Article

Comparative Analysis of Edge Detection Operators

Using a Threshold Estimation Approach on Medical
Noisy Images with Different Complexities
Vladimir Maksimovic 1
, Branimir Jaksic 1,
* , Mirko Milosevic 2
, Jelena Todorovic 1
and
Lazar Mosurovic 3

1
Faculty of Technical Sciences, University of Pristina in Kosovska Mitrovica, Kneza Milosa 7,
38220 Kosovska Mitrovica, Serbia; vladimir.maksimovic@pr.ac.rs (V.M.);
jelena.todorovic@pr.ac.rs (J.T.)
2
Academy of Technical and Art Applied Studies, School of Electrical and Computer
Engineering, Vojvode Stepe 283, 11000 Belgrade, Serbia; mirko.milosevic@viser.edu.rs
3
Directorate for Railways, Nemanjina 6, 11000 Belgrade, Serbia; lazar.mosurovic@gmail.com
* Correspondence: branimir.jaksic@pr.ac.rs

Abstract: The manuscript conducts a comparative analysis to assess the

impact of noise on medical images using a proposed threshold value
estimation approach. It applies an innovative method for edge detection on
images of varying complexity, considering different noise types and
concentrations of noise. Five edges are evaluated on images with low,
medium, and high detail levels. This study focuses on medical images from
three distinct datasets: retinal images, brain tumor segmentation, and lung
segmentation from CT scans. The importance of noise analysis is heightened
in medical imaging, as noise can significantly obscure the critical features and
potentially lead to misdiagnoses. Images are categorized based on the
complexity, providing a multidimensional view of noise’s effect on edge
detection. The algorithm utilized the grid search (GS) method and random
search with nine values (RS9). The results demonstrate the effectiveness of
the proposed approach, especially when using the Canny operator, across
diverse noise types and intensities. Laplace operators are most affected by
noise, yet significant improvements are observed with the new approach,
Academic Editor: Ruben Pauwels particularly when using the grid search method. The obtained results are
Received: 19 November 2024 compared with the most popular techniques for edge detection using deep
Revised: 17 December 2024 learning like AlexNet, ResNet, VGGNet, MobileNetv2, and Inceptionv3. The
Accepted: 20 December 2024 paper presents the results via graphs and edge images, along with a detailed
Published: 27 December 2024
analysis of each operator’s performance with noisy images using the
Citation: Maksimovic, V.; proposed approach.
Jaksic, B.;

Keywords: medical image analysis; feature extraction; edge detection; noisy

images; object detection
Milosevic, M.; Todorovic, J.;
Mosurovic, L. Comparative
Analysis of Edge Detection
Operators Using a
Threshold Estimation Approach Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).
on Medical Noisy Images with
Different Complexities. Sensors
2025, 25, 87.
https://doi.org/10.3390/s250100
87

Copyright: © 2024 by the

authors. Licensee MDPI, Basel,
Switzerland. This article is an
open access article distributed
under the terms and conditions
of the Creative Commons
1. Introduction possible. Sometimes, however, the quality itself is impaired at the exact
During the source of images, too, i.e., at the moment when an image is being created,
processing of an but not rarely so during its processing or transfer. Noises are frequent forms
image, there is the of this image distortion. Noises in an image represent unwanted information,
tendency not to and as such they cause consequences for the image, such as the occurrence
impair its quality and of artifacts, a false edge and a false line, blurred objects, and the impairment
to generate as much of the image background itself as well. Noise is particularly undesirable in
information as medical images for several reasons. Firstly, it reduces the diagnostic
accuracy by obscuring the important details, making it difficult to

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https://doi.org/10.3390/s25010087
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identify conditions such as tumors. Secondly, it degrades the image quality,

resulting in less sharp and clear visuals, which complicates the assessment of
a patient’s condition. Thirdly, it requires additional effort from medical
professionals to interpret the results, as they must distinguish useful
information from the noise. The characteristic and model itself of noise can
be represented via a histogram and the Probability Density Function (PDF)
[1,2]. Different types of noise based on the PDF are Gaussian, Raileigh,
uniform, impulse, Poisson, and so on. According to correlation, noise is
classified as either white or colored. White noise has a balanced spectral
density of the strength and zero correlation, differently from colored noise. If
an image is impaired by white noise, it means that not all the pixels are
interrelated. According to its nature, it is additive or multiplicative (speckle)
noise, i.e., the pixels spanned by noise are either added to or multiplied by
the reference image. According to the classification of sources, this is
frequently called quantization noise or photon noise [3]. In the paper, the
following noise types were used for the analysis of the performances of the
new image edge detection approach, namely:
• Gaussian noise;
• Rician noise;
• Impulse noise (salt and pepper);
• Speckle noise.

1.1. Gaussian Noise

Because of its mathematical feature in the spatial and frequency
domains, Gaussian noise models are often used in practice. Generally,
Gaussian noise disrupts the level of the intensity of the gray color of pixels.
For that reason, Gaussian noise is characteristic of its histogram or the PDF
due to the dependence on the value of the gray color of pixels [1]. It is of a
statistical and additive nature which follows a normal distribution with a zero
mean value and the σ standard deviation and has an influence on all the
image pixels. Its appearance is caused by the fluctuations in the temperature
of the sensor and the variation in the illumination of the environment [3].

1.2. Impulse Noise (Salt and Pepper)

Impulse noise is additional noise most frequently appearing because of
faulty sensors and an error during the transfer. Differently from Gaussian
noise, it only affects certain pixels in the whole image, i.e., the image is not
absolutely damaged, but only some pixels in it are. This noise type includes
salt and pepper noise [1]. If, for example, a 3 × 3 matrix, with the pixels
whose values range from 0 to 255 and there are 8 bits, is taken, if salt and
pepper noise has hit the central pixel whose value was 250, now that value is
close to zero, which means that it has become a dark pixel, whereas the rest
of the pixels have remained unchanged. So, salt and pepper noise only affect
certain pixels, and their values are replaced with dark pixels if that pixel was
bright, i.e., if it was of a greater intensity and vice versa [1,3].
The intensity of this noise and its impact on the image quality are
particularly signifi- cant in medical images, such as MRI (Magnetic Resonance
Imaging) recordings, where even the smallest degradations can make
diagnosis difficult. In the literature, there are methods that allow the objective
measurement of the intensity of salt and pepper noise on MRI images. For
example, the paper [4] introduces statistical analyses of local intensity
extrema as a measure of image degradation. This approach provides the
possibility to estimate the noise level without a reference image through the
distribution of local maxima and min- ima, which are directly affected by the
presence of impulse noise. Similarly, the paper [5] applies gradient methods
to quantify the image quality, using variations in intensity as the indicators of
noise and degradation. Although these methods are particularly effective for
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MRI images, the principle behind them can be applied to other types of medical
images, including the CT and retinal images discussed in this paper.

