1. Image Enhancement (Frequency Domain)

2. Frequency-Domain Filtering
Compute the Fourier Transform of the image
Multiply the result by filter transfer function
Take the inverse transform
Bahadir K. Gunturk

3. Frequency-Domain Filtering
Bahadir K. Gunturk

4. 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;
>> figure; imshow(H);
Separable
>> [f1,f2] = freqspace(256,'meshgrid');
>> H = zeros(256,256); d = abs(f1)<0.5 & abs(f2)<0.5;
>> H(d) = 1;
>> figure; imshow(H);
Bahadir K. Gunturk

5. Frequency-Domain Filtering
Butterworth Lowpass Filter
As order increases the frequency response approaches ideal LPF
Bahadir K. Gunturk

6. Frequency-Domain Filtering
Butterworth Lowpass Filter
Approach to a sinc function.
Bahadir K. Gunturk

7. Frequency-Domain Filtering
Gaussian Lowpass Filter
Bahadir K. Gunturk

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

9. Example
Bahadir K. Gunturk

10. Highpass Filters
Bahadir K. Gunturk

11. Example
Bahadir K. Gunturk

12. Homomorphic Filtering
Consider the illumination and reflectance components of an image
Illumination
Reflectance
Take the ln of the image
In the frequency domain
Bahadir K. Gunturk

13. 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

14. Homomorphic Filtering
Bahadir K. Gunturk