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Digital Image Processing 
Image Restoration 
Noise models and additive noise removal 
5/15/2013 COMSATS Institute of Infor...
Image Restoration 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 2
Image Restoration 
 What is noise (in the context of image processing) and how can it 
be modeled? 
 What are the main t...
Degradation Model for a Digital Image 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pro...
Noise Models 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 5
Noise and Noise Models 
 Gaussian (normal) 
 Impulse (salt-and-pepper) 
 Uniform 
 Rayleigh 
 Gamma (Erlang) 
 Expon...
Effect of Noise on Images & Histograms 
 Gaussian 
 Exponential 
 Impulse 
(salt-and-pepper) 
5/15/2013 COMSATS Institu...
Effect of Noise on Images & Histograms 
 Rayleigh 
 Gamma (Erlang) 
 Uniform 
5/15/2013 COMSATS Institute of Informatio...
Noise Models: Gaussian Noise 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing C...
Noise Models: Rayleigh Noise 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing C...
Noise Models: Erlang (Gamma) Noise 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Proces...
Noise Models: Exponential Noise 
Where 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pr...
Noise Models: Uniform Noise 
1 , if 
   
  
0 otherwise 
  
p ( z ) 
b a 
a z b 
The mean and variance are 
given...
Noise Models: Impulse (Salt and Pepper) Noise 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital I...
Effect of Noise on Images & Histograms 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pr...
Effect of Noise on Images & Histograms 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pr...
Effect of Noise on Images & Histograms 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pr...
Periodic Noise (Example) 
 Spatially Dependent Case 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Di...
Applicability of various noise models 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pro...
Estimation of noise parameters 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing...
Estimation of noise parameters (example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image ...
Estimation of noise parameters (example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image ...
Estimation of noise parameters 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing...
Restoration of noise-only degradation 
Filters to be considered 
5/15/2013 COMSATS Institute of Information Technology, Ab...
Mean Filters: Arithmetic mean filter 
Causes a certain amount of blurring (proportional to the window size) to 
the image,...
Mean Filters: Geometric mean filter 
– A variation of the arithmetic mean filter 
– Primarily used on images with Gaussian...
Mean Filters: Harmonic mean filter 
Harmonic mean filter 
– Another variation of the arithmetic mean filter 
– Useful for ...
Arithmetic and geometric mean filters (example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital...
Mean Filters: Harmonic mean filter 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Proces...
Mean Filters: Harmonic mean filter 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Proces...
Mean Filters: Contra-harmonic mean filter 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image...
Classification of contra-harmonic filter applications 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad D...
Contra-harmonic mean filter (example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pro...
Contra-harmonic mean filter (example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Pro...
Rank / Order / Order Statistics Filters 
– Known as Rank filters, Order filters OR Order Statistics filters 
– Operate on ...
Rank / Order Statistics Filters: Median filter 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital ...
Rank / Order Statistics Filters: Median filter 
– Most popular and useful of the rank filters. 
– It works by selecting th...
Median filter (Example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330...
Rank / Order Statistics Filters: Max and Min filter 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Dig...
Rank / Order Statistics Filters: Max and Min filter 
– Max filter also known as 100th percentile filter 
– Min filter also...
Max and Min filter (Example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing C...
Rank / Order Statistics Filters: Midpoint filter 
– Calculates the average of the highest and lowest pixel values 
within ...
Midpoint filter (Example) 
5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC3...
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Noise Models

