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 ChittaMentor: Prof. Saravanan Vijayakumaran

*The contents in this ppt are licensed under Creative Commons Attribution-NonCommercial-ShareAlike 2.5 India license

Learning ObjectivesAfter 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:

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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.

Definitions of the components/Keywords:

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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

Master Layout

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• Give a slider ranging from 0.5 to 10 so that user can select any one value of sigma.

Image after smoothingOriginal Image

Step 1: 1

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3x3 mask, Sigma 0.5

Instruction for the animator Text 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: 1

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3x3 mask, Sigma 0.8

Instruction for the animator Text 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: 1

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3x3 Mask, Sigma 1

Instruction for the animator Text 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: 1

5

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3x3 Mask , Sigma 3

Instruction for the animator Text 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: 1

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4

3x3 Mask, Sigma 5

Instruction for the animator Text 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: 1

5

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4

3x3 Mask, Sigma 8

Instruction for the animator Text 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: 1

5

32

4

3x3 Mask, Sigma 10

Instruction for the animator Text 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: 1

5

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4

5x5 Mask, Sigma 0.5

Instruction for the animator Text 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: 1

5

32

4

5x5 Mask, Sigma 0.8

Instruction for the animator Text 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: 1

5

32

4

5x5 Mask, Sigma 1

Instruction for the animator Text 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: 1

5

32

4

5x5 Mask, Sigma 3

Instruction for the animator Text 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: 1

5

32

4

5x5 Mask, Sigma 5

Instruction for the animator Text 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: 1

5

32

4

5x5 Mask, Sigma 8

Instruction for the animator Text 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: 1

5

32

4

5x5 Mask, Sigma 10

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 0.5

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 0.8

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 1

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 3

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 5

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 8

Instruction for the animator Text 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: 1

5

32

4

7x7 Mask, Sigma 10

Instruction for the animator Text 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

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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

Questionnaire1. If there are two values of Sigma and and

then which sigma value makes the image more blurred?

Answers: a) b)

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Questionnaire2. What is the mask value for =1?Hint: Take x and y values from the grid provided

Answers: a) b)

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0.36 0.6 0.36

0.6 1 0.6

0.36 0.6 0.36

0.6 0.36 0.6

0.36 1 0.36

0.6 0.36 0.6

c) d) 0.09 0.05 0.09

0.05 1 0.05

0.09 0.05 0.09

0.05 0.09 0.05

0.09 1 0.09

0.05 0.09 0.05

Links for further readingReference websites:http://en.wikipedia.org/wiki/Gaussian_blurhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htmhttp://homepages.inf.ed.ac.uk/rbf/HIPR2/gaussiandemo.htm

Books:Digital Image Processing – Rafael C. Gonzalez,

Richard E. Woods, Third edition, Prentice Hall