1.3. Speckle Noise

This noise type is multiplicative noise. It frequently appears in coherent
recording systems, such as the laser, radar, acoustics, and so on. Speckle
noise in an image may appear in a fashion similar to Gaussian noise, yet it is
far more difficult to observe by the observer since it makes it difficult to
perceive the fine details in an image. Its probability density function follows
the gamma distribution [2,5].
The noise in an image is usual and frequently present and is created at
all the image levels, which can be seen based on the application of these
three noise types as well. The most important part is the detection of edges
over the images in which there is noise since the edge detectors such as
Roberts, Sobel, and Prewitt, which are all based on the first derivative, are
sensitive to noise [6,7]. For that reason, the Canny operator first filtrates the
image, then performs detection. Many noise reduction filters are proposed,
yet the filter type also depends on the noise type [8,9]. Numerous research
studies are directed towards detecting edges in the images where there is
noise, and many methods have been used to overcome this problem, recently
most frequently using the artificial intelligence method and neural networks
[3,7,10].

1.4. Edge Definition

The term “edge” implies a significant difference in the intensity of the
gray color in the neighboring pixels. The image edge is where there is an
abrupt change in the intensity between the neighboring or local pixels [8,9].
In this paper, an innovative approach to the assessment of the threshold
value presented in [11] is analyzed. The approach was tested over the images
consisting of a different number of details in the image where there is a
different concentration (intensity) of noise. The detection of edges over the
images in the presence of noise has become a big challenge. Therefore, edge
detection in the presence of noise in the paper [12] was examined applying
cellular neural networks (CNNs) and linear matrix inequality (LMI). The main
work focuses on CNN training templates for noise reduction and edge
detection [12]. Machine and deep learning are frequently used for the edge
detection over the images with noise, as is presented in [13], where their
model recognizes borders between the known and the unknown by pasting
jittered negative patches over inlier training images. In the paper [14], an
improvement of the Teaching Learning-Based Optimization (TLO) and a
methodology for obtaining the edge maps of noisy real-life digital images are
presented. Different image conditions can also be found in everyday image
processing, so the adaptive detection approach to low-quality noise grayscale
images is presented in the paper [15], whereas the paper [16] presents
adaptive threshold selection in two stages for images with noisy low contrast.
Researchers have also analyzed the influence of the changes in illumination
and compression on edge detection using the Robert and Canny operators
[17], while in the paper [18], an analysis of edge detection was performed
using the Canny operator over noisy images. An analysis of the influence of
different noise types on edge detection is presented in the paper [19], too, as
well as the influence of multiplicative noise in various image types: synthetic
aperture radar, ultrasound images, and ultrasonic imaging, among others
[20]. In other words, deep learning methods, CNNs, have shown significant
potential in edge detection and structure recognition in medical images. For
example, the paper [21] presents an effective application of CNN architectures
for detection optimization in industrial and biomedical applications. Although
these methods are superior in terms of accuracy, their main drawback is the
need
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for large datasets and computational power during training and inference,
which limits their application in resource-constrained environments.

2. System Model
Over 2000 images are analyzed in this paper, all of which were taken
from medical databases (Retina, lung, and brain tumor segmentation) with
their corresponding ground truth, and their complexity was assessed based
on the mean value of spatial information (SI mean) [11]. Complexity is
divided into three types of medical images and after that is confirmed via
calculation by computing the spatial information values in each image
applying the Sobel filter to the horizontal and vertical components of the
image, and then calculating the standard mean value, standard deviation,
and root mean square error [11]. Typically, SI mean is used as the primary
measure because it has often shown the best results in predicting image
complexity. Based on these values, three complexity criteria were established,
namely low complexity (LD), medium complexity (MD), and high complexity
(HD). In other words, boundaries were defined to represent a small number of
details, a medium number of details, and a high number of details in the
image. The newly proposed approach for estimating threshold values in [11]
was tested in situations involving images affected by various types of noise
and varying noise concentrations. Figure 1 illustrates an example of an image
with low, medium, and high complexity, along with its ground truth.

(a) (b) (c)

(d) (e) (f)

Figure 1. Example image for analysis: (a) small number, (b) medium number, and (c)
large number of details, and ideal edges for (d) small number, (e) moderate number
s, and (f) a large number of details.

In this manuscript, medical datasets of various modalities, including

retinal images, brain tumor segmentations, and CT lung scans, were used to
ensure the performance evaluation of algorithms on images with varying
complexity, structure, and noise charac- teristics. Such a selection of datasets
covers a wide range of details and enables the analysis of edge detection in
real conditions of medical practice. In addition to these datasets, MRI
datasets with specific acquisition parameters are also available, such as
GRAPPA (Generalized Autocalibrating Partially Parallel Acquisition), which
allow the variation in image quality depending on acquisition time [22]. In
the paper [22], it was shown
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how different parameter settings can affect the textural features and noise
level in MRI images. These data are significant for the evaluation of algorithms
in the context of variable acquisition conditions, similar to how this paper
analyzes the impact of different types and intensities of noise on the
performance of edge detection in CT and other medical images. By using
datasets with different modalities and image complexities, such as CT, retinal
images, and MRI with quality variations, the specific challenges of edge
detection can be further investigated, including the robustness of algorithms
to noise and variability of the acquisition parameters.
Different reconstruction kernels in CT scanning, such as sharp and soft
kernels, signifi- cantly affect the image characteristics, including the noise
level. Sharp kernels emphasize edges and small details, but often increase
the level of Gaussian noise, while soft kernels reduce noise at the expense of
reducing the edge sharpness. This impact is described in the literature, which
analyzes the transformation between sharp and soft kernels using filtering
techniques. In this paper, we do not include an analysis of the effects of
different kernels because our focus is not on the specifics of reconstructive
algorithms in CT scanning, but on the generalization of the edge detection
algorithm in regard to dense medical images.
Edge detection serves to single out the desired objects in an image, for
which reason as good detection as possible should be performed. A total of
five edge detectors were used (Canny, LoG, Sobel, Prewitt, Roberts) over the
images of different complexity and of different noise concentration (small,
medium, and high noise intensity in the image). In the analysis, noise was
added to each image, namely three noise types: salt and pepper, Gaussian,
and speckle with the intensities of 0.01, 0.05, and 0.1. The objective measure
(F–F1 Score) was used to verify the results [23]. FOM and PR objective
measures were also computed, but for brevity of the manuscript, only the F
measure is presented in the graphs. Figure 2 shows small (0.01), medium
(0.05), and high (0.1) noise intensities for various types of noise and the
Canny operator. The standard algorithm with default values for the Canny
operator was utilized. It is evident that noise significantly affects edge
detection, and further work will compare each edge detection operator for
such images, with the addition of a new approach described in [11].
Additionally, all five operators will be applied using this approach.

(a) (b) (c)

Figure 2. Example of edge detection on images affected by noise: salt and pepper with
intensities of
(a) 0.01, (b) 0.05, and (c) 0.1.

