gaussian smoothing
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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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3
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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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3
2
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1
• 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
5
32
4
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
5
32
4
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
32
4
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
5
32
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
32
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
32
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
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
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