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DIP Lecture - 13

The lecture discusses edge linking and boundary detection, focusing on local and global processing methods, particularly the Hough Transformation (HT). HT simplifies pattern detection by allowing edges to 'vote' for possible lines or shapes, making it effective even when edges are not fully connected. A practical example demonstrates how to apply HT to draw a line from given points using the mc plane (Hough space).

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31 views16 pages

DIP Lecture - 13

The lecture discusses edge linking and boundary detection, focusing on local and global processing methods, particularly the Hough Transformation (HT). HT simplifies pattern detection by allowing edges to 'vote' for possible lines or shapes, making it effective even when edges are not fully connected. A practical example demonstrates how to apply HT to draw a line from given points using the mc plane (Hough space).

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 – 13

(Image Segmentation, Part - 3)


Edge Linking and Boundary Detection, Local Processing, Hough
Transformation(HT), mc plane and (Hough space), Problem with mc plane, ρθ-
plane, HT voting, Edge-Linking based on Hough Transformation
By,
Dr. Ramesh Kumar Thakur
Assistant Professor
Center of AI, MANIT Bhopal
M.Tech (NIT DGP), PhD (IIT Patna), Postdoc (Northwestern University, USA)
Edge Linking and Boundary Detection
• An edge detection algorithm are followed by linking procedures to assemble edge pixels into
meaningful edges.
• Basic approaches
• – Local Processing
• – Global Processing via the Hough Transform
Local Processing
Local Processing
Hough Transformation (HT)
• HT is an elegant method that maps a possibly difficult pattern detection problem in to a simple “peak” detection.
• One can think of HT as a fancy name for a voting scheme, since edges vote for the possible model.
• It is a traditional way to detect lines and circles.

• Advantages:

• Edges need not be connected

• The object (line, circle) may be only partially visible.

• Key Idea of HT for Line Detection:


• Each straight line in this image can be described by an equation.
• Each white pixel, if considered in isolation, could lie on an infinite number of straight lines.
• In the HT each pixel votes for every line it could be on.
• The line(s) with the most votes wins.
Image Space to 𝒎𝒄 plane (Hough Space)
Image Space to 𝒎𝒄 plane (Hough Space)
Problem with mc plane
𝝆𝜽 plane
Image Space to 𝝆𝜽 plane(Hough Space)
HT Voting - Points
HT Voting - Line
HT Voting – Noisy Line
HT Voting – No Line
Real World Example
Numerical
1. Use Hough Transform to draw line using below points?

(1,4), (2,3), (3,1), (4,1), (5,0)

Ans:- First we will convert these points into lines in mc plane (Hough space) using the formula y= mx +c

• For (1,4) => 4 = m*1 +c => c = 4 - m

• For (2,3) => 3 = m*2 +c => c = 3 - 2m

• For (3,1) => 1 = m*3 +c => c = 1 - 3m

• For (4,1) => 1 = m*4 +c => c = 1 - 4m

• For (5,0) => 0= m*5 +c => c = -5m

After plotting these lines in mc plane(Hough space), 4 of


these lines intersect at m=-1 and c = 5,

So the final line in image space is y = -1*x + 5 => y = 5 – x

Also this line does not contain the point (3,1)

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