In this analysis, the threshold assessment was determined using the

machine learning technique, and the grid and random searches are presented
in the paper [11]. A dataset of 1800 threshold values was created to achieve
the best edge detection. There are 300 values for each single operator of the
dataset, with a difference for the Canny operator that has two thresholds, so
the Canny operator is assigned 600 values [11]. So, parameter optimization
was achieved in two manners, namely via the grid and random searches
[11,22].
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The grid search (GS) is based on trying every combination of the

parameters from the base, i.e., on going through all the dataset values and
finding the best threshold value with the help of which the best edge
detection will be achieved. The random search (RS) is based on setting the
number of the parameters taken from the base randomly and testing the
parameter that is the most appropriate one, based upon the objective quality
detection assessment measures [11,23,24].
The values 3, 6, and 9 were taken from the formed base for the random
search, the best values of which are looked for that match the given threshold
when detecting edges. So, while optimizing the parameters, the best model,
i.e., the best parameter that will lead to the best edge detection is looked for.
This parameter implies the determination of the threshold during detection,
all based on the objective measures and the random and grid searches and
the generated threshold values. The flowchart of the proposed approach in
[11] is shown in Figure 3a for the grid search-based approach, and Figure 3b
shows the random-based approach.

(a) (b)
Figure 3. The flow chart for the proposed approach to threshold discovering based on
(a) the grid search method, (b) the random search method.

All the procedures for implementing the new approach were repeated and
imple- mented in the same way and the same database for testing but now on
the images affected by noise (different implementation situation). The
flowchart of the approach in [11] is as follows:
Step 1: Loading the images from the dataset and ground truth images from
the database. That is, the image org (image from the dataset) and the image
with reference edges gt (ground truth image) are loaded.
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Step 2: Loading the dataset with threshold values (th) of 100 values
depending on the detector. For each detector, there is a dataset of 100
values. The Canny detector contains 200 values because it has two
thresholds.
Step 3: Edge detection is performed over the images from the dataset
(edge(orgI, th)), but th is selected using the GS method so that the dataset
containing 100 values with thresholds is also selected for the best value, i.e.,
threshold th that gives the best edge detection. The threshold is selected by
using the GS method by going through the entire dataset and taking the
threshold that gives the best PR, F, and FoM value as the edge detection
threshold. Objective measures require a reference image with an ideal edge
(ground truth) and thus during the edge detection and finding the best
threshold PR, F and FoM are obtained by comparing the ideal image with the
detected edge and the image detected with the current threshold value.
When it comes to the RS3, RS6, and RS9 methods, unlike the GS method
where all values from the dataset are searched to find the best value, here 3,
6, and 9 random values from the dataset are taken.
Step 4: The output is an image with the best detected edges.
Figure 4a,b show the algorithm’s complexity. As evidenced by Figure 4, this
complexity hinges upon the level of detail within the image, specifically the
resolution and dataset size. As the dataset values and resolution increase, the
complexity escalates exponentially. The algorithm demonstrates robust
runtime performance across the tested medical images dataset. Based on
Figure 4, it is noteworthy that using the RS9 method yields notably high
performance even with larger datasets. The findings of this study underscore
the efficacy of RS9, recommending its application for optimizing algorithm
performance with larger datasets.

(a) (b)

Figure 4. Algorithm complexity using GS and RS9: (a) 2D, (b) 3D.

The measured computational time for the GS and RS methods shows

significant differences. GS requires an average of 2.15 s per image and with
memory consumption of 10 MB, while RS reduces the time to 0.87 s with a
minimal memory consumption of 0.01 MB. These results show that RS offers
better computational efficiency for applications that require a fast response,
while GS remains the more accurate choice for situations where time is not a
critical factor. In terms of memory usage, GS and RS9 have minimal
requirements because they work on 2D matrices, while deep learning models
require significantly more resources due to the large number of parameters.
Based on Figure 4, it can be concluded that larger datasets will significantly
compare to the GS method; however, during the research, a larger dataset
was also tested and it was concluded that the proposed method gives good
results with the dataset used in the manuscript, which has 1800 thresholds. In
other words, larger datasets achieve better results, but in real applications
this is not necessary. Computationally, a time comparison between the
traditional methods, the proposed GS and RS9 approaches, and the deep
learning methods shows that GS is the most accurate
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but slowest, and RS is faster with controlled reduced accuracy. CNN models
require more inference time on the GPU, but offer superior noise immunity
and higher accuracy.
The proposed method of estimating thresholds using GS algorithms offers
precise parameter setting for edge detection, but has certain limitations in
terms of computational efficiency, while RS9 provides better optimization of
the use of computer resources. GS, as a deterministic method, requires the
examination of all the possible combinations of thresholds, which increases
the execution time and memory consumption when working with high-
resolution medical images or large datasets. In comparison, RS reduces the
execution time with a trade-off in accuracy, as it randomly selects a subset of
possible thresholds. The main challenge of the proposed method lies in its
scalability to large datasets and high-resolution images. GS can become
computationally inefficient, and future work envisages possible solutions that
include parallel processing, the use of more efficient heuristic methods (e.g.,
Bayesian Optimization), or cloud computing.

3. Results
In Figure 5 [11], the results of edge detection at different image
complexities are given. A total of five detectors (Canny, LoG, Sobel, Prewitt,
Roberts) and three objective measures (F, FoM, PR) were used [9]. Based on
the obtained values of these measures, the quality of the detected edge
depends on the number of details. Based on that fact and the results
accounted for in Figure 5, for LD images, the best edge detection was
achieved by using the Roberts operator, but the Sobel and Prewitt operators
generated similar results. As for the MD images, the Roberts operator led to
the best results. The Canny operator was the best choice for HD images [11].

(a) (b) (c)

Figure 5. The values obtained by applying the standard approach for the images with
LD, MD, and HD using the five edge detectors (a) F, (b) FoM, (c) PR values.

First, edge detection was performed using the standard algorithm, and
then the proposed edge detection approach [11] was used, which selects the
best threshold value based on the random and grid searches to perform the
best possible edge detection.
Figure 6 shows the F values for the LD, MD, and HD images over which
edge detection was performed, and which contain in themselves the salt and
pepper noise with the intensities of 0.01, 0.05, and 0.1, respectively. Detection
was performed over these images for the five detection operators. According
to Figure 6, the best was the Canny detector for all the three complexity
levels. As the noise concentration increased to 0.05 (Figure 6b), Canny
recorded the best results, although all those values were but slightly lower in
comparison with 0.01 (Figure 6a), particularly so for the LD images. As the
noise concentration increased to 0.1 (Figure 6c), the values were considerably
lower, which means that the edge detection itself is worse as well. As in the
previous cases, Canny recorded the best results, and noise considerably
worsened the detection for the LD images. According to Figure 6, it can also
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be concluded that salt and pepper noise had an influence on the edge
detection to a great extent, particularly so in the LD images.

(a) (b) (c)

Figure 6. The F values obtained by applying the standard method for LD, MD, and HD
images in the presence of the salt and pepper noise with the intensities of (a) 0.01, (b)
0.05, and (c) 0.1.

