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DIP Lecture - 12

The lecture discusses advanced image segmentation techniques, focusing on image gradients, gradient operators, and edge detection methods such as Prewitt, Sobel, and the Marr-Hildreth algorithm. It compares zero crossing and gradient methods, highlighting their advantages and drawbacks in edge detection. The lecture also includes practical examples of applying Sobel filters to determine edge direction and magnitude.

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6 views14 pages

DIP Lecture - 12

The lecture discusses advanced image segmentation techniques, focusing on image gradients, gradient operators, and edge detection methods such as Prewitt, Sobel, and the Marr-Hildreth algorithm. It compares zero crossing and gradient methods, highlighting their advantages and drawbacks in edge detection. The lecture also includes practical examples of applying Sobel filters to determine edge direction and magnitude.

Uploaded by

unknownguy7705
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Lecture – 12

(Image Segmentation, Part - 2)


Image Gradient, Gradient Operators and Masks, Prewitt and Sobel Masks for
Diagonal Edges, Laplacian, Laplacian of Gaussian(LoG), Marr-Hildreth edge
detection algorithm, Zero crossing vs. Gradient
By,
Dr. Ramesh Kumar Thakur
Assistant Professor
Center of AI, MANIT Bhopal
M.Tech (NIT DGP), PhD (IIT Patna), Postdoc (Northwestern University, USA)
Image Gradient
Image Gradient
Gradient Operators and Masks
Prewitt and Sobel Masks for Diagonal Edges
Examples
Examples
Examples
Laplacian
Laplacian of Gaussian(LoG)
Marr-Hildreth edge detection algorithm
• 1. Filter the input with an n by n Gaussian lowpass filter.
• 2. Compute the Laplacian of the image of step 1.
• 3. Find the zero crossing of the image from step 2.
• Approximate the zero crossing from LoG image to threshold the LoG image by setting all its positive values to white and
all negative values to black.
• The zero crossing occur between positive and negative values of the thresholded LoG.
Zero crossing vs. Gradient
• Attractive
• – Zero crossing produces thinner edges
• – Noise reduction

• Drawbacks
• – Zero crossing creates closed loops. (spaghetti effect)
• – sophisticated computation.

• Gradient is more frequently used.


Zero crossing vs. Gradient
Numerical
1 2 5
1. Consider an image 5 5 5 . Show the output of any edge detection algorithm?
5 3 2

• Ans:- Let us consider the application of the Sobel’s edge detection filters. The edge detection filters are as below:

-1 -2 -1 -1 0 1
• gx = 0 0 0 gy = -2 0 2
1 2 1 -1 0 1

• Applying gx filter, we get gx = -1-4-5+5+6+2 = 3

• Applying gy filter, we get gy = -1-10-5+5+10+2 = 1

• The gradient, denoted by ∆f = grad(f) = (3 1)T

• Magnitude (length of vector) = mag(∆f) = (gx2 + gy2)1/2 = sqrt (9 + 1) = 3.16

• Direction of the edge = tan-1(gy/gx) = tan-1(1/3) = 18.26 degrees

• Thus, we see that the edge is located at an angle of 18.26 degrees wrt x-axis

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