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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
GAs are iterative procedures that maintain a population of 
candidate solutions encoded in the form of chromosome 
strings. A chromosome is a vector of length n of the form «x1, 
X2, ..., Xn?, where each xi is an allele or gene. The type of a 
gene can be binary digit, integer, or floating-point number. 
Binary genes are widely used in GA applications. The initial 
population can be generated randomly. Each candidate is 
evaluated and is assigned the fitness value that is generally a 
function of the decoded bits contained in each candidate's 
chromosome. These candidates will be selected using selection 
criteria for the reproduction, based on their fitness values. 
Reproduction process uses three basic genetic operations called 
Selection, Crossover and Mutation. 
The selected candidates are combined using the genetic 
recombination operation "crossover" to produce the next 
generation. The “mutation” is then applied to perturb the bits of 
the chromosome as to guarantee that the probability of 
searching a particular subspace of the problem space is never 
zero (Q. Zheng, 1993). It also prevents the algorithm from 
becoming trapped on local optima(Hongjie Xie, 2003, D.E. 
Goldburg 1989). The whole population is evaluated again in 
the next generation and the process continues until it reaches 
the termination criteria which can be triggered by finding an 
acceptable approximate solution, or reaching a specific number 
of generations, or until the solution converges. 
4.EXPERIMENTAL RESULTS 
Indian Remote Sensing (IRS) PAN data sets are used to test 
these algorithms. Common data set of 512X512 is used to test 
all the algorithms, which is extracted from larger data sets to 
reduce processing time. The two data sets are acquired by the 
same sensor but at two different times. Figure 1 shows the data 
that is used as a reference image. Figure 2 shows the data which 
Is to be warped. 
  
Figure-1 Reference Image 
4.1 WAVELET MODULUS MAXIMA APPROACH 
The wavelet decomposition is carried out upto the third level. 
The actual feature point matching is achieved by maximizing 
the correlation coefficient over small windows 
surrounding the points with the LL sub bands of the wavelet 
701 
  
^ F 
HET OMA: 
: i 
tel 
EH 
A 
Figure-2 Input Image to be warped 
transform. A point from the input image is taken and its 
correlations with all the points from the reference image are 
calculated. Then, the point with which it has the maximum 
correlation is its most similar feature point. À constant o=2.5 is 
used to control the number of feature points selected for the 
matching in the modulus maxima. In order to select the most 
significant feature points à is also in the higher levels. A 
Correlation threshold 7. = 0.85 is defined to limit the number 
of matched control point pairs. If the achieved correlation is 
greater than this threshold, then both the points are matched. 
The area of matching window w,. — 7, the size of refinement 
matching window w, — 3 is chosen for finding the correlation. 
We have taken care of the well distribution of the control points 
through out the image by splitting the image into 5X5 grids and 
in each grid minimum of one control point is selected. The 
actual consistency check(H. Li, 1995) is done in an iterative 
fashion through which the most likely incorrect match is 
identified recursively in each step. If RMSE is too large, 
another round of consistency check is carried out. The iteration 
continues until acceptable RMSE is achieved. This first part of 
the matching process is the crucial phase of the registration 
process. The algorithm is progressive at higher levels of 
wavelet sub bands to improve the registration accuracy. The 
RMSE at the finer level is achieved as 0.45 pixels. Fig 3 shows 
the warped image. : 
4.2 FAST FOURIER TRANSOFROM APPROACH 
Rotation and Scale can be represented as shifts in the log — 
polar coordinates. From this log — polar images (Young.D, 
2000) by using phase correlation and Fourier shift theorem 
rotation and scale is derived. But while computing the log — 
polar image from the original rectangular coordinates leads to 
points that are not located exactly at points in the original grid. 
This demands the interpolation. In this implementation bilinear 
interpolation is adopted. An image is simulated for known 
errors of translation and rotation. The simulated image is shown 
in Figure 4. The corresponding log — polar image is shown in 
Figure 5. To implement this algorithm IDL/ENVI(Hongjie 
Xie, 2003) is being used. The FFT of the log — polar images of 
both input and reference images are created. By using the 
Inverse FFT of the phase correlation ratio, the maximum