1. Math 3360: Mathematical Imaging
Lecture 16:
Image enhancement in the frequency domain
Prof. Ronald Lok Ming Lui Department of Mathematics,
The Chinese University of Hong Kong

2. Key steps for image enhancement in the frequency domain

3. Relationship between spatial and frequency domain
Flat filter
Low pass filtering

4. Spatial and frequency domain

5. Examples of LP and HP filters

6. Ideal Low Pass Filter

7. Ideal Low Pass Filter
Ideal Low Pass Filter with larger and larger radii D0

8. Explanation of ringing effect

9. Butterworth Low Pass Filter
n=1
n=2
n=5
n=20

10. Butterworth Low Pass Filter
Butterworth Low Pass Filter with larger and larger radii D0

11. Gaussian Low Pass Filter
Gaussian Low Pass Filter with larger and larger radii D0

12. Gaussian Low Pass Filter

13. Application: Low Pass Filter

14. High Pass Filter

15. Spatial representation of High Pass Filter
Ideal
Butterworth
Gaussian
(Ringing effect is expected)

16. Ideal High Pass Filter Butterworh D0 = 15 D0 = 30
(Ringing effect is observed)

17. Butterworth High Pass Filter
D0 = 15
D0 = 30

18. Comparison: High Pass Filter
D0 = 15
D0 = 30
D0 = 80

19. Highboost sharpening in the frequency domain
High-pass
Filtered image in frequency domain
Original image
Highboost filtering result in the frequency domain with different k1 and k2