# EE 7730 Lecture 1 by yaofenji

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

Frequency-Domain Filtering

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);

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

Frequency-Domain Filtering
     Butterworth Lowpass Filter

Approach to a sinc function.

Frequency-Domain Filtering
     Gaussian Lowpass Filter

u 2  v2

H (u, v)  e        D0

Frequency-Domain Filtering
Ideal LPF    Butterworth LPF   Gaussian LPF

Example

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

Example

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)

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.

Homomorphic Filtering

 L  0.5
 H  2.0