particular projection and reference system. Aerial photography and satellite images exhibit certain similarities and differences in terms of the parameters and issues to be dealt with during orthorectification. In both cases, the horizontal pixel displacement caused by off-nadir viewing increases with viewing angle Θ. Specifically, ∆=h tanΘ for aerial photography, as a back-of-the-envelope calculation shows, where ∆ = the terrain displacement and h = the terrain height of the pixel. For typical high-resolution satellites, ∆ increases somewhat faster than tan Θ as shown by Zhang, et.al. (2000). This parallax displacement error is usually corrected in a pixel-by-pixel manner during orthorectification, provided the elevation, h, of the ground pixel is known. However, the consequence of the viewing angle dependence is that the displacement correction required depends more critically on the vertical accuracy of the elevation information as Θ increases. A second elevation-related factor impacts the accuracy of the orthorectification: the spatial frequency of the terrain relief drives the requirement for spatial sampling density of the terrain elevation. For example, elevations sampled at 30 meter spacing would be inappropriate for retaining orthoimage accuracy along ditches or other land features that change more rapidly.

Traditional orthorectification involves the use of stereo pairs from which elevation is extracted directly to be used for production of contours and DEMs in addition to orthorectification of the images. However the cost of acquiring and processing stereo may not be justified if the purpose is to do orthorectification only. In the case of the high-resolution satellites, there is also an opportunity cost for stereo acquisition: the time spent in acquiring the stereo partner is time lost in acquiring additional primary images. Given the small footprint, (100-200) km2 per image, this is a serious cost factor. Provided a suitable DEM is available from external sources, it seems plausible and cost-effective to acquire single images and perform the orthorectification without invoking stereo requirements. The purpose of this paper is to demonstrate orthorectification results achievable using external DTMs derived from airborne IFSAR – specifically the Intermap STAR-3i system. We provide visual examples and quantitative accuracy results relating to the orthorectification of IKONOS and QuickBird images. Aside from the technical merits we also address the cost benefits of the process. We provide a brief review of the IFSAR data in section 2, describe the orthorectification methodologies used in section 3, and the data sets in section 4. We then present the results of the accuracy analysis along with visual examples in section 5. A demonstration of comparative cost is provided in section 6 followed by concluding remarks section 7.

2. THE IFSAR DATA

STAR-3i is an X-band interferometric SAR (IFSAR) carried in a Learjet (Mercer and Schnick (2000)) and has been operated commercially by Intermap Technologies since 1997. The core products generated include a Digital Surface Model (DSM) and an Orthorectified Radar Image (ORI). A Digital Terrain Model

(DTM) is extracted from the DSM in a process referred to as TerrainFit (Wang et. al., 2001). Current specifications for these products are shown in Table 1. A detailed description of these products may be found in Intermap’s Core Products Handbook at www.intermaptechnologies.com. The range of vertical accuracy specifications relate to economic trade-offs that are associated with the flying altitude (6,000 meters flying altitude permits better accuracy but 6 km swath compared to 9km altitude and 10 km swath at reduced accuracy) as well as other GPS and operational considerations.

ORI DSM DTM Units

Resolution 1.25, 2.5 - - meters

Posting - 5 5 meters

Accuracy (vertical) - 0.5, 1.0, 3.0 0.7, 1.0 m (RMSE)

Accuracy (horizontal) 2.0 2.5 - m (RMSE)

Table 1. STAR-3i core product specifications. Note that prior to 2001, ORI resolution was 2.5 meters while after a major upgrade it was reduced to 1.25 meters. A database of Core Products (currently >1 million km2) has been created and is growing rapidly. National programs have been completed recently and it is the intent to continue with the creation of similar data sets. The relevance to this paper relates to the ability to use the orthorectification possibilities from archival data that enhances the cost impact of the method. In the discussions that follow, it is the DTM rather than the DSM that is generally used for orthorectification in order to remove the effect of objects such as buildings or trees.

3. METHODOLOGIES

There are several approaches that may be taken to perform the orthorectification of satellite images. In the current work we focus on a specific Rational Functions approach. It is particularly suitable for the class of high-resolution satellites typified by IKONOS , QuickBird, EROS-A1, and Orbview-3 which are agile pointing and characterized by potentially large off-nadir viewing angles which are relatively uniform across each image. 3.1 Rational Functions

In the absence of camera model or other support information, one approach is to use a Rational Functions Model ( e.g. Tao and Hu (2000), Dowman and Doloff (2000), Fraser, et.al. (2001)). This involves solving the rational function expressions in equation (1) for their polynomial coefficients

)B(A ijkijk , which relate the normalized line and pixel numbers

(l,p) of GCPs (Ground Control Points) identified in the ‘raw’ satellite image to their object space coordinates (x, y, z).

