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Threshold Values of Different Classical Edge Detection Algorithms
İsa Avcı
Department of Computer Engineering, Faculty of Engineering, Karabuk University, Karabuk 78050, Turkey
Corresponding Author Email: isaavci@karabuk.edu.tr
https://doi.org/10.18280/ts.390536
ABSTRACT
Received: 22 August 2022
Accepted: 20 October 2022
The subject of Detecting edges in images is considered one of the main topics in digital
image processing and the most common one, due to its wide applications in many fields.
Classical methods for detecting edges in digital images still give excellent results if the
threshold is chosen correctly. In this paper, a group of classical edge algorithms was taken
and tested on different types of images, Canny edge detection algorithm gave the best results
in all circumstances if the threshold value of it was set between 0.30-0.45. The range of the
threshold values was from 0.1 to 0.45 in Roberts, Sobel, and Prewitt's edge detection
algorithms. In this paper, four famous classical algorithms were tested on some standard RG
BA images which had some noises by purpose and by holding different frequencies,
containing different types of noise. Since the number of images has reached 50 thousand in
total, a lot of data has been obtained and these algorithms have been tested on a large number
of images. Indicating the algorithms implemented to perform on different image types, the
threshold value was changed from 0 to 1 thousand times with each image by 0.001 value.
Keywords:
edge detection, threshold, edge algorithms,
Canny
1. INTRODUCTION
Along with the developing computer technologies, the
globally widespread qualified information infrastructure has
increased the processing and use of larger and more complex
data and has led to different application approaches in this
direction. It is especially evident in the more widespread and
frequent use of digital image data. The image data in question
is used in a wide range of applications, from autonomous
driving and parking functions of cars to statistical inferences
based on visual data and software for security purposes such
as face recognition. Most of these uses use pattern recognition,
object recognition, and feature extraction techniques. It is
possible to say that edge detection algorithms are among the
most important tools used in these techniques.
Edge detectors of some kind, particularly step edge
detectors, have been an essential part of many computer vision
systems. The edge detection process serves to simplify the
analysis of images by drastically reducing the amount of data
to be processed, while at the same time preserving useful
structural information about object boundaries. There is
certainly a great deal of diversity in the applications of edge
detection, but it is felt that many applications share a common
set of requirements. These requirements yield an abstract edge
detection problem, the solution of which can be applied in any
of the original problem domains.
Edge detection algorithms are among the most widely used
tools in digital image processing. These algorithms'
performance directly affects the applications' performance
based on the image processing in which they are used. It is
seen that the hit rates of edge detection algorithms decrease
under random noise conditions, which is one of the factors that
affect the performance the most. With the increase in the noise
level, the problem of separating the object pattern that needs
to be detected in the image with noise arises. In this context,
examining the existing edge detection algorithms has
developed a parametric edge detection model based on noise
conditions. Thus, a variable parameter-based edge detection
algorithm was created, which provides adaptation according to
noise levels [1].
Edge can be defined as high frequencies or the boundary
that separates two different regions or scenes in the image [ 2].
The term edge detection can also be considered as a type of
image segmentation that is an important topic [3, 4]. Edge
detection can be used to reduce image size [5, 6]. This will can
help with data compression, matching, and image
segmentation. Also, it can be used for scene anatomy and
pattern recognition. The ability of the eye to distinguish lines
is more understandable than distinguishing a normal image, as
there are details that are clearer when converting the image to
an edge image [7].
Many researchers have written in this field to accurately
determine the edges, especially in satellite images. Many
methods appeared to find the edges in the image, but the most
common one is through the derivative. In general, the gradient
is extracted from the first derivative, and the Laplacian is
extracted from the second derivative to find the edges in the
image [8].
Each algorithm has a threshold value, and if the threshold
value is chosen correctly, this will give a very accurate edge
image, so the threshold value is not a fixed value. If a slight
change happens to the raw image, for example, some noise
will change the threshold value. For that, it is necessary to do
a deep calculation of the threshold value to find out the range
of suitable values for the threshold that can be a reference to
any random entry.
The basic idea here is to take many different images with
frequency, lighting, and noise, then change the threshold value
for each image a thousand times from 0 to 1, increasing by
0.001. After that, the threshold value will be adopted that gives
Traitement du Signal
Vol. 39, No. 5, October, 2022, pp. 1775-1780
Journal homepage: http://iieta.org/journals/ts
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the best edge image.
