Optimum GCP distribution determination for geometric rectification of MODIS wide angle sensor images
S. Mohammad Sharhokhy
Email: s_m_sh@hotmail.com
M. Reza Saradjian
Email: mrsaradji@yahoo.com
Kourosh Karimi-zand
Email: ramin_karimizand@yahoo.com
Remote Sensing Division, Surveying and Geomatics Engineering Department,
Faculty of Engineering, University of Tehran, Tehran, Iran
Tel: +09821 8008841 Fax: +09821 8008837
Abstract
The geometry of images acquired by wide-angle sensors on board satellites is significantly distorted due to the panoramic and earth curvature affects. In order to geometrically rectify them, it is normally required to collect a large number of Ground Control Points (GCPs) that must have been well distributed throughout the image. On one hand, the GCP selection is a crucial stage because of matching problem, required updated map and user dependency. On the other hand, selection of too many GCPs takes unnecessary user and processing time. It may also cause the RMS error to be increased. If the transformation model is a Delaunay triangulation, the processing time will depend directly on the number of GCPs. Accordingly, optimum GCP distribution pattern is required to achieve the highest accuracy using minimum number of available GCPs. The data used in this study is a 1km resolution MODIS sensor false color composite image with a field of view about 110 degrees.
In order to construct and test a proper model it was necessary to obtain sufficient number of GCPs first. Hence, orbital parameters were used to generate a great number of points with their associated geographical coordinates. These points then could be used as GCPs in any region of the image. Using sufficient number of GCPs that were homogeneously distributed in the image, the maximum obtainable overall accuracy of the rectified image was determined by comparing it with an appropriate vector map.
The guideline of optimum distribution was defined theoretically using the geometry of the imaging sensor and the earth's shape and motion. Then the pattern was put in practice and confirmed the proposed theory. The main purpose of this investigation was to determine the maximum distance allowed between GCPs along the row and column directions of the raw image. Preliminary analysis showed acceptable stability in the vertical direction (along track) but considerable distortions in the horizontal direction (across track) especially for the view angles greater than 30 degrees. MODIS sensor images have approximately constant scale in the along track direction as ten scan-line width frames are tangent at the nadir with aspect ratio of width and height of pixels equal to one. Therefore, the only factor affecting the pixel size in off-nadir locations is the panoramic and the Earth curvature errors. The along track panoramic effect should be removed as a preprocessing step due to its cause in overlapping in the image scan-line frames (i.e. feature duplication). Therefore it is required to select the GCPs between pixel 5 or 6 as mean pixel location in the frame. Since the ground coordinates are in Geodetic system and the rectified image is supposed to have equal angular size for pixels, the latitude value affects the pixel size as in latitude of 0 degrees a 1km pixel takes a space of 0.009 of longitude but in latitude of 45 degrees the same pixel takes a space of 0.013 degrees. This could be worse when approaching the pole. But the important factors forcing the image to warp and consequently affect the GCP distribution pattern, is the along scan panoramic and Earth curvature impacts. These would cause the pixel size to be 2.5 times bigger at 45 degrees and 4.8 times bigger at 55 degrees of scan view angle in comparison with the nadir pixel size. The theoretical approach was used to obtain four profiles for Latitude-X, Latitude-Y, Longitude-X and Longitude-Y correlation. The Latitude-Y profile with a good approximation showed a linear correlation. The Longitude-Y profile also showed a near linear correlation. But the Latitude-X and Longitude-X profiles showed a highly curved shape with a degree of more than three for polynomial fitting. The aim was to keep the error of coordinates interpolation less than a specified value (i.e. 0.2 pixels). The interpolation method was considered as a linear function to simplify the solution. In other words, the error of proportional estimation of the two successive GCPs should be kept less than a desired value. A variety of distribution patterns were investigated to find the most effective pattern with highest accuracy using the minimum number of possible GCPs. The homogenous pattern, the vertically dense pattern, the horizontally dense pattern and a hybrid model were investigated. The results confirmed the theoretical predictions and showed that the density of GCPs must be much more in the cross-track direction than the along-track. It also showed that the GCP density must be increased when moving further away from the nadir (middle of the image). Some compensational GCP assignment was essential to adjust the earth rotation and spherical (elliptical) shape of the earth, so that the vertical distance between GCPs could not be too long.
In conclusions, a) the suggested pattern in this study may only be appropriate for the MODIS sensor or a sensor very similar to it. However, the approach of pattern definition may be used for any kind of sensors with any spatial resolution and any field of view, b) the optimum GCP distribution could considerably decrease the processing time (i.e. from 45 minutes to 1.8 minutes in this case) and increase the positional accuracy (i.e. from 10 pixels to 1-3 pixels in this case). Obviously non-optimized GCP distribution does not have both disadvantages of high processing time and low accuracy in the same time, basically because a desired accuracy using a lot of GCPs may be reached anyway but not in low processing time, c) it should be noted that in practice the GCP selection could not exactly follow the optimum pattern because many practical limitations will come into effect, and d) it is suggested that the practical tests to be assisted by theoretical background to decrease the investigation time.