An Improvement of Geometric Correlation of Satellite Image
3. Geometric transformation
The bilinear transformation (6) as discussed below is used to geometric transformation for image restoration. The image (f) is given by pixel coordinates (x,y) under geometric distortion to produce an image g with coordinates (x,y). This transformation can be expressed
x = r (x,y) and y= s(x,y)
where r(x,y) and s(x,y) represent the spatial transformation that produced the geometrically corrected image g (x,y). Suppose that the geometric distortion process within the quadrilateral regions is modeled by a pair of bilinear equations. So that,
r(x,y) = C1x + C2y + C3xy +C4 (20)
and
s(x,y) = C5x +C6y+ C7xy +C8 (21)
Since there are a total eight coefficients C
i,I = 1,2…. 8, eight GCPs are needed to solve. The method just discussed step through integer values of the coordinates (x,y) to yield the corrected image f(x,y). However, depending on the coefficients C1, can yield nomintage value for x and y. Inferring what the gray level value at those locations should be fit by bilinear interpolation for gray level interpolation, which can be expressed as
v(x,y) = ax + by +cxy +d (22)
where the four coefficients are easily determined from the four equation by using the four known neighbors of (x,y). v(x,y) is computed and assigned to the location in f(x,y).
4. Example of geometric correction with statistical correlation measurement technique
To completely the geometric correction, the first step is to choose the searching area and windows area, where cover on the points as expected t be ground control point (GCP). Fig 2(a) and 2(b) shows the full scene of OPS (Optical Sensor) image around north of Bangkok. Where are acquired by JERS-1 on January 29, 1997 and December 10, 1995, respectively. Fig. 2(b) has been corrected by GICS, image processing system installed in Ladkrabang ground station in Bangkok and used as reference image.
(a) raw data January 29, 1997
(b) geometric corrected December 10, 1995
Fig. 2 North of Bangkok OPS images
Fig. 3(a), shows corresponding window area cropped from uncorrected image. (Fig. 2 (a)) as Fig. 3(b) show the searching areas, where are spreadly selected through out the corrected image (Fig. 2 (b)) and cropped to be size of 32*32 pixel. Two sub images are used for typical experimentation.
Fig. 3 Window area and search area
The second step is to apply the statistical correlation as mentioned before on a pair of sub scene to carry out the correction point, Rs(u,v) peak. Fig. 4 show, the searching areas, where are decorrelated by whitening filter (G) with p = 0, 0.5, 0.9 and 1, respectively.
Fig. 4 Decorrelated search area p = 0, 0.5, 0.9 and 1 respectively
Fig. 5 shows the Simulation results of correlation measure with p=0, 0.5, 0.9 and 1. It is obviously shown that clearly show the two last results have the highest peak of correlation and easier to point out. By using the same procedure, the other 7 points are performed referring as ground control points (GCPs) and user for geometric transformation with bilinear technique (Eq. 20 and 21). They6 gray level interpolation have been performed with bilinear interpolation (Eq. 22) in last step and the final result of geometric correction has been shown in fig 6.
Fig 5. Simulation results of Static correlation measurement with p=0, 0.5, 0.9 and 1
Fig 6. Final result of geometric correction image.
5. Conclusion
The basic correlation has been developed for easily distinguish the peaks of Rs(u,v) with statistical correlation technique. The results show that Rs(u,v) peaks sharply at the correct pointand caan be the reliable automatically geometric based on image to image registration.
References
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