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The main purpose of this article was to study existing image processing methods, binarization and noise reduction, and to develop an improved adaptive thresholding algorithm. The analysis of methods and tools for eliminating distortions in image and video signals is an urgent task in numerous fields...
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Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
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| author | Денисюк, Орест Наконечний, Ростислав |
| author_facet | Денисюк, Орест Наконечний, Ростислав |
| author_institution_txt_mv | [
{
"author": "Орест Денисюк",
"institution": null
},
{
"author": "Ростислав Наконечний",
"institution": null
}
] |
| author_sort | Денисюк, Орест |
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| collection | OJS |
| datestamp_date | 2024-10-19T19:01:15Z |
| description | The main purpose of this article was to study existing image processing methods, binarization and noise reduction, and to develop an improved adaptive thresholding algorithm. The analysis of methods and tools for eliminating distortions in image and video signals is an urgent task in numerous fields, including medicine, computer vision, and document science. The article discusses in detail the existing binarization and noise reduction methods, highlighting their advantages and limitations. However, the main achievement is the development and implementation of an improved adaptive thresholding algorithm. This algorithm considers the specific features of the image and automatically adapts the binarization threshold for better processing quality. It is a significant contribution to the field of image processing and can be used in various fields, including medical diagnostics and visual object detection in images. |
| doi_str_mv | 10.15407/fmmit2023.38.058 |
| first_indexed | 2026-06-09T01:10:31Z |
| format | Article |
| fulltext |
58
УДК 681.3.01+681.325
DOI10.15407/fmmit2023.38.058
Analysis and improvement of methods and means for
eliminating distortions in image and video signals
Orest Denysiuk1, Rostyslav Nakonechnyi2
1Master student at Lviv Polytechnic National University, 12, Bandera Str, Lviv, 79013, email:
orest.denysiuk.mkiks.2022@lpnu.ua
2Ph.D., Assoc. Prof at Computer Engineering Department of Lviv Polytechnic National University, 12, Bandera Str,
Lviv, 79013, email: rostyslav.a.nakonechnyi@lpnu.ua
The main purpose of this article was to study existing image processing methods, binarization and
noise reduction, and to develop an improved adaptive thresholding algorithm. The analysis of
methods and tools for eliminating distortions in image and video signals is an urgent task in
numerous fields, including medicine, computer vision, and document science. The article discusses
in detail the existing binarization and noise reduction methods, highlighting their advantages and
limitations. However, the main achievement is the development and implementation of an
improved adaptive thresholding algorithm. This algorithm considers the specific features of the
image and automatically adapts the binarization threshold for better processing quality. It is a
significant contribution to the field of image processing and can be used in various fields,
including medical diagnostics and visual object detection in images.
Keywords: Adaptive thresholding, Analysis of image processing methods,
Image binarization, improved adaptive thresholding algorithm, Reducing noise
in images.
Introduction. In the field of image processing, converting raw visual data into a more
advanced and usable form is a fundamental step. Whether it's document identification,
medical diagnostics using X-rays, or a host of other applications, image processing
plays an important role in extracting meaningful information from visual content.
However, this conversion process is often accompanied by various challenges, one of
the most important of which is noise.
Noise in the context of images refers to unwanted variations or distortions that
interfere with the discernment of the image's essence. Overcoming this challenge is
essential for accurate and reliable image analysis. In this study, we thoroughly
investigate various image processing techniques, in particular those designed to reduce
noise and perform adaptive thresholding. Our goal is not only to introduce and analyze
these methods but also to present an improved adaptive thresholding algorithm as a
valuable addition to the existing arsenal of techniques.
mailto:orest.denysiuk.mkiks.2022@lpnu.ua
mailto:rostyslav.a.nakonechnyi@lpnu.ua
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59
The methods studied include median equalization [1], Gaussian equalization [2],
bilateral equalization [3], Gathos thresholding [4], maximum entropy thresholding [5],
wavelet transform [6], a mathematical method for analyzing signals and images, finds
various applications in the field of medicine due to its ability to analyze signals and
images with high resolution in both the time and frequency domains. Recently, it has
been widely used for medical purposes to store, compress and transmit large data sets,
as well as to analyze biomedical signals such as (ECG) and (EEG).Sauvola
thresholding [7], Bernsen thresholding [8], Niblack thresholding [9], and the improved
adaptive thresholding algorithm. Each of these methods is thoroughly investigated in
terms of their applicability, advantages, and limitations.