In Figure 7, the F values for the LD, MD, and HD images over which edge
detection was performed and which contain the speckle noise with the
intensities of 0.01 (Figure 7a),
0.05 (Figure 7b), and 0.1 (Figure 7c), respectively, are shown. In the case of
the noise concentration being 0.01, the gradient operators recorded
considerably better results for the LD images in relation to the LoG and Canny
operators. These operators proved to be the better solution for both the MD
and HD image as well. However, when there was a further increase in the
level of noise in the image with the noise with the intensity of
0.05 and when the number of details in the image was small, Prewitt and
Sobel recorded good results, whereas Roberts recorded considerably lower
values, which can be seen in Figure 7. For MD and HD images, the Roberts
operator recorded extremely bad results, particularly so for the MD images.
For the HD images, all the operators, except for the Roberts operator,
recorded quite similar results. Comparing it with Figure 5 which shows the
absence of noise, it can be noticed that the results are satisfactory to a good
extent. With high noise concentration and the speckle noise with the intensity
of 0.1 is concerned, the Canny operator recorded the best results for the MD
and HD images, whereas the Prewitt operator did so for the LD images. In this
case as well, Roberts led to the worst results, i.e., the worst edge detection
whose detection was not usable for further processing. In comparison with
the lower noise concentration, the detection was the worst, i.e., lower F
values were obtained, as expected.

(a) (b) (c)

Figure 7. The F values obtained by applying the standard method for the LD, MD, and
HD images in the presence of the speckle noise with the intensities of (a) 0.01, (b) 0.05,
and (c) 0.1.

Figure 8 shows the F values for the images with LD, MD, and HD over
which edge detection was performed and which contain the Gaussian noise
with the intensities of
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0.01 (Figure 8a), 0.05 (Figure 8b), and 0.1 (Figure 8c), respectively. For
noise with the
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intensity of 0.1, the best results were obtained by using the Sobel and Prewitt
operators. For the MD images, the best results were obtained by using the
Prewitt operator. The Roberts operator also recorded very bad results in this
case as well. The increase in noise concentration to 0.5 and then to 0.1 (Figure
8b,c) allowed one to see the operator’s behaviors similar to one another to a
great extent and the obtained edge detection values. The reason for this is
attributed to the very model of Gaussian noise. Comparing it with Figure 5
showing the absence of any noise at all in the image, however, allows one to
notice that Gaussian noise had a considerable influence on the edge detection
for all the categories of complexity, but the most for the LD images.

(a) (b) (c)

Figure 8. The F values obtained by applying the standard method for the LD, MD, and
HD images in the presence of Gaussian noise with the intensities of (a) 0.01, (b) 0.05,
and (c) 0.1.

If the noise types are compared with edge detection, it can be noticed
that to a great extent, noise exerts an influence on the quality of edge
detection. Salt and pepper and speckle influenced the LD images, particularly
so when there was a greater intensity of noise. When salt and pepper noise is
present, Canny proved to be the best operator for all the three complexity
categories. Canny also generated the best results in the case of the speckle
noise type for the LD and HD images, while the Prewitt operator provided the
best results for LD images. When speaking about Gaussian noise, Prewitt was
the best operator for all the three complexity categories.

3.1. The Results of Edge Detection by Applying the Proposed

Approach Based on the GS Estimating Threshold Value Method
Unlike the previous cases, the proposed approach to the assessment of
the value of the edge detection threshold was based on the grid threshold
search method.
Figure 9 shows the F values for the LD, HD, and MD images over which
edge detec- tion was performed, and which contain the salt and pepper noise
with the intensities of
0.01 (Figure 9a), 0.05 (Figure 9b), and 0.1 (Figure 9c), respectively. According
to Figure 9, the best detection was achieved by applying the Canny operator
for the LD images. For the MD and HD images, the best and similar results
were obtained when applying the Canny and Roberts operators. By increasing
the noise intensity in the image to 0.05, the results accounted for in Figure 9b
were obtained. According to Figure 9, the best detection was achieved for all
the three complexity categories by applying the Canny operator. There was
also identical behavior noticeable for a high concentration of noise in the
image, i.e., when there was the noise intensity of 0.1 in the image (Figure 9c).
However, when the noise intensity was 0.1 in the LD images, the values
were lower in relation to the HD images, which was not the case when a lower
concentration was present. Comparing these results with the results obtained
when the algorithm without improvement and salt and pepper noise was used
(Figure 6), it can be seen that a better edge detection was achieved to a great
extent. Also, comparing this with the results shown
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in Figure 5 when the proposed approach was used but only over the images
without noise, it can be seen that there were very good improvements, i.e.,
very good edge detection, even in the images with a high concentration of
noise.

(a) (b)
(c)

(d) (e) (f)

Figure 9. The F values obtained by applying the proposed approach based upon the
GS threshold search method for LD, MD, and HD images in the presence of salt and
pepper noise with the intensities of (a) 0.01, (b) 0.05, and (c) 0.1 and visual edge
detection on that image using Canny operator for noise intensities of (d) 0.01, (e)
0.05, and (f) 0.1.

Due to the volume of the work, only the detection for the Canny operator
is shown when the sum intensity was 0.01, 0.05, and 0.1. The images for the
other edge detection operators are also available on request. Comparing this
image with the results when the standard approach was used, it is noticed
that when the intensity of the sum was small, and the number of details was
medium, better results were obtained. As can be seen from the results, the
best results were obtained for a small number of details in the image.
Figure 10 shows the F values for the LD, MD, and HD images over which
edge detection was performed, and which also had speckle noise with the
intensities of 0.01 (Figure 10a),
0.05 (Figure 10b), and 0.1 (Figure 10c), respectively.
The best detection for all the levels of details in the image was achieved
by applying the Canny operator for a low concentration of noise, i.e., 0.01
(Figure 10a). When the noise in the image had the intensities of 0.05 (Figure
10b) and 0.1 (Figure 10c), the best results were also recorded by using the
Canny operator. Although the values were slightly lower in the case of a high
noise concentration, better results were to a great extent obtained by
applying the proposed approach based upon the grid threshold search
method. If it is compared with the situation when there was salt and pepper
noise for the LD images, the values were better in relation to speckle noise, so
that salt and pepper affected the edge detection more, whereas the influence
was to a great extent similar in the case of the MD and HD images. Figure
10d–f show the detection for the Canny operator for all three levels of speckle
sum intensity in the image. Also, as in the previous case, the best results
were achieved for a low intensity in the image, but were visibly better than the
original approach.
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(a) (b) (c)

(d) (e) (f)

Figure 10. The F values obtained by applying the proposed approach based on the GS
threshold search method for LD, MD, and HD images in the presence of the speckle noise
with the intensities of
(a) 0.01, (b) 0.05, and (c) 0.1 and visual edge detection on that image using Canny
operator for noise intensities of (d) 0.01, (e) 0.05, and (f) 0.1.

Figure 11 also shows the F values for the images with LD, MD, and HD
over which edge detection was performed, which on their part also contain
the Gaussian noise with the intensities of 0.01 (Figure 11a), 0.05 (Figure
11b), and 0.1 (Figure 11c), respectively.

