Noise and Filtering

1. Basis beeldverwerking (8D040) dr. Andrea FusterProf.dr. Bart terHaarRomenydr. Anna VilanovaProf.dr. Marcel Breeuwer Noise and Filtering

2. Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed

3. Gaussian Noise Gaussian noise follows a Gaussian distributionAverage =Standard deviation = Good approximation of noise that occurs in practical cases.

4. Additive Gaussian Noise Example

5. Impulse Noise Model Bipolar impulse noise follows the following distributionIf or is zero, we have unipolar impulse noiseIf both are nonzero, and almost equal, this is also called salt-and-pepper noise

6. Impulse Noise • Impulses • can be positive and negative • are often very large • can go out of the range of the image • appear as black and white dots, saturated peaks

7. Impulse Noise Example

8. Periodic Noise Original Image Abs of Fourier Transform Periodic noise can be generated during image acquisition due to electrical interference

9. Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed

10. Mean Filters Blurring used to smooth images by e.g. convolution with smoothing kernel Can be used to suppress noise

11. Arithmetic Mean Filter Arithmetic mean filter replaces the current pixel with a uniform weighted average of the neighbourhood

12. Geometric Mean Filter Like arithmetic mean filter, but loses less detail

13. Harmonic Mean Filter Works well for Gaussian noise Works well for salt noise, but fails for pepper noise

14. Contraharmonic Mean Filter Is very effective in eliminating Salt-and-Pepper noiseQ is the order of the filter

15. Contraharmonic Mean Filter If Q=0, this is the arithmetic mean filter If Q=-1, this is the harmonic mean filter If Q<0, salt noise is eliminated If Q>0, pepper noise is eliminated For examples, see book page 324-325

16. Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed

17. Order-statistic filters median min max Result is based on ordering pixel values in the neighbourhood Examples: median, max, min filters

18. Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed

19. Median Filter Replaces value of a pixel by the median of its neighbourhood

20. Median filter Mean filtering 3x3 Mean filtering 9x9 Median filtering 3x3 Median filtering 9x9 Can be used to reduce random noise Less blurring than linear smoothing filter Very effective for impulse noise (salt-and-pepper noise)

21. Max and min filters • Max filter: • Take maximum of ordered pixel values • Find brightest points of an image (so: filters pepper noise) • Min filter: • Take minimum of ordered pixel values • Find darkest points of an image (filters salt noise)

22. Max filtered Midpoint filtered Original Salt-and-Pepper noise 3rd quartile filtered 1st quartile filtered Median filtered Min filtered

23. Contents • Noise • Mean Filters • Order-statistic filters • Median • Alpha-trimmed

24. Alpha-trimmed mean filter Delete d/2 lowest and d/2 highest values of from neighbourhood remains d=0 arithmetic mean filter d=mn-1 median filter

25. Alpha-trimmed image (5x5, d=6) Image with S&P noise and Gaussian noise Median filtered image (5x5) Alpha-trimmed mean filter works good for combination of S&P noise and Gaussian noise