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Math 3360: Mathematical Imaging

Learn key steps for image enhancement in the frequency domain, explore spatial and frequency domain relationships, and examples of LP and HP filters such as Ideal, Butterworth, and Gaussian filters explained with applications and comparisons.

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Math 3360: Mathematical Imaging

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  1. Math 3360: Mathematical Imaging Lecture 16: Image enhancement in the frequency domain Prof. Ronald Lok Ming LuiDepartment 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 Butterworth Gaussian Ideal (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 = 30 D0 = 15 D0 = 80

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

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