1. Digital Image Processing Chapter 4
Image Enhancement in the Frequency Domain
Part II

2. 2D-DFT (Frequency) Domain Filtering

3. Convolution Theorem f (x,y) h(x,y) g(x,y) G(u,v) = F(u,v) H(u,v)
input image
impulse response
(filter)
output image
DFT
IDFT
DFT
IDFT
DFT
IDFT
G(u,v) =
F(u,v)
H(u,v)

4. Frequency Domain Filtering
Filter design: design H(u,v)

5. 2D-DFT Domain Filter Design
Ideal lowpass, bandpass and highpass

6. 2D-DFT Domain Filter Design
Ideal lowpass, bandpass and highpass

7. 2D-DFT Domain Filter Design
Ideal lowpass filtering with cutoff frequencies set at radii values of 5, 15, 30, 80, and 230, respectively

8. 2D-DFT Domain Filter Design
Gaussian lowpass

9. 2D-DFT Domain Filter Design
Effect of Gaussian lowpass filter

10. 2D-DFT Domain Filter Design
Effect of Gaussian lowpass filter

11. 2D-DFT Domain Filter Design
Effect of Gaussian lowpass filter

12. 2D-DFT Domain Filter Design
Gaussian lowpass filtering
Gaussian highpass filtering

13. 2D-DFT Domain Filter Design
Choices of highpass filters
Ideal
Butterworth
Gaussian

14. 2D-DFT Domain Filter Design
Ideal
Butterworth
Gaussian
Obtained by applying inverse 2D-DFT to the corresponding frequency domain filters

15. 2D-DFT Domain Filter Design
Ideal
Butterworth
Gaussian

16. 2D-DFT Domain Filter Design
Gaussian filter with different width

17. 2D-DFT Domain Filter Design
Orientation selective filters

18. 2D-DFT Domain Filter Design
Narrowband Filtering
by combining radial and orientation selection *