On error correction and accuracy assessment of satellite imagery registration.

Digital images recorded by satellite detectors contain detailed information on ground cover types of the Earth. However, satellites data need to be used in conjunction with traditional maps, aerial photography and ground observation to reveal the information of interest. These reference data are required for rectifying geometric errors in satellite images and they can aid in data interpretation and information verification. In this paper, sources of geometric distortion in satellite images are discussed. The rectification method using the polynomials mapping functions is addressed with a case study of Landsat ETM+ data over the Canberra region.

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Remote sensing involves mounting detectors on aircraft or spacecraft platforms and acquire images of the earth's surface. Optical remote sensing records reflected solar irradiation in the wavelength range of 400 to 2400 nm. Fig. 1 shows an overview of the optical remote sensing system (Jia, 1996). Spatial information is determined by the spatial resolution element, or pixel, while spectral information is determined by the spectral resolution, or bandwidth of each band. Reflectance from different ground cover types varies with different spectral wavelengths. Remote sensing imagery has been used in many applications, including Earth resources monitoring, land use and urban change study (Lillesand and Kiefer, 2000).

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How to extract the rich information contained in the remote sensing digital data is challenging. Data calibration and image registration are required before an appropriate classification technique can be applied. The geometric errors of satellite images and their correction are addressed in this paper.

GEOMETRIC ERRORS & CORRECTION

Remote sensing image data contain several sources of geometric distortion. The important factors include the rotation of the earth during image acquisition, platform movement, and the use of a fixed angular instantaneous field of view (Richards and Jia, 1999). The two main consequences are overviewed as follows.

Image skew: This is due to the earth rotation effect and platform travel as illustrated in Figs. 2 (a) and (b). The platform travelling from north to south makes the sensor scan the area further to the south and the earth rotation makes the sensor scan the area further to the west during image acquisition. The scanned area is as shown in Fig. 2 (c); however, when the data are displayed, the image looks as shown in Fig. 2 (d).

[FIGURE 2 OMITTED]

Panoramic Distortion: The instantaneous look angle of a whiskbroom detector is constant. Therefore, the effective pixel sizes on the ground are larger towards the edges of the scan than at nadir as shown in Fig. 3. This effect is stronger when the curvature of the earth is taken into account for a large image.

[FIGURE 3 OMITTED]

Pixel Shape Distortion: Pixels may have irregular shapes if there are variations in platform altitude, velocity and attitude.

Rectification of all sorts of errors is often achieved with the aid of conventional map, aerial photography and ground observation. Polynomial functions are normally adopted as mapping functions that associate the pixels on the image (u, v) to the true locations on the reference map (x, y) (Richards and Jia, 1999). The simple polynomials of second degree are:

(1) u = [a.sub.0] + [a.sub.1]x + [a.sub.2]y + [a.sub.3]xy + [a.sub.4][x.sup.2] + [a.sub.5][y.sup.2]

v = [b.sub.0] + [b.sub.1]x + [b.sub.2]y + [b.sub.3]xy + [b.sub.4][x.sup.2] + [b.sub.5][y.sup.2]

The first-degree polynomials contain only the first 3 terms in (1). To determine the coefficients in (1), we need to identify a number of spatially small features on both the reference image (map, or a correct image) and the image to be corrected. These features are referred to as ground control points. Their coordinate pairs are used to determining the mapping functions. After the mapping functions are established, each pixel on the image will be mapped to the right location by applying an appropriate interpolation technique, for example, nearest neighbour or bilinear resampling.

There are several issues in image geometric correction. The reference data need to be reliable with comparable spatial resolution. Adequate ground control points are expected to cover the whole image area to avoid biased estimates. The selection of mapping functions and resampling techniques play an important role as well. Next section, a case study of ETM+ image registration is presented.