∑∑ ∑∑∑ ∑ ==

==

kjiijk

kjiijk

2

2

1

1

zyxBQ zyxAP

z)y,x,(Q)zy,x,(P

z)y,(x,Qz)y,(x,P

pl

(1)

Normally the polynomials are terminated at 3rd order, although as noted below our best results occur for lower order. The raw image is then re-sampled on a pixel-by-pixel basis where z(x,y) comes from the DTM. The software implementation used in this work is from PCI’s Geomatica OrthoEngine Rational Functions Module. The GCPs are taken from the STAR-3i ORI and are ‘manually’ matched to mutually visible features such as road intersections in the raw satellite image. The advantage of this approach is that it is usually possible to acquire reasonably large numbers of GCPs that sample the horizontal as well as vertical terrain surface. Extensive tests have been performed with ‘real’ data and independent checkpoints to ascertain the trade-offs between accuracy, number of coefficients and number of GCPs as input. Typically, 20-30 GCPs are acquired, for a single satellite image of dimension 10-18 km using only the linear terms of the polynomial expressions. Several IKONOS images, a QuickBird image and an EROS-A1 image have been orthorectified in this manner with results comparable to those presented below. There have been no apparent issues with stability to date, perhaps because of the quantity, quality and distribution of the GCPs. The IKONOS test results indicated that most of the ‘signal’ was in the linear terms, while the higher terms appeared merely to add noise. This appears understandable with recognition that systematic errors remaining in the image are probably linear while the terrain correction is also linear (to first approximation) because the viewing angle is almost constant across a single image (for off-nadir viewing). Hence terrain displacement will scale with height independently of (x,y) within the image. The fortunate implication of this result is that there is significant redundancy possible for a reasonable number of GCPs, thus allowing matching errors to be partly alleviated by the averaging effect of the redundancy. Attempts are made to distribute the GCP samples well in x, y, and z, although experience so far indicates that the method is not highly sensitive to the z distribution as long as approximate min/max is included. The latter statement is specific to the use of low order solutions where Z is de-coupled from x and y. An alternative, but still rational functions-based approach to orthorectification, is through the use of ‘RPCs (Rational Polynomial Coefficients)’. Although the camera models for IKONOS and QuickBird are generally not available to the user, RPCs, which have been derived from the camera models and orbital information, are now provided by Space Imaging (Grodecki and Dial (2001) and by DigitalGlobe. GCPs and DTM are still required to perform the orthorectification. The use of these RPCs may provide different results than those computed directly from the data as described above, at least in areas of significant topography, since the coefficients in the latter case will be topography dependent, while the RPCs are not. A comparative test is currently being done using the Geomatica RPC module. 3.2 Rigorous Model

A ‘rigorous’ model, based upon deterministic considerations has been developed by Toutin (2003) and has been implemented in the PCI Geomatica software package. Because many of the required parameters are unknown there is still a need to insert GCPs into the model implementation (6 GCPs required as a minimum, but more preferred) as well, of course, as a DTM. In principle, because it is based on a physical model, it should be able to produce superior results using fewer GCPs than the numbers described in the previous section. Moreover the claim

(ibid) is that the method should be more robust in that it is less dependent upon the number and choice of GCPs. We provide a comparison below, of the results obtained when using the method described in section 3.1 versus the rigorous method of Toutin (2003).

4. THE DATA SETS

4.1 IKONOS: Morrison

A major test site has developed within the Morrison Quad, a 7.5’ x 7.5’ USGS mapsheet, located west of Denver CO, USA. Data sets from several sensors have been acquired in the area over the past few years, including several STAR-3i data sets, several IKONOS images, lidar acquisitions, GPS control and the establishment of some photo-control at various scales. The relevant details related to this paper are described in Table 2.

