International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
  
Figure 3 Warped Imge using Wavelet Modulus Maxima 
absolute value and location indicates the rotation and scale. A 
new image constructed by applying the rotation and scale and it 
is created by using bilinear interpolation. Once again by finding 
the phase correlation ratio of the newly generated image with 
the reference image, shift between the images are identified. 
The maximum absolute value of the Inverse FFT of this ratio 
provides the shifts in both x and y directions. After deriving all 
  
Figure 4 Simulated Image to be warped using FFT 
the three parameters of translation, rotation and scale, the input 
image is warped by taking care of all the three errors 
simultaneously, to avoid multiple re-sampling of the image. To 
test this algorithm an IRS PAN images of different dates are 
“simulated” for rotation of 9 degrees, translation in X is 12 
and in Y is —10 pixels. Due to the same sensors data scale 
factor is same. This algorithm could identify the shifts exactly 
but only the rotation is identified as 9.09 degrees instead of 9 
Figure 5 Log — Polar image of simulated image 
degrees. When the rectified image is swiped on the reference 
image it could be observed easily for its well registration. 
Figure 6 shows the rectified image. 
  
Figure 6 Warped Image using FFT 
4.5 MORPHOLOGICAL PYRAMID APPROACH 
The MPIR technique minimizes the SSE between two images 
based on the intensity for matching, since registration methods 
based on initial intensity values can make effective use of all 
data available. This technique uses an optimization scheme of 
coarse-to-fine iterative refinement strategy over the MP pair 
(Zhongxiu Hu, 2000). Based on the matching criteria, 
convergence indication can be obtained. Once convergence has 
been achieved at a particular pyramid level a transition to finer 
level is made. The solution from the previous pyramid level is 
used as an initial estimate. The new incremental estimate is 
  
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