1. Math 3360: Mathematical Imaging
Lecture 19:
Image denoising in the spatial domain
Prof. Ronald Lok Ming Lui Department of Mathematics,
The Chinese University of Hong Kong

2. Laplacian mask
Original image
Laplacian mask

3. Laplacian mask
Original image
Laplacian mask

4. Laplacian mask
Original image
Laplacian mask

5. Unsharp masking

6. Unsharp masking

7. Linear filter = Convolution
Linear filtering of a (2M+1)x(2N+1) image I (defined on
[-M,M]x[-N,N]) = CONVOLUTION OF I and H
H is called the filter.
Different filter can be used:
Mean filter
Gaussian filter
Variation of these filters (Non-linear)
Median filter
Edge preserving mean filter

8. Type of filter

9. Mean filter

10. Mean filter
Impulse noise
After mean filter

11. Mean filter
Gaussian noise
After mean filter

12. Mean filter
Real image
After mean filter

13. Gaussian filter Define a function using Gaussian function
Definition of H

14. Gaussian filter
Real image
After Gaussian filter

15. Gaussian filter
Real image
After mean filter

16. Gaussian filter
Real image
After Gaussian filter

17. Gaussian filter
Real image
After mean filter

18. Gaussian filter
Real image
After Gaussian filter

19. Median filter Median Nonlinear filter
Take median within a local window

20. Median filter
Real image
After median filter

21. Median filter
Salt & Pepper
Mean filter
Median filter

22. Median filter
Noisy image
Median filter

23. Median filter

24. Median filter
Noisy image
Median filter

25. Median filter

26. Median filter
Noisy image
Can you guess what it is?
Median filter

27. Edge preserving filtering
Step 1: Consider all windows of fixed size around a pixel (not necessarily centered at that pixel)
Step 2: Find a window with the least variance
Step 3: Do a linear filter in that window.

28. Edge preserving filtering

29. Edge preserving filtering

30. Non-local mean filter

31. Non-local mean filter

32. Non-local mean filter
Noisy image
Non-local mean

33. Non-local mean filter
Flat filter
Non-local mean

34. Isotropic diffusion

35. Isotropic diffusion Original image Sigma = 1.98 Sigma = 4.28

36. Anisotropic diffusion