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EE 7730 Lecture 1

VIEWS: 12 PAGES: 14

  • pg 1
									EE 4780



    Image Enhancement (Frequency Domain)
Frequency-Domain Filtering
        Compute the Fourier Transform of the image
        Multiply the result by filter transfer function
        Take the inverse transform




Bahadir K. Gunturk                                         2
Frequency-Domain Filtering




Bahadir K. Gunturk           3
Frequency-Domain Filtering
        Ideal Lowpass Filters
Non-separable                                                >> [f1,f2] = freqspace(256,'meshgrid');
                                                             >> H = zeros(256,256); d = sqrt(f1.^2 + f2.^2) < 0.5;
                                                             >> H(d) = 1;
                                 1, for u 2  v 2  D
                                                            >> figure; imshow(H);
                     H (u , v)                      0

                                 0, otherwise
                                 




   Separable
                                                             >> [f1,f2] = freqspace(256,'meshgrid');
                                 1, for u  Du and v  Dv   >> H = zeros(256,256); d = abs(f1)<0.5 & abs(f2)<0.5;
                      H (u, v)                             >> H(d) = 1;

                                 0, otherwise
                                                             >> figure; imshow(H);




Bahadir K. Gunturk                                                                                              4
Frequency-Domain Filtering
        Butterworth Lowpass Filter

                                            1
                     H (u, v)                           2n
                                  1   u 2  v 2 D0 
                                                            As order increases the
                                                              frequency response
                                                              approaches ideal LPF




Bahadir K. Gunturk                                                                 5
Frequency-Domain Filtering
        Butterworth Lowpass Filter




                              Approach to a sinc function.

Bahadir K. Gunturk                                           6
Frequency-Domain Filtering
        Gaussian Lowpass Filter

                                           u 2  v2
                                       
                        H (u, v)  e        D0




Bahadir K. Gunturk                                    7
Frequency-Domain Filtering
        Ideal LPF    Butterworth LPF   Gaussian LPF




Bahadir K. Gunturk                                    8
Example




Bahadir K. Gunturk   9
Highpass Filters
                                 0, for u 2  v 2  D
                                 
                     H (u , v)                      0

                                 1, otherwise
                                 



                                             1
                     H (u, v)                           2 n
                                  1   u 2  v 2 D0 
                                                    


                                            u 2  v2
                                          
                      H (u, v)  1  e       D0




Bahadir K. Gunturk                                              10
Example




Bahadir K. Gunturk   11
Homomorphic Filtering
        Consider the illumination and reflectance components of
         an image    f ( x, y)  i( x, y)* r ( x, y)


                        Illumination      Reflectance


        Take the ln of the image
                     ln  f ( x, y)  ln i( x, y)  ln r( x, y)

        In the frequency domain
                         F (u, v)  Fi (u, v)  Fr (u, v)




Bahadir K. Gunturk                                                     12
Homomorphic Filtering
        The illumination component of an image shows slow
         spatial variations.
        The reflectance component varies abruptly.
        Therefore, we can treat these components somewhat
         separately in the frequency domain.




                 1




             With this filter, low-frequency components are attenuated, high-frequency
             components are emphasized.


Bahadir K. Gunturk                                                                       13
Homomorphic Filtering




                         L  0.5
                         H  2.0




Bahadir K. Gunturk                  14

								
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