Distance and Angles Effect in Hough Transform for
line detection
Qussay A. Salih
Abdul Rahman Ramli
Faculty of Engineering
University Putra Malaysia
Faculty of Information Technology
Multimedia University
Tel:+603-8312-5498
Fax:+603-8312-5264
.
Abstract
In this paper, we study the Hough transform theory
images by generating the peak point from gray scale
images, and seek for the effect caused by the distance
and the angles. Lines will appear on the edge of
images, which has been processed edge detection
theorem.
The input to a Hough transform is normally an image
that has been edge detected with a Robert, Sobel or
Canny edge detector, for instance.
Problems occur in lines detection due to several
reasons. They are noise, low resolution and un-sharp
object boundaries. The Hough Transform is a
standard tool in image analysis that detects lines in
an image, by grouping isolated collinear or almost
collinear points into image structures.
To simplify the computation, the paprameter can be
divbided into distance and angles paprameters where
both parameter to achieve the enhancment of straight
line detection using Hough Transform.
Hough Transform can be regarded as an edge linker
since it groups edge pixels together and describes by
a higher order entity such as a line equation.
However the Hough transform can be used to extract
circles and even generalised (perhaps nonsymmetrical) shapes. In this case it is more like a
pattern matcher. Even though that the Hough
transform is invariant to rotation and translation.
Key word: (Auto lines, Hough transform)
Detection
1. Introduction
Hough Transforms method is useful to find
simple shapes straight lines, circles, ellipses
in images [2]. Man-made objects, for
instance, frequently have shapes with
straight and circular edges, which project to
straight and elliptical boundaries in an
image[3]. One kind of algorithm for
identifying these extended image features
involves following edges, and linking
together edge lets which seem to lie on
straight lines or smooth curves [4]. An
alternative approach, which is the subject of
this teach file, involves accumulating the
evidence provided by each edge element for
the shape being sought. Since, usually, the
shape can be at any position in the image,
any orientation and any size as well, the
whole set of different possibilities has to be
taken into account.
The Hough transform used in a variety of
related methods for shape detection [1].
The goal of this paper is to study the effect
of the distance and angles, to achieve the
accurate image detection for straight lines
using Hough Transform method.
2. Implementation
As a Hough transform method, assume that
we have some data points in an image,
which are perhaps the result of an edge
detection process, or boundary points of a
binary. To recognize the points that form a
straight line in an image has two ends, for
Hough transform finds the infinite straight
lines on which the image edges lie. In Figure
below a points (x',y') in the image, all lines
which pass through that pixel have the form
y’=mx’+c
(1)
for varying values of m and c. See Fig.1.
For more accuracy an alternative
representation of a line is given by
x cosθ + y sinθ =r
Where r is the distance of the line from the
origin and θ is the angle between this
perpendicular and x-axis [8]. Our parameter
space is presented now in θ and r, where 0 ≤
θ ≤ 2π and r is limited by the size of the
image.
x cosθ + y sinθ = r1
Fig. 1 Lines through a point
There are infinitely many lines that pass
through this point, but they all satisfy the
condition [5][6]. If we divide parameter
space into a number of discrete accumulator
cells we can collect votes in (c, m) space
from each data point in (x, y) space. Peaks in
(c, m) space will mark the equations of lines
of co-linear points in (x, y) space [7].
By Quantise (m,c) space into a twodimensional array A for appropriate steps of
m and c.
Initialise all elements of A(m,c) to zero,
straight line well be detected in an image.
For the pixel (x',y') which lies on some edge
in the image, we add 1 to all elements of
A(m,c) whose indices m and c satisfy
y' = mx' + c.
Fig. 2 Line Representations
(3)
According to the equation (3), that a point in
(x, y) space is now represented by a curve
in (r, θ) space rather than a straight line, the
line position in the image has been
represented by coordenates corresponding to
the coloum and row indices of array
elements, the hough transform used the data
from edge detector operator, however you
need to creat an array and initialize it to zero
[8]. And loop scan the edge array, for each
non-zero pixel enccunteard, the proposed
method appear the effect of the distace and
angles [9].
As mentioned befor, Hough transform can
be used to detect other shapes in an image as
well as straight lines.