Morrison IKONOS IKONOS STAR-3i Photo-Truth

Acq'n date Feb 1, 2000 Aug 19, 2000 Oct 23, 1998 1998

Product Geo Geo GT2 15 CPs

Type Pan-Sharpened MS ORI, DTM Pan ORI

Resolution 1 m 1 m 2.5 m 1 m

Off-Nadir 23.7 deg 13.2 deg 30-60 deg NA

Table 2. IKONOS Morrison tests – summary of input data. The Morrison quad (approximately 10 km x 14 km) includes the Rocky Mountain range in the west, and moderate to steep relief in the east with urban tracts and other forms of development. A colour-coded STAR-3i DSM of the area along with the corresponding IKONOS winter scene is shown in Figures 1 and 2. Topographic relief extends beyond the 700 meters shown on the colour legend. The DSM is shown to illustrate surface roughness, although the DTM was used in the orthorectification. The GCPs (28) extracted from the radar ORI are shown in red, distributed across the IKONOS scene. The IKONOS winter scene (Feb 13, 2000) came as two image sets that covered the whole quad between them. The summer scene (September 13, 2000), shown in Figure 3, covers only the western portion of the quad. Another partially overlapping image acquired August 19, 2000, covered the eastern portion. Both were orthorectified and mosaicked together to form a composite full-quad summer scene.

The ‘truth’ for purposes of this test was an orthorectified air-photo that was created using standard photogrammetry. The AT control was from GPS and the underlying DEM was from stereo extraction. The horizontal accuracy of this ‘photo-truth’ is 1 meter (CE(90)). The coverage unfortunately only overlapped about a third of the Morrison tile in the southeast (see Figure 1), and from this 15 well-distributed independent CPs (check points) were selected for accuracy validation of the overlapping orthorectified IKONOS images. Moreover the air-photo was used to assess the apparent accuracy of the pre-upgrade (2.5 meter) radar ORI insofar as uncertainties in matching common features allows. This assessment showed that typical manual feature-matching

uncertainties plus inherent errors in both ORIs result in overall single-point errors of about 2-3 meters RMSE in northing and easting. It should be noted that the IKONOS orthorectification described below used GCPs acquired from the 2.5-meter radar ORI. Also, while comparative testing was done on the orthorectified IKONOS mosaics as a whole (summer/winter), the absolute error statistics relate only to the area overlapping the photo-truth. 4.2 QuickBird: Castle Rock

The Castle Rock test area is to the south of Denver, and covers an area approximately 17 km x 17 km, about 2/3 of which is mountainous. The relevant details of the data are shown in Table 3 and a DSM of the area is shown in Figure 6. The QuickBird files were quite massive and arrived in the form of a 3x3 matrix of sub-tiles (500 MB each as there were 4 channels of pan-sharpened 0.6 meter data included). Initially the sub-tiles were individually orthorectified but this of course led to boundary problems. However it was possible to create a single large model into which each of the nine sets of GCPs derived from the sub-tiles contributed. This worked well and eliminated the internal boundary issues.

Castle Rock QuickBird STAR-3i Truth

Acq'n date July 9, 2002 2001 2001

Product Basic GT1 25 Check Pts

Type Pan-Sharpened MS ORI, DTM GPS

Resolution 0.7m 1.25 m Acc~ 0.5mRMS

Off-Nadir 12 deg 30-60 deg -

Table 3. QuickBird Castle Rock tests – summary of input data. Because there were about 25 GCPs per sub-tile initially acquired (radar/QuickBird match points), all 206 GCPs were used in the model determination. Subsequently the GCP numbers were reduced by factors of 2 for accuracy comparison. Independent ground points (25), used as checkpoints (CPs) were supplied by DigitalGlobe and included GPS coordinates and field descriptions as well as photographs of the features they referenced. These points are shown, overlaid on the DSM in Figure 6.

5. RESULTS

5.1 IKONOS (Morrison)

An overview of the topography and the appearance of the Morrison quad is provided in Figures 1 and 2, showing a STAR-3i DSM and the orthorectified IKONOS winter mosaic respectively. The location of the 28 GCPs used in this particular example is shown as well as the 15 checkpoints that were acquired from the independent orthorectified aerial image (the photo-truth). In Figure 3 we show an enlargement of part of the orthorectified summer IKONOS scene showing the

Figure 1. Morrison DSM with dotted outline showing the sub-area where ‘photo-truth’ is available.

