The document describes how to detect lines in an image using the Hough transform. It explains that the Hough transform represents lines in a polar coordinate system and works by plotting the curves for each edge point and finding the intersections, which indicate collinear points that make up a line. It then outlines the steps to apply this technique: 1) load an image, 2) optionally convert to grayscale and blur, 3) perform edge detection using Canny, and 4) detect lines using Hough transform by finding intersections above a threshold.

1. Individual Assignment
11. Line Detection of an Image
MCS3108 – IMAGE
PROCESSING AND VISION
U. V Vandebona
13440722

2. Tools and Techniques Used
 Java
 OpenCV
 HoughLinesP Function
 Canny Operation
 Gaussian Smoothing

3. Hough Line Transform
 It is a transformation technique used to detect
straight lines.
 To apply the Transform, first an edge detection pre-
processing is desirable.

4. Line in an Image expressed as…
 Cartesian coordinate system
 Polar coordinate system
For Hough Transforms, we will express lines in
the Polar system

5. How it Works
θ
r
x
y
Arranging the terms:

6. How it Works…
 In general, for each point (x0, y0) , we can define the family
of lines that goes through that point as:
 Meaning that each pair (rθ,θ ) represents each line that
passes by (x0, y0)

7. How it Works…
 If for a given (x0, y0) we plot the family of lines that
goes through it, we get a sine wave.
 For instance, for x0 = 8 and y0 = 6 and we get the
following plot (in a plane coordinates with θ and r)
We consider only points
such that
r > 0 and 0 < θ < 2π

8. How it Works…
 We can do the same operation above for all the points in
an image.
 If the curves of two different points intersect in the
plane coordinates with θ and r, that means that both
points belong to a same line.
 For instance, following with the example above and
drawing the plot for two more points: x1 = 9, y1 =
4 and x2 = 12, y2 = 3, we get:

9. The three plots intersect in one single point (0.925, 9.6),
these coordinates are the parameters ( θ, r) or the line in
which (x0, y0) , (x1, y1) and (x2, y2) lay.

10. So it means…
 A line can be detected by finding the number of
intersections between curves.
 The more curves intersecting means that the line
represented by that intersection have more points.
 In general, we can define a threshold of the
minimum number of intersections needed to detect a
line.

11. Hough Line Transform
 It keeps track of the intersection between curves of
every point in the image.
 If the number of intersections is above
some threshold, then it declares it as a line with the
parameters ( θ, rθ) of the intersection point.

12. Application
1. Loads an image
2. (Optional) Convert to grayscale
3. (Optional) Blur Image
 Gaussian Smoothening
4. Edge Detection
 Canny Operation
5. Line Detection
 Hough Line Transformation

13. Application