3. Methodology
The Hough transform is a method that can
be used to find features of any shape in an
image. To find straight lines accurately we
need to find and manipulate the variables
that can guide us to best result in the other
hand the challenges are where the
computational complexity of the method
grows rapidly with shapes that are more
complex.
In this paper we developed a program for
straight line detection by employing Hough
transfrom method with using MATLAB
software.
In Figure (3) illustrated, the flow operation
and the procedure of the program applied on
the image.
The following are steps to straight line
detection implementation.
• Run edge detection operator for the
image has been captured. the edge
operator will implement some theory
such as sobel, prewit and canny. One
should choose the right theory for a
particuler image to get the best result.
• Suggest a suitable values of distaance
and angles of the image untill a better
result is obtaind.
• Detecte the peak point in the image
histogram from paramiter space by
changing the image from image space to
parametter space.
• Apply the Hough transfrom for straight
line detection as illustrated in Figure (3)
to detect the straight lines.
4. Result
By using the formulas in the previous
section, the Hough transform for image
straight line detection was achieved and the
study according of effect of distance and
angles appear in these two images each
containing of a real object inside. The object
in the second image appears unclear. By
changing the distance and angles during line
detection for the image, we can see the
effect of the parameters on the line
detection.
We adjust the distance and angles between
pixels from the range 50 to 250 by applying
the suitable edge detection theory for the
image. The canny edge filter is choused for
the images because it gives the best edge
detection.
5. Discussion
We design this section by summarizing the
experimental results of straight line
detection using Hough transform method. In
this paper, we develop image straight line
detection software using MATLAB
compiler.
We explain these results by highlighting the
H.T method, way for line detection, and the
important variables, which will effect to
detect the object in image. Where there are
two different parameters called distance and
angles, which applied in parameter space.
Consider that directly implementing the
Hough transform for lines detection would
require a peak point in the parameter space.
The peak points are describing all the lines
in the image. The more point detected, more
lines will appear and hence better the result.
The graph of Figure (4) are the results for
first image, it shows the number of lines
accurately and correctly found, plotted
against the number of distance when the
angle is fixed at 200o, for the pentagon
object, the number of lines and peak point
appear in the image space started from 3
until 5, both factors increased in the same
way through the graph, the number of 5
indicated the final result of the image
detection seems the object being detected is
a pentagon.
In the same time graph of Figure (4) shows
the number of lines accurately and correctly
found, plotted against the number of Angles
when the distance is fixed at 200o, for the
pentagon object, the number of lines and
peak point appear in the image space started
from 3 until 5, the number of lines detected
are change from 6 to 5 where the number of
peak points increased from 3 to 5, when the
angle a is increasing, from the graph, we can
notice that the number of peak point is not
moving along with the number of lines.
The graph of Figure (5) are the results for
second image, it shows the number of lines
correctly found, plotted against the number
of Angles when the distance is fixed at 200o,
3D object, the number of lines and peak
point appear in the image space started from
4 until 20, both factors increased in the same
way through the graph, the number of 20
indicated the final result of the 3D object
image detection, for Hough transform lines
detection.
In the same graph of Figure (5) shows the
number of lines correctly found, plotted
against the number of distance when the
angle is fixed at 200o, for the 3D object, the
number of lines and peak point appear in the
image space started from 4 until 20 in best
case, both factors increased in the same way
through the graph, the lines appear are not
exactly on the edge of the 3D object, when
the angles changed, the number of lines
changed to.
The minimum number of lines detected in
the image is 17. These lines give the exact
shape of the edge and lied on the edge of the
image. The peak points and the lines
achieved on the two test images, by using
the program illustrated in the tables (1, 2).
6. Conclusion
In this paper, we have proposed an
algorithm for line detection using the Hough
transform. We considered the task of finding
the unique lines passing through an n-tuple
of pixel in the image.
From the result, we can conclude that the
larger is the angle, the clearer and accurate
the lines will appear. For the unclear image,
H T can detect the line for the edge of the
object and gives all the possibility of the
shape for the object.
The object will be detected as several pieces
of object by the theory. This is differ from
the edge detection which just gives the
overall shape of the distance and angles.
A good result can be obtained by adjusting
the both parameters.