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Noise Models

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Noise Models

  1. 1. Digital Image Processing Image Restoration Noise models and additive noise removal 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 1
  2. 2. Image Restoration 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 2
  3. 3. Image Restoration  What is noise (in the context of image processing) and how can it be modeled?  What are the main types of noise that may affect an image?  What are the possible solutions?  Subjective Vs Objective (Enhancement Vs Restoration) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 3
  4. 4. Degradation Model for a Digital Image 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 4
  5. 5. Noise Models 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 5
  6. 6. Noise and Noise Models  Gaussian (normal)  Impulse (salt-and-pepper)  Uniform  Rayleigh  Gamma (Erlang)  Exponential 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 6
  7. 7. Effect of Noise on Images & Histograms  Gaussian  Exponential  Impulse (salt-and-pepper) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 7
  8. 8. Effect of Noise on Images & Histograms  Rayleigh  Gamma (Erlang)  Uniform 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 8
  9. 9. Noise Models: Gaussian Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 9
  10. 10. Noise Models: Rayleigh Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 10
  11. 11. Noise Models: Erlang (Gamma) Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 11
  12. 12. Noise Models: Exponential Noise Where 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 12
  13. 13. Noise Models: Uniform Noise 1 , if      0 otherwise   p ( z ) b a a z b The mean and variance are given by    a b 2 b  a , ( ) 12     2 2  5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 13
  14. 14. Noise Models: Impulse (Salt and Pepper) Noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 14
  15. 15. Effect of Noise on Images & Histograms 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 15
  16. 16. Effect of Noise on Images & Histograms 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 16
  17. 17. Effect of Noise on Images & Histograms 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 17
  18. 18. Periodic Noise (Example)  Spatially Dependent Case 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 18
  19. 19. Applicability of various noise models 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 19
  20. 20. Estimation of noise parameters 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 20
  21. 21. Estimation of noise parameters (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 21
  22. 22. Estimation of noise parameters (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 22
  23. 23. Estimation of noise parameters 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 23
  24. 24. Restoration of noise-only degradation Filters to be considered 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 24
  25. 25. Mean Filters: Arithmetic mean filter Causes a certain amount of blurring (proportional to the window size) to the image, thereby reducing the effects of noise. Can be used to reduce noise of different types, but works best for Gaussian, uniform, or Erlang noise. 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 25
  26. 26. Mean Filters: Geometric mean filter – A variation of the arithmetic mean filter – Primarily used on images with Gaussian noise – Retains image detail better than the arithmetic mean 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 26
  27. 27. Mean Filters: Harmonic mean filter Harmonic mean filter – Another variation of the arithmetic mean filter – Useful for images with Gaussian or salt noise – Black pixels (pepper noise) are not filtered 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 27
  28. 28. Arithmetic and geometric mean filters (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 28
  29. 29. Mean Filters: Harmonic mean filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 29
  30. 30. Mean Filters: Harmonic mean filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 30
  31. 31. Mean Filters: Contra-harmonic mean filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 31
  32. 32. Classification of contra-harmonic filter applications 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 32
  33. 33. Contra-harmonic mean filter (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 33
  34. 34. Contra-harmonic mean filter (example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 34
  35. 35. Rank / Order / Order Statistics Filters – Known as Rank filters, Order filters OR Order Statistics filters – Operate on a neighborhood around a reference pixel by ordering (ranking) the pixel values and then performing an operation on those ordered values to obtain the new value for the reference pixel – They perform very well in the presence of salt and pepper noise but are more computationally expensive as compared to mean filters 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 35
  36. 36. Rank / Order Statistics Filters: Median filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 36
  37. 37. Rank / Order Statistics Filters: Median filter – Most popular and useful of the rank filters. – It works by selecting the middle pixel value from the ordered set of values within the m × n neighborhood (W) around the reference pixel. • If mn is an even number, the arithmetic average of the two values closest to the middle of the ordered set is used instead. – Many variants, extensions, and optimized implementations in the literature. 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 37
  38. 38. Median filter (Example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 38
  39. 39. Rank / Order Statistics Filters: Max and Min filter 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 39
  40. 40. Rank / Order Statistics Filters: Max and Min filter – Max filter also known as 100th percentile filter – Min filter also known as zeroth percentile filter – Max filter helps in removing pepper noise – Min filter helps in removing salt noise 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 40
  41. 41. Max and Min filter (Example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 41
  42. 42. Rank / Order Statistics Filters: Midpoint filter – Calculates the average of the highest and lowest pixel values within a window – What would it do with salt and pepper noise ? 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 42
  43. 43. Midpoint filter (Example) 5/15/2013 COMSATS Institute of Information Technology, Abbottabad Digital Image Processing CSC330 43

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