2. LITERATURE REVIEW
Sobel and Ruman did some calculations based on the
Prewitt algorithm, and they are reached that this algorithm
cannot work so well with noisy images [9]. Himanshu &
Truman concluded that the Canny edge algorithm is not easy
to use and get the results because the operator of it is so
complex compared to other edge operators [10, 11].
Nandhitha and Manoharan researched the wavelet
algorithm, and they reached the result that if the noise is
removed from the input image, this will make the wavelet
algorithm work so well [12].
Luo researched using the Canny edge detector on the colony
images, and he found that this detector works so well from the
visual and quantitative sides [13].
Nadernejad et al. concluded that the Boolean edge detector
works to the same level or gives close results as the Canny
edge detector [14]. Joshi and Koju compared two different
edge algorithms, and they reached that the Canny work better
than the Haar-Prewitt edge algorithm [15].
Bin and Yeganeh called Canny the ideal edge detection for
its great impact on their results. They found that Canny
detected the edges of the noisy images even if the noise was
not removed from the image. For that, they gave it this name
[16]. Chandrasekar and Shrivakshan worked on several edge
algorithms, and they concluded that the Canny edge works
better than others if its parameters are set perfectly [17].
3. METHODOLOGY
Some raw images were used MATLAB 2021 tools to
implement this work. A lot of classical edge detection
techniques were applied to this study, and as it is known, each
edge algorithm has a threshold value that can be changed.
Every algorithm has a threshold value the minimum value of
the threshold is 0 and the largest value is 1. Changing the
threshold value in each algorithm from zero to one by an
increment of 0.01 for each edge image entered the system.
This was done using MATLAB code. It was observed by
changing the values that the best edge image for all types of
images and all types of algorithms was between 0.2 and 0.45.
As for the canny algorithm, it was the highest threshold value
among all algorithms, as it was between 0.3 and 0.45. The
object of this study is to find out what the best threshold values
range for each edge algorithm that gives the best detection
even if the input is a random input image [18, 19].
The raw images that are used were varied as follows: image
with a small number of edges (image with low frequencies),
image with a big number of edges (high-frequency image),
image with two kinds of pixel values 0 or 1 (binary image) and
the texture image, the edge image for each raw image was
found by changing the threshold value until all edges of each
image are visible. Those edge images will be used later as a
reference [20]. The next step is the noise added to the original
images. The noise used is Salt and pepper and the Gaussian
noise, then the edge images were found for the noisy images
whose correlation values to the raw edge images are as high as
possible [21]. Everything has been repeated, but this time by
gradually increasing the degree of noise in both Gaussian and
Salt and Pepper noise types. Figure 1 shows the methodology
flowchart, making the whole idea faster to understand [22].
Figure 1. Methodology flowchart
4. FINDINGS AND RESULTS
The results in this paper are not much different from the
results of the previous researchers, especially since the issue
of finding edges in images is one of the topics researchers have
discussed. However, the difference that occurred here,
thousands of samples were taken and tested on a bunch of
classic edge algorithms. These algorithms are classical
algorithms, but even if the threshold of the algorithm is chosen
correctly, it still may not give good results. As it is known, the
threshold value for the algorithm changes according to the
image entered by the algorithm and factors such as noise
affecting the image, change in the illumination intensity of the
image, and even different capture angles [23, 24].
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In this paper is that four famous classical algorithms were
tested on several types of images by holding different
frequencies and adding different types of noise to them, this
generated many data. The number of images reached 50
thousand images in total, and this allowed the experiment of
these algorithms on a big number of images [25].
Many possibilities to know how those algorithms perform
in different types of images, and with each image, the value of
the threshold is changed a thousand times from 0 to 1 with a
degree of 0.001, and the values of the threshold that give high
correlation values are recorded and saved [26]. This huge work
is done by fast GPU because it takes much time to get the final
results. The following Table 1 shows the threshold values of
the raw edge images, the threshold values of the noisy edge
images, and the correlation between the raw edge images and
the noisy edge images.