centrelines of roads overlaid from the winter scene, illustrating the small relative error found between the summer and winter image mosaics overall. Total relief in this sub-area is about 200 meters. The same DTM and GCPs were used in each orthorectification. As noted in Table 1, the imaging parameters were quite different. Random inspection of the images when enlarged to about 1:1,000, as illustrated in Figure 5, indicates differences of 1-3 meters typically which is consistent with the absolute accuracies reported in Table 4. The absolute error statistics are reported in Table 4 and are with respect to the CPs extracted from the ‘photo-truth’. In this example, 28 GCPs were used in the Rational Function solution. The CE(90) from both sets is less than 4 meters which is the specification set by Space Imaging for their ‘Precision Product’. This is the NMAS standard for 1:4,800 scale mapping. It is interesting to note that the summer image exhibits lower error than the winter scene. This is probably due to better observable detail in the summer scene, permitting better feature matching for both GCPs and CPs. It was possible to extract large numbers of GCPs from the radar ORI and for test purposes over 200 GCPs were acquired. The Rational Functions coefficients were re-computed and the GCP and CP residuals were determined and the statistics calculated. The CE(90) error with respect to the CPs is plotted in Figure 4 as a function of the number of GCPs in the solution. It is notable that after a ‘spike’ at the beginning, which is likely a statistical vagary, the results show CE(90) ~ 3.4 meters consistently, dropping to about 3.3 meters at 200 GCPs. The CE(90) results from using the Toutin Rigorous model are also plotted in Figure 4. Over most of the range they perform similarly, although for large and small GCP numbers the accuracy is slightly worse than for the Rational Functions method.

Figure 2. Morrison IKONOS ORI. There are 28 GCPs (from radar ORI) overlaid in red, and 15 CPs (Check Points) in light blue. The dark blue box shows the area enlarged in Figure 3.

IKONOS Mean Std Dev'n RMSE CE90

(meters) DX DY DX DY DX DY

Winter GCPs 0.0 0.0 3.3 1.9 3.3 1.9 5.5

CPs -1.7 0.8 1.0 1.0 2.0 1.2 3.5

Summer GCPs 0.0 0.0 2.1 1.6 2.1 1.6 4.0

(east) CPs 0.3 -0.9 0.8 0.9 0.8 1.3 2.3

Summer GCPs 0.0 0.0 2.8 2.7 2.8 2.7 5.8

(west) CPs - - - - - - -

Table 4. IKONOS ORI difference statistics for Morrison. Results from both winter and summer scenes are shown. DX, DY are the differences (IKONOS - GCP, CP). 28 GCPs; 15 CPs 5.2 QuickBird

An overview of the Castle Rock topography is presented in Figure 6. The QuickBird ORI is displayed in Figure 7 as an overview. The associated inset is an enlargement of the sub-scene shown in the small box on the overview. The quality of the ORI sub-area shown here is characteristic of the remainder of the scene. No local distortions are evident, indicating that even at this or larger scales the orthorectification remains robust. Quantitative results are shown in Table 5. Overall, the results (CE(90) < 4.0 meters) are similar to those obtained for IKONOS. Thus the method appears appropriate for mapping at scales of 1:4,800 or better. DigitalGlobe orthorectified the same image using their camera model and made it available for comparison. Although we don’t show examples here, the results were consistent with the accuracies quoted in Table 5. Apart from a systematic easterly offset (~1.5 meters) of unknown origin, the centrelines of roads and other features

Figure 3. This is an enlargement (about 500 meters x 500 meters) from the IKONOS summer ORI (see blue box in Figure 1) shows road centrelines overlaid that were transferred (without adjustment) from the winter ORI. The box indicates the location of further enlargement (Figure 5). Also shown is a transferred ridgeline segment.

Figure 4. CE(90) as a function of the number of GCPs used for the (a) the Rational Functions Model (low order coefficients) and (b) the Rigorous Model of Toutin

Morrison Ikonos

3.00

3.20

3.40

3.60

3.80

4.00

4.20

4.40

4.60

0 25 50 75 100 125 150 175 200 225

Number of GCPS

CE

90 (m

)

Toutin's Rigorous ModelRational Functions Model

QuickBird Mean Std Dev'n RMSE CE90(meters) DX DY DX DY DX DY

GCPs 206 0.0 0.0 2.1 1.9 2.10 1.87 4.26CPs 14 -1.2 0.6 1.2 1.4 1.63 1.50 3.37

Table 5. QuickBird ORI error statistics for Castle Rock. were generally within 2 meters of each other in the two resulting ORIs.

6. COMPARATIVE COSTS

According to the information published on the web site of Space Imaging, for example, the difference between the prices of pan-sharpened MS orthorectified images (‘Precision Product’) and

Figure 5. Further enlargement, showing winter and summer road centrelines overlaid. The 2-meter difference is typical of the differences observed.

