1. Gaussian Smoothing Gaussian Smoothing is the result of blurring an image by a Gaussian function. It is also known as Gaussian blur.  Course Name: Digital Image Processing Level(UG/PG): UG  Author(s) : Phani Swathi Chitta  Mentor: Prof. Saravanan Vijayakumaran *The contents in this ppt are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 2.5 India license

2. Learning Objectives After interacting with this Learning Object, the learner will be able to: Explain how the smoothing of an image is done using a Gaussian filter

3. Definitions of the components/Keywords: 5 3 2 4 1 Smoothing filters are used for blurring and for noise reduction. –Blurring is used in preprocessing steps, such as removal of small details from an image prior to object extraction, and bridging of small gaps in lines or curves –Noise reduction can be accomplished by blurring In edge detection, Gaussian smoothing is done prior to Laplacian to remove the effect of noise. Gaussian smoothing is a special case of weighted smoothing, where the coefficients of the smoothing kernel are derived from a Gaussian distribution. The 2D Gaussian smoothing filter is given by the equation where σ is the variance of the mask The amount of smoothing can be controlled by varying the values of the two standard deviations.

4. Definitions of the components/Keywords: 5 3 2 4 1 For a 3x3 mask, the values of x and y are taken from the below grid. -1,-1 0,-1 1,-1 -1,0 0,0 1,0 -1,1 0,1 1,1

5. Master Layout 5 3 2 4 1 Give a slider ranging from 0.5 to 10 so that user can select any one value of sigma. Image after smoothing Original Image

6. Step 1: 1 5 3 2 4 3x3 mask, Sigma 0.5 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 0.5, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

7. Step 2: 1 5 3 2 4 3x3 mask, Sigma 0.8 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 0.8, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

8. Step 3: 1 5 3 2 4 3x3 Mask, Sigma 1 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 1, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

9. Step 4: 1 5 3 2 4 3x3 Mask, Sigma 3 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 3, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

10. Step 5: 1 5 3 2 4 3x3 Mask, Sigma 5 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 5, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

11. Step 6: 1 5 3 2 4 3x3 Mask, Sigma 8 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 8, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

12. Step 7: 1 5 3 2 4 3x3 Mask, Sigma 10 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 10, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 3x3

13. Step 8: 1 5 3 2 4 5x5 Mask, Sigma 0.5 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 0.5, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

14. Step 9: 1 5 3 2 4 5x5 Mask, Sigma 0.8 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 0.8, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

15. Step 10: 1 5 3 2 4 5x5 Mask, Sigma 1 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 1, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

16. Step 11: 1 5 3 2 4 5x5 Mask, Sigma 3 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 3, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

17. Step 12: 1 5 3 2 4 5x5 Mask, Sigma 5 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 5, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

18. Step 13: 1 5 3 2 4 5x5 Mask, Sigma 8 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 8, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

19. Step 14: 1 5 3 2 4 5x5 Mask, Sigma 10 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 10, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 5x5

20. Step 15: 1 5 3 2 4 7x7 Mask, Sigma 0.5 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 0.5, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

21. Step 16: 1 5 3 2 4 7x7 Mask, Sigma 0.8 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 0.8, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

22. Step 17: 1 5 3 2 4 7x7 Mask, Sigma 1 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 1, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

23. Step 18: 1 5 3 2 4 7x7 Mask, Sigma 3 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 3, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

24. Step 19: 1 5 3 2 4 7x7 Mask, Sigma 5 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 5, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

25. Step 20: 1 5 3 2 4 7x7 Mask, Sigma 8 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 8, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

26. Step 21: 1 5 3 2 4 7x7 Mask, Sigma 10 I nstruction for the animator T ext to be displayed in the working area (DT) The first fig. should appear and then when the slider points at 10, the second fig. should be shown The text in DT should appear in parallel to the figures The original image The resulting image after Gaussian smoothing is done The filter mask used for smoothing is of size 7x7

27. Introduction Credits 27 Definitions Test your understanding (questionnaire) ‏ Lets Sum up (summary) ‏ Want to know more… (Further Reading) ‏ Try it yourself Interactivity: Analogy Slide 1 Slide 3 Slide 28,29 Slide 30 Electrical Engineering  Select any one of the figures a b c d  Select the value of sigma

28. Questionnaire 1. If there are two values of Sigma and and then which sigma value makes the image more blurred? Answers: a) b) 1 5 2 4 3

29. Questionnaire 2. What is the mask value for =1? Hint: Take x and y values from the grid provided Answers: a) b) 1 5 2 4 3 0.36 0.6 0.36 0.6 1 0.36 0.6 0.36 0.6 0.36 0.6 0.36 1 0.6 0.36 0.6 c) d) 0.09 0.05 0.09 0.05 1 0.09 0.05 0.09 0.05 0.09 0.05 0.09 1 0.05 0.09 0.05

30. Links for further reading Reference websites: http://en.wikipedia.org/wiki/Gaussian_blur http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm http://homepages.inf.ed.ac.uk/rbf/HIPR2/gaussiandemo.htm Books: Digital Image Processing – Rafael C. Gonzalez, Richard E. Woods, Third edition, Prentice Hall