The statistical correlation with invariant moments for
Geometric correction improvement
3. An Invariant Moments Consideration
The 2-D continuous function f(x,y), the moment of order (p+q) is
Equation - 13
The central moments is
Equation - 14
where
For digital image, the central moments is
Equation - 15
The 3 order central moments are
Equation - 16
So, A set of invariant moments is
Equation - 17
4. Geometric Trasformation
The geometric transfoemation in this paper using the bilinear transformation method for image restoration.The image, f is given with pixel coordinates (x,y) undergoes geometric distortion to produce an image g with coordinates (x,y)This transformation can be expressed as follow:
where r(x,y) and s(x,y) repesent the spatial transformation that produced the geometrically corrected image g(x,y) Suppose that the geometric distortion process within the quadrifateral regions is modeled by a pair of bilinear equations. sothat,
Equation - 18 & 19
The resampling for noninteger value of x and y according to the coefficients Ci will be interferren with bilinear interpolation for gray level interpolation, which can be express as
Equation - 20
5. Example of Geometric Correction with Statistical Correlation Measure Technique based-on Invaraint Moment Criteria
For completly geometric correction, frist step is choosed for searching areas and window areas, where cover on the points as expected tobe ground control point (GCP). Fig 2(a) and 2(b) show full scence OPS image around north of Bangkok which are acquired by JERS-1 on Jan, 29, 1997 and Dec, 10, 1995, respectively. Evenmore, Fig2(b) has been corrected by GICS, image processing system installed in Ladkrabang Ground station and used as reference image.
(a) raw data January 29,1997
(b) geometric corrected December 10,1995
Figure 2 North of Bangkok OPS images
Figure 3 shows window sub-image, where selected from corrected image (Figure 2b). Whileas, Figure 4 shows corresponding searching area from uncorrected image (Figure 2a) that has almost same correlation value and difficultly distinguish the correct area.
Figure 3 Typical window area
Figure 4 Seaching area with the almost-same correlation value.
Second step, to apply the invaraint moment calculation to such images and the results as shown in table 2. The window image has nearest value with Figure4C. After applying the statistical correlation as mentied before on a pair of sub scence to find out the best-correction point, Rs (u,v) peakes. Figure 5 shows the searching areaes, where are decorrelated by whitening filter (G) with . = 0, 0.5, 0.9 and 1, respectively.
