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

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

Definitions of the components/Keywords: 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.

Definitions of the components/Keywords: 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

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

Step 1: x3 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

Step 2: x3 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

Step 3: x3 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

Step 4: x3 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

Step 5: x3 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

Step 6: x3 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

Step 7: x3 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

Step 8: x5 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

Step 9: x5 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

Step 10: x5 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

Step 11: x5 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

Step 12: x5 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

Step 13: x5 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

Step 14: x5 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

Step 15: x7 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

Step 16: x7 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

Step 17: x7 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

Step 18: x7 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

Step 19: x7 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

Step 20: x7 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

Step 21: x7 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

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

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

Questionnaire 2. What is the mask value for =1? Hint: Take x and y values from the grid provided Answers: a) b) c) d)

Links for further reading Reference websites: Books: Digital Image Processing – Rafael C. Gonzalez, Richard E. Woods, Third edition, Prentice Hall