This document discusses techniques for line detection in digital images. It covers the Hough transform and convolution-based techniques. The Hough transform allows identifying lines and other shapes by converting the representation from the original (x,y) plane to the parameter space of (m,c) representing lines. An example shows how to use the Hough transform to demonstrate that three points lie on the same line and find the line's equation. Convolution-based techniques use kernels tuned to detect lines of a particular width and orientation by convolving the kernels with the image.

1. NADAR SARASWATHI COLLEGE OF ARTS AND SCIENCE
LINEDETECTION
P.Gayathri
II M.Sc Computer Science
Digital image processing

2. Line Detection:
In image processing, line detection is an
algorithm that takes a collection of n edge
points and finds all the lines on which these
edge points lie. The most popular line
detectors are the Hough transform and
convolution-based techniques.

3. Hough transform:
The Hough transform is an
incredible tool that lets you identify
lines. Not just lines, but other shapes
as well.

4. Example: Using Hough transform show that the points (1,1),
(2,2), and (3, 3) are collinear find the equation of line.
Solution:
The equation of line is y=mx+c
In order to perform Hough transform we need to convert line
from (x,y) plane to (m,c) plane Equation of (m,c) plane is
Step 1: C=mx+y For (1,1)
y=mx+c 1=m+c
C=-m+1 If c=0 then ( 0=-m+1 ) m=1 If m=0 then ( c=1 ) c=1
(m,c) = (1, 1) Similarly for

5. If (x,y)= (2,2) then (m,c) = (1,2) If (x,y)=
(3,3) then (m,c) = (1,3) Step 2: Plot a
graph for (mc) = (1, 1), (1,2), and (1,3)

6. Convolution-Based Techniques:
The line detection operator consists of a
convolution kernel tuned to detect the presence
of lines of a particular width n, at a particular
orientation. Figure 1 shows a collection of four
such kernels, which each respond to lines of
single pixel width at the particular orientation
shown

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