Gaussian Smoothing

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: 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. 2 3 4 5

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

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

Step 1: 3x3 mask, Sigma 0.5 1 2 3 4 5

Step 2: 3x3 mask, Sigma 0.8 1 2 3 4 5

Step 3: 3x3 Mask, Sigma 1 1 2 3 4 5

Step 4: 3x3 Mask , Sigma 3 1 2 3 4 5

Step 5: 3x3 Mask, Sigma 5 1 2 3 4 5

Step 6: 3x3 Mask, Sigma 8 1 2 3 4 5

Step 7: 3x3 Mask, Sigma 10 1 2 3 4 5

Step 8: 5x5 Mask, Sigma 0.5 1 2 3 4 5

Step 9: 5x5 Mask, Sigma 0.8 1 2 3 4 5

Step 10: 5x5 Mask, Sigma 1 1 2 3 4 5

Step 11: 5x5 Mask, Sigma 3 1 2 3 4 5

Step 12: 5x5 Mask, Sigma 5 1 2 3 4 5

Step 13: 5x5 Mask, Sigma 8 1 2 3 4 5

Step 14: 5x5 Mask, Sigma 10 1 2 3 4 5

Step 15: 7x7 Mask, Sigma 0.5 1 2 3 4 5

Step 16: 7x7 Mask, Sigma 0.8 1 2 3 4 5

Step 17: 7x7 Mask, Sigma 1 1 2 3 4 5

Step 18: 7x7 Mask, Sigma 3 1 2 3 4 5

Step 19: 7x7 Mask, Sigma 5 1 2 3 4 5

Step 20: 7x7 Mask, Sigma 8 1 2 3 4 5

Step 21: 7x7 Mask, Sigma 10 1 2 3 4 5

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

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

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

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

Gaussian Smoothing

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