The distance will bring the effect on the
number of lines where as the angles will
effect the accuracy of the lines to the edges
illustrated in Figure (6). The larger distance
is more number of lines can drawn in image
space. The angles will give a best result for
an object at a particular value only.
7. References
[1] P.R. Bevington and D.K. Robinson.
Data Reduction and Error Analysis for the
Physical Sciences. McGraw-Hill, second
edition, 1992.
[2] R.C. Lo and W.H. Tasi, Gray-scale
Hough Transform for Thick Line detection
in Gray- Scale images, “ pattern recognition,
Vol, 28, No.5, pp.647-661,1995.
[3] K.Murakami and T.Naruse, High speed
Line detection by Hough transform in local
area. In proceeding of the internation
conference
on
pattern
recognition
(ICPR’00), 2000.
[4] M .Nakanishi and T.Ogura, Real-Time
extraction using a highly parallel Hough
Transform board. In proceeding of the
International
conference
on
Image
processing (ICIP’97)1997.
[5] A.L. Kesidis and N. Papamarkos. On the
Inverse Hough Transform. In IEEE
Transactions on pattern and machine
intelligence, Vol 21, No. 12, Dec 1999.
[6] D. X. Le, G. Thoma. Document skew
angle detection algorithm. Proc. SPIE, 1993
Symposium on Aerospace and Remote
Sensing-Visual Information Processing II,
Orlando, FL, 14-16, Vol. 1961, pp. 251-262,
April 1993
[7] J.Hun Jang and K.Sang Hong. Detection
of linear Bands in Gray-Scale Image Based
on the Euclidean Distance Transform and
the Hough transform. In proceeding oft eh
10’th international conference on image
analysis and processing 1998.
[8] P.Franti, A. Mednonogov and H.
Kaliviainen. Hough transform for Rotation
invariant matching of line drawing Image. In
proceeding of the International conference
on pattern Recognition (ICPR’00), 2000.
[9] K.Murakami and T. Naruse. High speed
line detection by Hough Transform in local
Area In proceeding of the conference on
pattern Recognition (ICPR’00) 2000.
[10] Dong-Gyu Si and Rae-Hong Park.
Two-dimensional object alignment based on
the robust oriented Hausdorff similarity
measure. Image Processing, IEEE
Transactions, 2001.
Captured image
Edge detection operator
Suggested value of angles
Suggested value of distance
Peak point detector
Peak point accumulator
Inverse Hough Transform
Straight line detected
Fig. (3) Flow chart implement the line detection of the Hough transform on 3D images.
6
5
Peak point Disance
4
Line Distance
Num ber of Peak
3
Point/Lines
Peak point Angles
2
Lines Angles
1
0
50
100
150
Distance/Angles
200
250
30
25
Peak point Distance
20
Fig.Number
(4) Distance/Angles
vs. number of peak point / lines for pentagonLine
image.
Distance
of Peek
Point/Lines
15
Peak point Angles
10
Lines Angles
5
0
50
100
150
200
250
Distance/Angles
Fig. (5) Distance/Angles vs. number of peak point / lines for 3D object image.
Table .1 Peak points of distance and angles
Image No.
Image feature
Distance
Angles
50 100 150 200 250 50 100 150 200 250
Image 1
Pentagon
3
4
5
5
5
3
4
5
5
5
Image 2
3-D object
4
6
14 21 20 24 22 18 21 17
Table .2 Lines detected of distance and angles
Image No.
Image feature
Distance
Angles
50 100 150 200 250 50 100 150 200 250
Image 1
Pentagon
3
4
5
5
5
5
5
5
5
5
Image 2
3-D object
4
6
14 21 20 21 17 22 24 18
The pentagon image.
The Original image
The Edge detection image
The peak point for varied distance and lines detected of the pentagon object
Distance=250
The 3D object image
Distance=250
The Original image
The edge detect image
The peak point for varied distance and lines detected of the 3D object
Distance=250
Distance=250
The peak point for the angles and lines detected for the 3D object
.
Angles=250o
Angles=250o
Accuracy Ratio
100
80
60
3 D object
40
Pentagon
20
0
50 100 150 200 250
Lines accuracy, Pear
Angles
Fig (6) Lines Detected Accuracy Pear Different scale of Angles