Table 1. Threshold values of the raw images
Input
Edge algorithm
Canny
Sobel
Prewitt
Roberts
Binary image
0.30
0.20
0.20
0.30
High Freq. image
0.33
0.10
0.12
0.10
Low Freq. image
0.32
0.10
0.11
0.10
Texture image
0.35
0.35
0.35
0.35
Figure 2 shows that the highest threshold values were with
the Canny edge detection algorithm, and in the case of the
texture input image, the threshold values obtained in all types
of edge detection algorithms are high compared to other types
of images. Edge determination is used the Canny algorithm,
which has several working steps that make it different from the
rest of the other algorithms. The steps are noise reduction,
gradient computation, non-maximum suppression, use of two
thresholds, and edge tracking. These steps, in particular the
step of using two thresholds, make the threshold values
slightly larger than the rest of the algorithms, arguably starting
from 0.3.
It manually checked the threshold and optimized the code
based on the result of the Gaussian noise optimization. The
ground truth noise detection samples are proposing the Canny
algorithm in the paper is highly responsive in comparison with
the existing Sobel, Prewitt, and Roberts algorithms. The
Mean-Square-Error (MSE) which is representing the
cumulative squared error between the noisy image instance
and the original image demonstrates that the optimization of
the proposed algorithm is showing a distinguished novelty in
the case of computational mechanism.
Figure 2. Threshold values of the raw images
Table 2. Threshold values - gaussian noise
Input
Edge algorithm
Canny
Sobel
Prewitt
Roberts
Binary image
0.35
0.20
0.21
0.30
High Freq. image
0.30
0.15
0.15
0.25
Low Freq. image
0.40
0.20
0.21
0.30
Texture image
0.45
0.35
0.33
0.20
So just like the images that did not contain noise, here for
the noisy Gaussian Images, the previous Table 2 and Figure 3
show that the highest threshold values were with the Canny
edge detection algorithm, and in the case of the texture input
image, the threshold values were obtained in all types of the
edge detection algorithms was high compared to other types of
images [27].
Figure 3. Threshold values of the gaussian noisy edge
images
The texture input image is known to all that this image
consists of low and high frequencies more than other images.
If it cut the image into several small pieces, each piece will
consist of a group of high and low frequencies, in other words,
this type of image has a sharper and more sudden gradation
than the rest of the image types.
The work will be within the lower and higher frequencies
more than the rest of the frequencies and is exactly made the
values of all the thresholds for all algorithms close in this type
of image. Moreover, the threshold values for both Sobel and
Prewitt were almost the same.
Table 3. Threshold values – salt and pepper noise
Input
Edge algorithm
Canny
Sobel
Prewitt
Roberts
Binary image
0.35
0.26
0.25
0.30
High Freq. image
0.30
0.15
0.15
0.10
Low Freq. image
0.42
0.12
0.10
0.10
Texture image
0.45
0.40
0.43
0.45
Table 3 shows high values of binary images, high
frequencies images, low frequencies images, and texture
images. Also, it already gave the same results Canny, Sobel,
Prewitt, and Roberts in texture images. Salt & pepper noise is
one of the types of noise in the image. De-noising is a process
of removing and limiting the effect of noise in the image,
which helps in better interpretation and analysis of the image.
With the salt and pepper noise edge detection, the above
Table 3 and Figure 4, the heights threshold values were with
Canny edge detection, also the results of Sobel, Roberts and
Prewitt were close.
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Figure 4. Threshold values of the salt and pepper noisy edge
images
Table 4. Correlation values – Gaussian noise
Input
Edge algorithm
Canny
Sobel
Prewitt
Roberts
Binary image
0.98
0.96
0.96
0.97
High Freq. image
0.75
0.65
0.65
0.55
Low Freq. image
0.6
0.45
0.45
0.25
Texture image
0.99
0.60
0.60
0.98
Figure 5. Correlation Gaussian noisy edge images / raw edge
images
The above Table 4 and Figure 5 clearly show the highest
correlation values with the Canny edge detection in all types
of images. Moreover, as it is known that the correlation values
are between - 1 and 1, whenever the value is close to 1, the
correlation is very strong, and if the value is 0, there is no
correlation, and in the case of a -1, that means they are opposite.