(a) (b) (c)

(d) (e) (f)

Figure 11. The F values obtained by applying the proposed approach based on the GS
threshold search method for LD, MD, and HD images in the presence of Gaussian noise
with the intensities of
(a) 0.01, (b) 0.05, and (c) 0.1 0.1 and visual edge detection on that image using Canny
operator for intensities of (d) 0.01, (e) 0.05, and (f) 0.1.
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As in the previous cases, the Canny operator recorded the best results for
all the three complexity categories and for all the three noise intensity levels.
In comparison with the previous noise types, a lower value was only recorded
for the LD images, whereas better results were obtained for the MD and HD
images when there was the Gaussian noise type with a great noise intensity
in the image. The results show that even in this case, an improvement was
made if detection is compared with the results when the proposed ap- proach
was not used. Comparing the results obtained for the Canny operator and
when the Gaussian sum was present for all three intensities, the new method
achieved significantly better results compared to the standard one, so it
detected the edge very efficiently.
Figure 12 shows what can be seen that when the Rician type of noise
intensity was present. Figure 12 shows the results for (a) 0.05, (b) 0.1, and (c)
0.15, and the F values are shown. Figure 12 also shows the edge detection
when the Canny operator was applied, while Figure 12g–i show the detection
when the Sobel operator was applied for the de- scribed noise intensity. The
results show that when Rician noise was present, algorithms based on a
simple technique with masks such as Sobel, Prewitt, and Roberts gave better
results than by using the Canny and LoG edge detection methods, especially
when low- and medium-intensity noise was present. By comparing the one
shown in Figure 12 with the results shown in Figure 9, Figure 10, and Figure
12, it can be seen that the GS method, when Rician noise of low and medium
intensity is present, is much more effective than if methods such as Sobel,
Prewitt, and Roberts are used. Also, the conclusion is reached when the GS
method is effective and when a high intensity of Rician noise is present.

3.2. The Results of Edge Detection by Applying the Proposed

Approach Based on the RS9 Estimating Threshold Value Method
This section presents the results of the testing of the proposed approach
to the assess- ment of the values of the edge detection threshold based on
the random threshold search method, i.e., on the nine random threshold
values from the base. In the results obtained so far, this approach has proven
to be quite efficient in respect to the execution speed and the obtained
results.
Figure 13 shows the F values for the LD, MD, and HD images over which
edge detection was performed, and which contain the salt and pepper noise
with the intensities of 0.01 (Figure 13a), 0.05 (Figure 13b), and 0.1 (Figure
13c), respectively. Figure 13d–f show the detection for the Canny operator
when it was the used approach based on nine random values for the
threshold for the images with salt and pepper noise with 0.01, 0.05, and
0.1 intensities.
When there was a small 0.01 noise concentration in the image (Figure
13a), the best detection was achieved through the Canny operator for the LD
and MD images, whereas the Roberts operator generated the best results for
the HD images. Comparing it with the approach when three and six threshold
values were used, the results were better when there were three values, but
they were alike to quite an extent when six values were used. Further
increasing the noise to 0.05 (Figure 13b) with this approach, the detection was
better in relation to the three or six values for all the operators. The Roberts
operator achieved the best detection for all the three complexity levels. Under
the conditions of high noise with an intensity of 0.1 (Figure 13c), the results
behaved in a comparable way to that for the detection of the six-threshold
value approach. However, comparing the results presented in Figure 13, the
values are greater by applying this approach. The best detector for all the
three complexity categories is the Roberts operator, but the other operators
also recorded comparable results. It should be mentioned that all these
results are considerably better in relation to the situation when the standard
approach was applied.
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(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 12. The F values obtained by applying the proposed approach based on the GS
threshold search method for LD, MD, and HD images in the presence of Rician noise
with the intensities of
(a) 0.05, (b) 0.1, and (c) 0.15 and visual edge detection on that image using Canny
operator for noise intensities of (d) 0.01, (e) 0.1, and (f) 0.15 and for Sobel (g) 0.05, (h)
0.1, and (i) 0.15.

Figure 14 also shows the F values for the LD, MD, and HD images over
which edge detection was performed, and which also contained speckle noise
with the intensities of
0.01 (Figure 14a), 0.05 (Figure 14b), and 0.1 (Figure 14c), respectively. Figure
14d–f show the detection for the Canny operator when it was the used
approach based on nine random values for the threshold for the images with
speckle noise with 0.01, 0.05, and 0.1 intensities.
The Canny detector recorded the best results when noise with the
intensity of 0.01 of the speckle noise type in the LD images. However, good
detection was also achieved by the other operators, except for the Roberts
operator. The Roberts operator recorded the best detection for the MD and HD
images. A further increase in noise to an intensity of 0.05 led to the detection
in which the Prewitt operator achieved the best results for the LD images,
whereas the Sobel, Prewitt, and Roberts operators recorded comparable
results for the MD and HD images. Also, the Canny operator recorded good
detection for the HD images. In the case when the intensity of noise in the
image was 0.1, the Prewitt operator recorded the best detection for all the
three complexity levels, but the values generated by the other operators were
approximate for the HD images.
Figure 15 shows the F values for the LD, MD, and HD images over which
edge detection was performed, and which were affected by Gaussian noise
with the intensities of 0.01 (Figure 15a), 0.05 (Figure 15b), and 0.1 (Figure
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15c), respectively. Figure 15d–f show
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the detection for the Canny operator when it was the used approach based on
nine random values for threshold for the images with Gaussian noise with
0.01, 0.05, and 0.1 intensities.

(a) (b) (c)

(d) (e) (f)

Figure 13. The F values obtained by applying the proposed approach based on the
RS9 threshold search method for LD, MD, and HD images in the presence of salt and
pepper noise with the intensities of (a) 0.01, (b) 0.05, and (c) 0.1 and visual edge
detection on that image using Canny operator for noise intensities of (d) 0.01, (e)
0.05, and (f) 0.1.

(a) (b) (c)

(d) (e) (f)

Figure 14. The F values obtained by applying the proposed approach based on the
RS9 threshold search method for LD, MD, and HD images in the presence of speckle
noise with the intensities of
(a) 0.01, (b) 0.05, and (c) 0.1 and visual edge detection on that image using Canny
operator for noise with intensities of (d) 0.01, (e) 0.05, and (f) 0.1.
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(a) (b) (c)

(d) (e) (f)

Figure 15. The F values obtained by applying the proposed approach based on the
RS9 threshold search method for LD, MD, and HD images in the presence of Gaussian
noise with the intensities of
(a) 0.01, (b) 0.05, and (c) 0.1 and visual edge detection on that image using Canny
operator for noise intensities of (d) 0.01, (e) 0.05, and (f) 0.1.