Figure 6. Castle Rock DSM (approximately 16.5 km x16.5 km). Topographic relief is about 500 meters. CPs are shown overlaid. their non-ortho images (‘Geo’ Product) is in the range 55-150 US$/km2 depending on whether it is a North American or International scene. On the other hand, the cost of IFSAR DSMs, DTMs and ORIs in the Intermap archival database is in the range of 6-20 US$/km2 depending on location. Experience (in a research, not a production environment) suggests that the cost of doing the IKONOS orthorectification should be less than

$10/km2 under similar conditions. These considerations indicate that where archival IFSAR exists there are substantial savings to be made by the user by following this approach rather than the stereo approach. Even when new IFSAR data must be acquired, provided it is for large enough areas, the economics still appear very favourable for this approach. A smaller economic benefit is to be recognized for the DigitalGlobe product only because its current high-end ortho product is specified at 1:12,000 (USA) and 1:25,000 scale (International). In this case the major benefit is product accuracy improvement.

Figure 7. QuickBird orthorectified image of Castle Rock area. The red box in the overview image is enlarged in the inset to about 250 meters extent.

7. CONCLUSIONS

Orthorectification of IKONOS and QuickBird images at off-nadir viewing angles to 23 degrees, has been demonstrated using a Rational Functions method. CE(90) values better than 4 meters were obtained when compared to independent check points over full image scenes. The method utilized external IFSAR-derived DTMs and associated ORIs as prolific sources of GCPs. The ORIs (2.5 meter pixels) and DTMs ( 1-2 meter vertical accuracy, extracted from 5 meter-posted DSMs) were from the STAR-3i airborne IFSAR system prior to its recent upgrade. Both sets of images sampled highly diverse topography. Two IKONOS images were compared over the same area (the Morrison, CO quad, a 7.5’ tile) but at different times and with different viewing angles, while the larger QuickBird image was of the Castle Rock, CO area. Relative comparison of features (usually road centrelines) showed consistency with the absolute checkpoint measurements. An assessment of the absolute accuracy as a function of GCP numbers indicated reasonable performance at about 20 GCPs improving somewhat out to 200 GCPs. A comparison between the Rational Functions method and the Toutin model showed similar results as a function of GCP number. We believe this is because the dominant terms in both models are linear. Lastly, a brief review of the comparative economics of this approach versus a stereo extraction approach

was provided. There appears to be strong economic incentive to use this approach where possible.

ACKNOWLEDGEMENTS

We wish to acknowledge with gratitude, Space Imaging for providing both sets of IKONOS Morrison images and Digital Globe for providing the QuickBird Castle Rock images and checkpoints. In particular we thank Gene Dial and Jacek Grodecki for information and encouragement.

REFERENCES

Di, K., Ma, R., and R.X. Li, 2003, Rational Functions and Potential for Rigorous Sensor Model Recovery. Photogrammetric Engineering & Remote Sensing, Vol. 69, No. 1, January 2003, pp. 33-41. Dowman, I., and J.T. Dolloff, 2000. An Evaluation of Rational Functions for Photogrammetric Restitution, International Archives of Photogrammetry and Remote Sensing, 33(B3/1):252-266. Fraser, C.S., H.B Hanley, and T. Yamakawa, 2001. Sub-metre Geopositioning with IKONOS Geo Imagery, Proc. Joint ISPRS Workshop “High Resolution Mapping from Space 2001,” 19-21 September, Hannover, Germany, (on CD ROM). Mercer, J. B., and S. Schnick, (1999). Comparison of DEMs from STAR-3i Interferometric SAR and Scanning Laser: Proceedings of the Joint Workshop of ISPRS III/5 and III/2, La Jolla, November, 1999 Grodecki, J., and G. Dial, 2001, IKONOS geometric accuracy, Proceedings of Joint International Workshop on High Resolution mapping from Space, 19-21 September 2001, Hanover, Germany, pp. 77-86 (CD ROM). Tao, C.V., and Y. Hu, 2001. 3D reconstruction algorithms with the rational function model and their applications for IKONOS stereo imagery, Proc. Joint ISPRS Workshop “High Resolution Mapping from Space 2001,” 19-21 September, Hannover, Germany, 12 p. (on CD ROM). Toutin, T., 2003, Error Tracking in IKONOS Geometric Processing Using a 3D Parametric Model, Photogrammetric Engineering & Remote Sensing, Vol. 69, No. 1, January 2003, pp. 43-51. Wang, Y., B. Mercer, V. C. Tao, J. Sharma, and S. Crawford, 2001, Automatic Generation of Bald Earth Digital Elevation Models From Digital Surface Models Created Using Airborne IFSAR, ASPRS 2001 Proceedings, (on CD ROM). Zhang, Y., V. Tao, and J.B. Mercer, 2000, Assessment of the Influences of Satellite Viewing Angle, Earth Curvature, Relief Height, Geographical Location, and DEM Characteristics on Planimetric Displacement of High-Resolution Satellite Imagery, ASPRS 2000 Proceedings, (on CD ROM).