It is clear from Table 5 and Figure 6 that correlation values
are all high with the Canny edge detection algorithm and with
the image of a type of texture with all kinds of edge detection
algorithms. The correlation value of the binary image added
by salt and pepper noise with threshold 0.35 in Table 3, its
edge found with Canny edge algorithm is 0.99 in Table 5, and
so on for the other values.
All edge detection worked so well when the input was a
binary image; see the correlation tables. The pixel probability
here is either 0 or 1, so there are no other possibilities. See
Table 4, Table 5, Figure 5, and Figure 6.
Table 5. Correlation values – salt and pepper noise
Input
Edge algorithm
Canny
Sobel
Prewitt
Roberts
Binary image
0.99
0.98
0.98
0.97
High Freq. image
0.85
0.75
0.73
0.76
Low Freq. image
0.80
0.50
0.45
0.65
Texture image
0.99
0.92
0.90
0.98
Figure 6. Correlation salt and pepper noisy edge images /
raw edge images
When the input was a texture image, Robert’s edge
detection did the best here; see the correlation tables, and this
is because the synthesis of the texture image is more
compatible with Robert's operators. Table 4, Table 5, Figure 5,
and Figure 6. inform this.
For all algorithms, the performance was not so good in the
case of the image that contains a huge number of edges. See
the correlation tables for the high-frequency image. The
possibilities of the edge here are many, leading to taking some
of the image pixels and treating them as not edge pixels, which
may be the opposite. See Table 4, Table 5, Figure 5, and Figure
6.
For all cases, the threshold values range for the Canny edge
detection was from 0.30 to 0.45. This range is the most suitable
for all images, and this is what is done here. It is known that
the threshold values are from 0 to 1. This study's main subject
is finding the best threshold values that make the edge
algorithm give the best edge detection. See Table 1, Table 2,
Table 3, Figure 2, Figure 3, and Figure 4.
The threshold values of Sobel and Prewitt algorithms were
close to each other; see the threshold tables. The operators of
Prewitt and Sobel are similar and are used to detect the vertical
and horizontal edges. Check it out in Table 1, Table 2, Table
3, Figure 2, Figure 3, and Figure 4.
For Roberts, Sobel, and Prewitt edge detection algorithms,
the range of the threshold values was from 0.1 to 0.45; see the
threshold tables. So, this range is the most suitable for all
images. Moreover, this study's main subject is finding the best
threshold values that make the edge algorithm give the best
edge detection. See Table 1, Table 2, Table 2, Figure 2, Figure
3, and Figure 4.
5. CONCLUSIONS
Canny edge detection is demonstrating a good result based
on the threshold and Mean Square Error (MSE) computation
in all cases of input images, even if the noise degree was high
and with a randomly modified seed. All edge detection
algorithms had a good result for the input type Binary image.
For the input type texture image, it is good to use Robert's edge
detection algorithm. All edge detection algorithms face
difficulties if the input image contains many edges. The canny
edge detection threshold range was from 0.30 to 0.45. Sobel
and Prewitt's algorithms had a close result to each other. For
Roberts, Sobel, and Prewitt's edge detection algorithms, the
range of the threshold values was from 0.1 to 0.45. In this
article, four famous classical algorithms have been tested on
many types of frames by keeping different frequencies and
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adding different types of noise to them, it produces a lot of data
because the total frames reach 50,000 frames, this allows
testing of these algorithms on a large number of images.
Among the four algorithms used, the Canny algorithm proved
the best in all input cases. It came following Bin and Yeganeh
[16], Chandrasekar and Shrivakshan [17], and Maini and
Aggarwal [10], and this is because this algorithm makes
smoothing to the input image due to the Gaussian filter that it
has, calculates the gradient depending on the gradient of Sobel
or Prewitt, and find the image edge by using the non-maximum
suppression and connect the thresholding based on the
hysteresis [28, 29]. A large number of possibilities to know
how those algorithms perform in different types of images, and
with each image, the value of the threshold is changed a
thousand times from 0 to 1 with a degree of 0.001, and the
values of the threshold that give high correlation values are
recorded and saved. This huge work is done by fast GPU
because it takes much time to get the final results. This study
is important in terms of setting an example for future studies
in terms of edge detection. In addition, which algorithms and
methods used are more important are given comparatively.
This will shed light on future researchers.
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