Edge Detection using Laplacian of Gaussian Edge detection is a fundamental tool in image processing and computer vision. It identifies points in a digital image at which the image brightness changes sharply or has discontinuities. Laplacian of Gaussian is used to filter noise before edge detection. This method combines Gaussian filtering with the Laplacian for edge detection.  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 the method of edge detection using Laplacian of Gaussian (LoG) filter

Definitions of the components/Keywords: In Laplacian of Gaussian edge detection there are mainly three steps: - Filtering - Enhancement - Detection Laplacian is a measure of the second spatial derivative of an image Very useful in detecting abrupt changes In edge detection, Gaussian smoothing is done prior to Laplacian to remove the effect of noise. The operations are linear and can be interchanged Gaussian smoothing is a special case of weighted smoothing, where the coefficients of the smoothing kernel are derived from a Gaussian distribution.

Definitions of the components/Keywords: The 2-D Laplacian of Gaussian (LoG) function centered on zero and with Gaussian standard deviation has the form: where σ is the standard deviation The amount of smoothing can be controlled by varying the value of the standard deviation.

Master Layout Give a slider to select any one value of sigma. Image after edge detection Original Image

Step 1: Thresh =0.1,Sigma =1.0 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: Thresh = 0.1, Sigma 0.05 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: Thresh = 0.1, 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 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: Thresh = 0.1, 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 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: Thresh = 0.5, 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 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: Thresh = 0.5, 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 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: Thresh = 0.01, 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 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: Thresh = 0.01, 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 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

Introduction Credits 14 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 23, 24,25 Slide 26 Electrical Engineering  Select any one of the figures a b c d  Select the value of sigma

Questionnaire 1.If and are the two threshold values and then which threshold value gives more edges? Answers: a) b)

Questionnaire 2. What is the resulting image if proper threshold is applied to the given image ? Answers: a) b)

Questionnaire 2. What is the resulting image if proper threshold is applied to the given image ? Answers: c) d)None

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