When there was a noise intensity in the image of 0.01, Figure 15a allows
one to notice that the values are to a great extent similar to when there were
six random values, which can be seen in Figure 15a, but there is still
improvement, particularly so in regard to the Canny operator. The Sobel and
Prewitt operators achieved the best detection for all the three complexity
levels. For the HD images, Canny and Roberts achieved almost equal
detection. When the intensity of noise in the image was 0.05 (Figure 15b), the
situation was quite similar even when there was a lower noise concentration
(which was expected due to the very nature of noise) and exerted an
influence on the Canny operator when there were LD images. When the
intensity of noise in the image was 0.1 (Figure 15c), it could be noticed that it
influenced the Canny operator and LD images the most, whereas the
detection was similar for the other operators to what it was under the
previous conditions of noise concentration for all the complexity categories.
Figure 16 shows what can be seen that when the Rician type of noise
intensity was present. Figure 16 shows the results for (a) 0.05, (b) 0.1, and (c)
0.15 where the F values are shown. Figure 16 also shows the edge detection
when the Canny operator was applied, while Figure 16g–i show the detection
when the Sobel operator was applied for the de- scribed noise intensity. The
results show that when Rician noise is present, algorithms based on mask
techniques such as Sobel, Prewitt, and Roberts give better results than by
using the Canny and LoG edge detection methods, especially when low- and
medium-intensity noise was present. By comparing the obtained results with
the results when the other types of noise were present, it can be seen that
the proposed method using Sobel, Prewitt, and Roberts operators is more
efficient than Canny and LoG.
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(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Figure 16. The F values obtained by applying the proposed approach based on the
RS9 threshold search method for LD, MD, and HD images in the presence of Rician
noise with the intensities of
(a) 0.05, (b) 0.1, and (c) 0.15 and visual edge detection on that image using Canny
operator for noise intensities of (d) 0.01, (e) 0.1, and (f) 0.15 and for Sobel (g) 0.05, (h)
0.1, and (i) 0.15.

Recent advances in edge detection algorithms emphasize deep learning

techniques. Notable methods include DeepEdge, which combines
classification and regression, and Holistic Edge Detection (HED) that employs
multi-scale deep learning for hierarchical edge representations [25,26]. The
solution named LPCB improves HED with VGG16 (Visual Geometry Group),
while ECDN uses a convolutional codec for better edge localization. PiDinet
introduces a pixel difference convolution operator, and CHRNet maintains
high- resolution edge maps. Both papers show that Canny is the best option
when the use of a regular algorithm is necessary, but the DL and ML
approaches give better results [27]. In [28,29], more focus was gained to
overview and review the state of the art in edge detections using regular and
DL algorithms. The paper [30] used Dynamic Threshold Neural P Systems
with Orientation (ODTNP), a neural-like computing model designed to
overcome the common edge detection shortcomings such as discontinuous
edges, weak edges, noise sensitivity, and difficulty in setting the gradient
thresholds. In [25–30], the BSD500 dataset and performance metrics such as
precision, recall, F-score, ODS, and OIS are used for evaluating these
algorithms’ effectiveness in edge detection, but there is no computational
time for these algorithms and approaches. In [7], a method is proposed to
address the challenge of edge detection in noisy digital images. The approach
involves partitioning the image into equal segments and calculating an initial
threshold for each
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segment based on the highest frequency of brightness intensity rather than

the mean brightness, which is adversely affected by noise. The experimental
results demonstrate the method’s effectiveness, with a PSNR (Peak Signal to
Noise Ratio) of 61.4896 for one test image compared to lower values
achieved by the baseline methods. This indicates the proposed method’s
robustness in maintaining the edge continuity and clarity despite the
presence of noise, but there are only PSNR metrics which are not fully
reliable. Also, there is no computational time. As Canny proved to be the best
edge operator in [31], the authors reconfigured the Canny detector and its
hardware realization for noisy images.
Although the grid and random search approach optimizes the threshold
values effi- ciently, the computational cost can still be significant, especially
for high-resolution images or large datasets, especially if using the GS
method. Based on the results where the images from the medical dataset
were used and where different sum intensities were used, a large number of
examples of images found in everyday cases were covered. Datasets have
images that are from real examples, so by categorizing them into groups by
the different numbers of details and different intensities of noise, this
algorithm becomes meaningful. However, using a larger number of images
leads to better results, especially using the GS method, but this is also a
potential limitation of the algorithm because it may require considerable
memory resources to store and process the numerous threshold values and
intermediate results, which can be a constraint on systems with limited
memory capacity. The proposed method has been primarily tested on the BSD
dataset and after that on the medical datasets, which consist of real example
images with specific characteristics. Its performance on other types of
images, such as medical images, satellite images, or images from other
domains with different noise characteristics, remains to be studied in future
directions, especially when noise and compression are present. Considering
that a larger database of images, especially specialized images, can be
tested, the future direction may be the specialized optimization of the
algorithm under conditions of images when noise or compression is present.
Therefore, the optimization and application of parallel processing techniques
can help distribute the computing load across multiple processors, reducing the
time required for optimization. This may involve using GPU or cloud-based
computing resources. For each image category, the edge detection
performance of five models was evaluated: AlexNet, ResNet, VGGNet,
MobileNetv2, and Inceptionv3. Performance was measured using the F-score
metric, where images were exposed to different types of noise and different
intensities. Figure 17 shows a comparison of the salt and pepper noise intensi-
ties of (a) low (0.01), (b) medium (0.05), and (c) high (0.1). Figure 18 shows a
comparison for speckle noise intensities of a) small (0.01), (b) medium (0.05),
and (c) large (0.1). Figure 19 shows a comparison of Gaussian noise
intensities of (a) small (0.01), (b) medium (0.05), and (c) large (0.1). Each of
these models has specific architectural features that affect their edge
detection ability and noise immunity. AlexNet is one of the first deep
convolutional neural network (CNN) models to achieve significant success in
the ImageNet competition. AlexNet has a relatively simple architecture with
eight layers (five convolutional and three fully connected layers). This model
is good for basic detection tasks, but may have lim- itations in more complex
scenarios. ResNet is known for its 50-layer deep architecture, using “residual”
connections that allow gradients to flow more efficiently through the net-
work. This model is very robust and efficient in complex detection and
classification tasks. VGG-16 is a deep convolutional network with 16 layers,
known for its simple and uniform architecture. All the convolutional layers use
3 × 3 filters, which allows for the more accurate detection of the local
features. However, this model may be sensitive to noise due to its deep
structure. MobileNetv2 is an optimized version of the MobileNet architecture,
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which uses “depthwise separable convolutions” to reduce the number of
parameters and computational requirements. This model is ideal for
applications on resource-constrained
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devices, but may show different performance depending on the type of noise.
Inceptionv3 is a complex model that uses multiple convolutional filters of
different sizes in each layer. This architecture allows for better edge detection
in the presence of complex noises, but can be computationally demanding.

(a) (b) (c)

Figure 17. Comparison of proposed approach and other approaches using Canny edge
detection on the noisy image affected by salt and pepper: (a) low intensity, (b) medium
intensity, and (c) high intensity.

(a) (b) (c)

Figure 18. Comparison of proposed approach and other approaches using Canny edge
detection on the noisy image affected by speckle: (a) low intensity, (b) medium
intensity, and (c) high intensity.

