1. Practical TULIP lecture next Tues 12th Feb. Wed 13th Feb 11-1 am.
Thurs 14th Feb am.
Practical notes on Q ueen’s on-line.

2. CSC312-4 Noise Reduction
Paul Miller

3. Image Enhancement  Brightness control Contrast enhancement
Noise reduction
Edge enhancement
Zooming  

4. Objectives What is noise? How is noise reduction performed?
Low-pass
Median
How they can be implemented using neighbourhood operators.

5. Noise Source of noise = CCD chip.
Electronic signal fluctuations in detector.
Caused by thermal energy.
Worse for infra-red sensors.

6. Noise + =
image
noise
‘grainy’
image

7. Noise Plot of image brightness. Vertical slice through image.
Noise is additive.
Noise fluctuations are rapid, ie, high frequency.

8. Noise Histogram Plot noise histogram
Histogram is called normal or Gaussian
Mean(noise)  = 0
Standard deviation 
i is the grey level. 2 

9. Noise Histogram
=10
=20
=30

10. Noise Histogram
=10
=20
=30

11. Noise Reduction - Low pass
Noise varies above and below uncorrupted image.

12. Noise Reduction - Low pass
How do we reduce noise?
Consider a uniform 1-d image A and add noise.
Focus on a pixel neighbourhood.
Central pixel has been increased and neighbouring pixels have decreased.
Ai-1 Ai Ai+1 Ci

13. Noise Reduction- Low pass= =3 = = = Ci
Ai-1 Ai Ai+1 =0

14. Noise Reduction - Low pass
Averaging ‘smoothes’ the noise fluctuations.
Consider the next pixel Ai+1
Repeat for remainder of pixels.
Ai-1 Ai Ai+1 Ai+2
Ci+1

15. Low pass Neighbourhood operator
All pixels can be averaged by convolving 1-d image A with mask B to give enhanced image C.
Weights of B must equal one when added together.

16. Low pass Neighbourhood operator
Extend to two dimensions.

17. Noise Reduction - Low pass

18. Noise reduction Low pass
Technique relies on high frequency noise fluctuations being ‘blocked’ by filter. Hence, low-pass filter.
Fine detail in image may also be smoothed.
Balance between keeping image fine detail and reducing noise.

19. Noise reduction - Median
Saturn image coarse detail
Boat image contains fine detail
Noise reduced but fine detail also smoothed

20. Noise Reduction- Median
How do we reduce noise without averaging?
Consider a uniform 1-d image A and add noise.
Focus on a pixel neighbourhood.
Non-linear operator?
Median filter!
Ai-1 Ai Ai+1 Ci

21. Noise Reduction- Median= 1 = = = = = Ci
Ai-1 Ai Ai+1 2 = 3

22. Noise reduction - Median
Consider a uniform 1-d image A with a step function.
Step function corresponds to fine image detail such as an edge.
Low-pass filter ‘blurs’ the edge.

23. Noise reduction - Median
Consider a uniform 1-d image A with a step function.
Step function corresponds to fine image detail such as an edge.
Median filter does not ‘blur’ the edge.
Ai Ai+1Ai+2
Ci+1
Ai-1 Ai Ai+1 Ci

24. Median Neighbourhood operator
All pixels can be replaced by neighbourhood median by convolving 1-d image A with median filter B to give enhanced image C.

25. Median Neighbourhood operator
Extend to two dimensions.

26. Noise reduction
Original
Low-pass
Median

27. Noise reduction Low-pass: fine detail smoothed by averaging
Median
Low-pass: fine detail smoothed by averaging
Median: fine detail passed by filter

28. Summary Conclusion What is noise? Noise reduction Neighbourhood
Gaussian distribution
Noise reduction
first principles
Neighbourhood
low-pass
median
Averaging pixels corrupted by noise cancels out the noise.
Low-pass can blur image.
Median can retain fine image detail that may be smoothed by averaging.