EXPERIMENTS

A subset of Landsat Enhanced Thematic Mapper Plus (ETM+) data recorded over the Canberra region on 2 February 2000 has been used for this case study. The ETM+ sensor records data in six spectral bands in the visible and middle infrared range and one in the thermal infrared wavelength. The spatial resolution is 30 x 30 [m.sup.2]. The band 4 data (760-900 nm) is shown in Fig. 4. Fig. 5 shows a corrected image (band 4 of ETM+ data) over the same area recorded on 25 April 2001. We can see the geometric errors in the former one.

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Seventeen ground control points were selected as shown in Fig. 5 (1 to 10 and 'a' to 'g'). They are road intersections, airport runway, and sharp corners. The first-degree and second-degree polynomials were tested, respectively. Points 1 to 10 were used as training data to estimate the coefficients in the polynomials. The quality of the correction was assessed by both the training points (1 to 10) and the testing points ('a' to 'g'). The mapping functions generated were:

first degree :

u = 6.8874 + 0.8256x . 0.1191y

v = .30.4882 + 0.1287x + 0.8230y

second degree:

u = 6.7255 + 0.8461x -0.1304 y + 0.0000xy - 0.0001[x.sup.2] + 0.0000[y.sup.2]

v = -31.7923 + 0.1559x + 0.8193y + 0.0000xy - 0.0001[x.sup.2] + 0.0000[y.sup.2]

The fitting results are given in Table 1. While the fitting accuracy on the training points are improved with the second-degree polynomials comparing with the results from using the first-degree polynomials, the testing points cannot be fitted properly.

We can see that the squared terms are insignificant when the second-degree polynomials were used. Also, considering that the panoramic distortion and the error caused by the earth's rotation are in the horizontal direction only, the modification was made by adopting the mapping functions as follows.

(2) u = [a.sub.0] + [a.sub.1]x + [a.sub.2]y + [a.sub.3][x.sup.2]

v = [b.sub.0] + [b.sub.1]x + [b.sub.2]y

The number of unknown coefficients is reduced in the modified mapping functions (Eqs. (2)). As expected, the new estimates results fit testing data better (see Table 1) than using the original second-degree polynomials. However the best fit is provided by the linear functions; the average registration errors are 26.66 m and 31.76 m for training points and testing points, respectively. The results show us it is not wise to use higher ordered mapping functions when there is a limited number of control points available. The reliability of the coefficient estimates reduces with the drop of the ratio of the number of training points to the number of unknown coefficients. This is related to the Hughes Phenomenon (Hughes, 1968).

Fig. 6 shows the image after correction using the linear function generated together with the nearest neighbour resampling technique. The two data sets are displayed together as shown in Fig. 7. Further detailed analysis can be conducted on these registered data sets, including identification of any changes over the one year's period between the data recording.

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DISCUSSION AND CONCLUSION

Digital images recorded by satellite detectors contain geometric errors. They need to be rectified with the aid of traditional maps, aerial photography and ground observation. Ground control points play an important role and some of them should be used as testing points to make sure the mapping functions generated by the training points fit the whole image. With a limited number of control points, the first-degree polynomials normally perform better.

Table 1. Ground Control Points Fitting Results
Comparison (Average registration error in metres)

Mapping Functions                    Training Points   Testing Points

First-degree polynomials             26.66 m           31.76 m
Second-degree polynomials            16.53 m           43.68 m
Modified second-degree polynomials   26.54 m           32.54 m

REFERENCES

Hughes, G. H. (1968). On the mean accuracy of statistical pattern recognizers, IEEE Trans. Information Theory. 14: 55-63.

Jia, X (1996). Classification techniques for hyperspectral remote sensing image data, PhD thesis, UNSW.

Lillesand, T. M. and Kiefer, R. W. (2000). Remote Sensing and Image Interpretation, 5th ed., John Wiley.

Richards, J. A. and Jia, X. (1999). Remote Sensing Digital Image Analysis, 3rd ed., Springer-Verlag, Berlin.

Dr. Xiuping Jia is a lecturer at the School of Electrical Engineering, University College, The University of New South Wales, Australian Defence Force Academy, Canberra, ACT 2600, Australia. Tel: [phone], Fax: [phone], email: [e-mail]