(a) (b) (c)

Figure 19. Comparison of proposed approach and other approaches using Canny edge
detection on the noisy image affected by Gaussian: (a) low intensity, (b) medium
intensity, and (c) high intensity.

The proposed approach shows a significant advantage in edge detection

compared to other methods. The difference in the quality of edge detection
between the proposed approach and alternative methods is visible. The
proposed model retains more details and has less noise, which shows better
efficiency. Although the proposed approach shows a better edge detection
ability in most cases, the high intensity of salt and pepper noise presents a
significant challenge. In some cases, alternatives such as methodologies
based on median filtering or adaptive thresholding may show better
robustness to the high
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intensity of this type of noise. Such approaches can preserve more detail in
some scenarios, especially when the noise intensity is extremely high.
Although the proposed model shows solid performance, at a moderate
Gaussian noise intensity, methods that combine Gaussian filtering with
sophisticated edge detection algorithms can show better results in certain
aspects, such as edge smoothness and noise reduction without a significant
loss of detail. As the noise intensity increases, the performance of all the
methods decreases. However, the proposed approach still shows good results.
The difference in performance is still significant, but slightly less pronounced
than at a low intensity. At a high noise intensity, all the models experience a
large drop in performance. Nevertheless, the proposed approach manages to
maintain relatively better results, with clearer edges and less noise. The
difference compared to other models is smaller, but still significant. In these
cases, methods using advanced speckle noise filtering techniques, such as
Wavelet decomposition, can provide better results in certain aspects, such as
preserving the edge structure while reducing noise.
There are more advanced models within machine learning that belong to
the subcat- egory of deep learning such as DexiNet (Dense Extreme Inception
Network) [32], LDC (Lightweight Dense CNN) [33], or CATS (Context-Aware
Tracing Strategy) [34]. DexiNet is a deep learning model designed for edge
extraction in images, known for its extremely detailed edge detection. It uses
an architecture inspired by Inception blocks, but is modified to include dense
connectivity and multiscale feature extraction. The goal of the model is to
identify the edges of objects in images with a higher level of detail, especially
in scenarios where the edges are thin and indistinct. They are used for
multiscale analysis, allowing the model to identify edges at different
resolutions. Each layer is connected to all the previous layers, thus improving
the feature propagation and optimization during training. Thanks to the
densely connected architecture and multiscale analysis, it is suitable for
images with a large number of details, but also for images covered by forest.
However, due to its architecture, DexiNet requires significant processing
resources [32]. Even better results are shown by the LDC method, which is
also based on the DexiNet algorithm; however, in order to seek a better
compromise between performance and application, a smaller filter size and
compact modules were considered. As a result of the modification, a model
with less than 1 M parameters is obtained, which is fifty times smaller than
Dex- iNet, as well as lighter than most state-of-the-art approaches [33]. CATS
is a model based on a context-aware tracking strategy for ivic detection based
on an observation that the localization ambiguity of deep edge detectors is
mainly caused by the mixing phenomenon of convolutional neural networks:
feature mixing in edge classification and side mixing during fusing side
predictions [34]. The results in the paper [34] show that CATS provides better
detection than RCF (Richer Convolutional Features) and BDCN (Bi-Directional
Cas- cade Network) by factors of 12% and 6%, respectively, when evaluating
without using the morphological non-maximal suppression scheme for edge
detection [34]. AI models have demonstrated state-of-the-art performance in
edge detection tasks, especially in complex and noisy images. However, it is
important to note that AI-based solutions, particularly deep learning models,
are not entirely robust or safe. Recent studies have demonstrated that even
minor perturbations, such as changing the value of a single pixel, can
drastically alter the results of classification or edge detection. This
phenomenon, known as adversarial attack, raises concerns about the reliability
of AI in sensitive domains like medical imaging. For instance, in [35], it is
highlighted how adversarial attacks could compromise medical image
classification, emphasizing the need for robust AI models that are resilient to
such manipulations. This represents an important challenge for future work,
particularly in ensuring the robustness of AI-based edge detection methods
under adversarial conditions.
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DL models like DexiNet, LDC, and CATS and hyperparameter optimization

methods like Random Search and Grid Search discussed in the paper cannot
be directly compared because they have fundamentally different purposes and
functions within machine learning. DL models are complex architectures
designed for specific tasks such as edge detection, semantic segmentation,
and spatio-temporal analysis, where the model is trained on large amounts of
data to directly achieve specific results. On the other hand, Random Search
and Grid Search are techniques used to optimize the hyperparameters within
a model, regardless of which model is used, with the aim of improving the
performance of already existing algorithms. While DL models learn from data
and directly affect the performance in specific tasks, Random Search and Grid
Search only optimize the model parameters and are not directly related to the
learning and data processing process, but indirectly. Table 1 shows the
characteristics of the model for parameter optimization and the model that
directly affects edge detection.

Table 1. Characteristics of the edge detection model.

Characteristi DexiNet LDC CATS RS9 GS

c
Parameter Parameter
Category DL DL DL optimization optimization
(indirect DL) (indirect DL)
Variable: depends
Medium:
Computation on the size of the
depends on the
al complexity High Medium High search space and
number of
the number of
combinations in
hyperparameters
the search space
Time High Medium High Low Medium
requirement training training training training training
s’ impact on requiremen requirements requiremen requiremen requirements
model ts ts ts
Directly affects Indirectly through
performance
Directly performance Directly Indirectly optimization
affects affects through
Adaptable to
performance Specific tasks: performance optimization
Application any ML model
Edge
Adaptable to for
Specific tasks: detection in Specific tasks:
any ML model hyperparameter
Edge images, Edge
for optimization,
detection in computer detection in
hyperparameter e.g., edge
images, vision images,
optimization, detection
computer computer
e.g., edge
vision vision
detection

Edge-preserving filtering such as Sigma Filter, Anisotropic Diffusion,

Bilateral Filter, and Non-Local Means (NLMs) are widely applied in noise
reduction while preserving the key desired information. Although these filters
effectively reduce the noise in images, their application can significantly
affect the optimization process of the edge detection algorithm. Including
additional filtering before edge detection introduces an additional step that can
upset the existing balance between the computational complexity and
detection accuracy. Considering that the Canny algorithm showed the best
results while preserving performance, it is recognized as a proctor for
improving the existing preprocessing such as regarding the difference
between an original image and the image processed using edge-preserving
filtering. The focus of this work was on the direct impact of noise on the
performance of edge detection algorithms, thus avoiding additional
interventions that could obscure the interpretation of the results and the
effectiveness of the proposed approach. Nevertheless, the difference between
the original image and the image filtered by using edge-preserving
techniques can provide additional information which is useful for improving
edge detection, especially in environments with a high level of noise, and the
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absence of such filters can be cited as a shortcoming of the algorithm. The
integration of these techniques with the proposed method represents a
promising direction for future
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research, where their influence on the trade-off between noise reduction, edge
preservation, and computational efficiency of the algorithm would be examined
in detail.

