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					                                                Image Processing



Q1-Dennis Gabor, a Hungarian-born British electrical engineer who won a Nobel Prize in
Physics for the invention of optical holography, was also interested in Image Processing. In
his paper published 45 years ago, Gabor suggested interesting modifications of a standard
image enhancement procedure.

A common way to enhance a given monochrome (grey-scale) image I  x, y  is to amplify
linearly the high frequencies of the image
                          0           I enhanced  x, y   I  x, y   C I  x, y 
where  is the Laplacian and C is a constant to be determined empirically.

Gabor suggested two non-linear modifications of (0):
                                                                          2I
                   1              I enhanced  x, y   I  x, y   C 2
                                                                         n
                                                                           2I 1 2I 
                    2              I enhanced  x, y   I  x, y   C  2      2 
                                                                           n 3 s 

where n is the coordinate in the direction of the gradient of I  x, y  and s is the coordinate
in the direction orthogonal to n . It is not difficult to show that
                                                      2                         2
          2 I  I       2 I I I  2 I  I                      2 I  I       2 I I I  2 I  I 
                     2                                                                                            2

                    2                                                          2                    
2 I     x 2  x      xy x y y 2  y 
                                                           2 I     x 2  y 
                                                                                    xy x y y 2  x 
                                                                 
n 2                      I   I 
                                2          2
                                                             s 2                    I   I 
                                                                                         2          2

                                                                                  
                          x   y                                                x   y 


Your task is to implement and compare image enhancement methods (1), (2), and (3|).


Reference:

M. Lindenbaum, M. Fischer, and A. Bruckstein, “On Gabor’s Contribution to Image


Enhancement”, Pattern Recognition, Vol. 27, No. 1, pp. 1-8, 1994.




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Q2 -Given an grey-scale image I(x,y), consider the following non-linear iterative process:

I 0  x, y   I  x, y 

                                                               wij  exp  k I n x, y   I n x  i, y  j  
                      1                         1
I n1 x, y        w I  x  i, y  j   w
                                ij n                      ij
                   i , j  1                i , j  1
where k is a positive constant. Note that the weights {wij} depend on the pixel positions (x,y)
and the iteration number n. After a certain number of iterations you should get results similar
to those shown in the picture below: small-scale image details are removed while salient
image edges are sharpened. Your task is to implement the above non-linear iterative
procedure, perform a number of experiments (with different images, various numbers of
iterations and k).




In your report, please describe your experiments and try to address the following issues:
     Is the proposed non-linear averaging procedure good for generating cartoon-like
        images?
     Is it difficult to find an appropriate number of iterations and K for a given image?
     Is your implementation of the procedure time-consuming?
     Can similar results be achieved using simpler tools?
     Propose possible applications for the procedure.
     Try to suggest some improvements.




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