4. Contributions
The results make a contribution to the field of medical image processing,
with a special emphasis on edge detection in images affected by different
types of noise. The key contributions of the paper can be summarized as
follows:
Two proposed methods were tested for evaluating the optimal edge
detection thresh- olds over medical images affected by different types and
intensities of noises that are mainly found in nature images.
First, a GS method that searches the threshold parameter and provides
the most accurate edge detection results was tested. The testing has shown
that GS achieves the maximum F-measure even for highly complex images
(with a high number of details), which confirms its accuracy in difficult
conditions.
Second, the RS9 method significantly reduces the processing time (0.75 s
per image) with minimal memory usage (0.01 MB), providing a balance
between efficiency and accu- racy. This contribution is particularly significant
for real-time applications and applications in systems with limited computing
resources.
Also, a comparative analysis of the performance of five traditional
detectors (Canny, LoG, Sobel, Prewitt, and Roberts) on medical images
affected by different noises is pre- sented: salt and pepper, speckle, Gaussian,
and Rician noise. The Canny operator achieves the best edge detection
accuracy on images with Gaussian and speckle noise, especially when a high
complexity exists. The Sobel and Prewitt operators show greater resistance to
Rician noise, while the results are stable on images of medium complexity.
The Roberts operator gives the most efficient results for low-complexity
images, with a significantly shorter execution time. These results provide a
clear framework for algorithm selection depending on the complexity of the
image and the type of noise present.
Compared with deep learning methods, the proposed approach shows the
following results: With regard to the execution time, GS requires 7.35 s per
image, while RS9 achieves processing in 0.75 s, thus confirming its suitability
for applications that require fast data processing. For memory load, the RS9
has negligible memory usage (0.01 MB), while DL models require significantly
more resources due to the large number of parameters and the need for GPU
inference. By comparison with CNN models (e.g., U-Net, DexiNet, and LDC), it
was concluded that the traditional threshold optimization methods, especially
RS9, offer a sufficiently high accuracy with far lower computational usages.
By testing on images with three levels of complexity (low, medium, and high)
and different noise intensities (0.01, 0.05, and 0.1), the robustness of the
proposed methods was confirmed. Threshold optimization enables efficient
edge detection even in high-noise images, thus contributing to the better
segmentation of structures in medical images. The research results are
directly applicable in medical image processing.
The proposed approach can improve edge detection, especially when
there is noise in the image, for example the detection of blood vessels in
retinal images, which is crucial for the early recognition of diabetic
retinopathy or the segmentation of tumor edges in brain MRI images,
enabling the more precise monitoring of changes or the detection of nodules
in lung CT scans, which facilitates the early detection of malignancy. The
proposed approach shows robust performance even in the presence of noise,
while its efficiency in terms of time and memory requirements opens
possibilities for application in systems with limited resources, as well as in
real-time applications for medical diagnostics.
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As part of the contribution, the potential directions for further
development are iden- tified, such as the integration of an edge-preserving
filter (Bilateral Filter, Anisotropic
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Diffusion) to improve the edge detection in images with extreme noise levels.
The optimiza- tion of the execution time can be achieved through the parallel
processing and application of Bayesian Optimization algorithms. The
development of hybrid systems that combine the advantages of traditional
algorithms with deep learning methods can achieve an optimal balance
between the accuracy and speed. One of the potential limitations is the
longer execution time of the GS method with larger datasets. Nevertheless,
the research results show that the proposed number of thresholds and the
tested dataset provide good enough results, and it is not necessary to
additionally increase the volume of datasets for practical applications (except
in cases where a specific application requires it). On the other hand, the RS9
method shows significantly less sensitivity to the size of datasets and
successfully maintains the efficiency, even when applied to larger datasets.

5. Conclusions
In the paper, an analysis of the impact of noise on edge detection was
conducted as well as a comparative analysis of the impact of noise on the
effectiveness of the proposed threshold value estimation approach [9]. For
the analysis of a medical images dataset together with its appropriate
reference, an ideal-edge image (ground truth) was used. The analysis was
performed for the noise types, namely salt and pepper, speckle, Rician, and
Gaussian. For each noise type, a different intensity, i.e., different
concentrations of noise in the image (0.01, 0.05, and 0.1, respectively), was
used. The images were categorized as per their complexity (low, medium, and
high), which was determined based upon the spatial information in the image.
The results of the analysis show that the proposed approach was quite
suitable when images affected by noise are concerned, particularly so when
the Canny operator was applied. The approach has demonstrated remarkable
resilience across the varied terrains of noise. Also, the findings not only
underscore the importance of a tailored threshold value estimation method
but also highlight its adaptability to different noise scenarios. This adaptability
is particularly vital in the real-world application of edge detection, where
images often contend with a multitude of noise sources. Furthermore, the
categorization of images into complexity classes based on their spatial
characteristics has enriched our understanding of noise’s impact. We
observed that the effectiveness of the proposed approach remains
consistent, regardless of an image’s complexity. This observation bodes well
for practical applications, as real-world images are seldom uniform in their
spatial characteristics.
The results provide a good analysis and a good comparison for further
research efforts, such as the optimization of the access parameters with the
help of machine learning for image filtering in the presence of noise. The
findings presented in this study offer a strong foundation for future research
endeavors, in particular, the application of machine learning techniques for the
optimization of edge detection parameters in noisy conditions. Machine
learning’s adaptive capabilities may offer a dynamic solution to the persistent
challenge of noise in image processing. This avenue of research has the
potential to refine the existing techniques achievable in real-world
applications.
The direction of future research will be the additional optimization of
algorithms over a dataset consisting of a larger number of images, as well as
specialized images such as MRI, CT, satellite images, etc. and also the
application of new optimization techniques, especially those based on deep
learning and machine learning.

Author Contributions: Conceptualization, V.M.; Methodology, V.M. and B.J.;

Software, V.M. and M.M.; Validation, V.M., M.M., J.T. and L.M.; Writing—original draft, V.M.
and J.T.; Writing—review & editing, B.J. All authors have read and agreed to the
Sensors 2025, 29 of
25, 87 33
published version of the manuscript.

Funding: This research received no external funding.

Sensors 2025, 30 of
25, 87 33

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: The data supporting the findings of this study are
derived from the Kaggle website which is publicly accessible at
https://www.kaggle.com/datasets/beosup/lung- segment (accessed on 12 November
2024) for the lung segmentation dataset, https://www.kaggle.
com/datasets/nikhilroxtomar/brain-tumor-segmentation (accessed on 12 November
2024) for the brain tumor segmentation dataset, and
https://www.kaggle.com/datasets/andrewmvd/drive- digital-retinal-images-for-vessel-
extraction (accessed on 12 November 2024) for the Retina dataset. The dataset
includes images and their ground truth edge maps used in our analysis. Simulated
noisy images and the results of the edge detection experiments can be obtained from
the corresponding author upon reasonable request.

Referenc Conflicts of Interest: The authors declare no conflicts of interest.

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