The essence of "intelligent" programs is that using data from sensors that signal
changes in environmental parameters as quickly and as accurately as possible, special
algorithms engage higher-level automation to perform adequate actions. CPS goes
beyond the conventional product, system, and application architecture [10].
They combine traditional information technologies: from receiving data from sensors
with their processing using built-in computing power or using cloud technologies, to
traditional operational control and management technologies [11].
There are many needs for filtering signals in images. Digital images are exposed
to various types of noise during capture, storage, or other factors affecting their quality,
so it is necessary to remove these noises by preserving the image as much as possible
[12]. In today's world, images and videos are everywhere. From video surveillance to
medical imaging and entertainment, they are essential to our lives. However, these
images and videos often contain large amounts of data that require a significant amount
of memory and bandwidth. This led to the development of various methods of reducing
the size of image and video signals while preserving their quality. Despite these efforts,
images and video signals can still be distorted by various factors such as noise,
compression, and transmission errors [13]. A noisy image becomes a problem for
information retrieval. The process begins with improving the quality of the image by
applying various filters that can subjectively improve the image [14].
Eliminating distortion in video and image signals is critical for a variety of
reasons, ranging from aesthetic considerations to technical requirements [15, 16].
Distortions can significantly degrade the quality of the result, making it difficult to
view or interpret. It can alter the colors and contrast [17].
1. Median equalization
The Median Equalization method is based on analyzing and modifying the
histogram of an image. The main goal is to equalize the distribution of pixel brightness
using the median of the histogram. Let's take a closer look at this method using
mathematical formulas.
The Median Equalization method is based on the analysis of the histogram of
pixel brightness in the input image. A histogram is a graphical representation of the
number of pixels for each brightness value from 0 to 255 (in the case of 8-bit images).
Steps of the method:
Orest Denysiuk, Rostyslav Nakonechnyi Analysis and improvement of methods and means for
eliminating distortions in image and video signals
60
Histogram calculation: First, a histogram is created, where the X-axis shows the
brightness value, and the Y-axis shows the number of pixels with this brightness value
in the image.
Finding the median: The median of a histogram is defined as the luminance
value that divides the histogram into two equal halves. This means that half of the
pixels have luminance less than or equal to the median, and the other half have
luminance greater than or equal to the median.
Replace pixel values: Each pixel in the image is replaced with the median value.
This results in a luminance distribution in which half of the pixels have a value less
than or equal to the median and the other half have a value greater than or equal to the
median.
The median has a value of that divides the histogram into two equal planes
below the histogram graph. This can be expressed mathematically as:
𝑚 = 𝑎𝑟𝑔𝑚𝑖𝑛
𝑖
|∑𝐻(𝑗)
𝑖
𝑗=0
− ∑ 𝐻(𝑗)
255
𝑗=𝑖+1
|
where 𝐻(𝑗) −intensity (brightness) of pixels in the image.
Advantages of the Median Equalization method:
Improved contrast: By equalizing the brightness distribution, the image becomes more
contrast, and details stand out.
Reduces the effect of "overexposure" and "backlighting": Areas that are too bright or
too dark become less visible.
Limitations of the Median Equalization method:
Loss of information: Because all pixels with the same brightness are replaced by the
median, some detail may be lost.
Computational complexity: Calculating the histogram and median can be
computationally intensive, especially for large images.
The result of the algorithm is shown in Figure 1:
Fig.1 Median filter realization
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2. Gaussian equalization
Gaussian Equalization is another effective image-processing method for improving
contrast and equalizing brightness distribution. This method uses the Gaussian function
to modify the brightness of pixels, which helps to make the image more expressive and
preserve its details.
The Gaussian Equalization method is based on the idea of using the Gaussian function
to create a new distribution of pixel brightness. The main goal is to make the pixel
brightness distributed according to a Gaussian law, where values close to the mean
have a higher probability of occurrence and values that deviate from the mean have a
lower probability.
Steps of the method:
Generation of the Gaussian function: First, a Gaussian function is created that defines
the new pixel brightness distribution. The Gaussian function has parameters, such as
mean ( ) and variance ( ), which can be adjusted as needed.
Replace pixel values: Each pixel in the image is replaced with a value determined by
the Gaussian function of its original brightness.
The Gaussian function has the following form:
𝐺(𝑥, 𝑦) =
1
2𝜋𝜎2
𝑒
−
(𝑥2+𝑦2)
2𝜎2
Advantages of the "Gaussian Equalization" method:
Improved contrast: By distributing the brightness according to a Gaussian law,
the image becomes more contrasty and expressive.
Preservation of details: This method improves contrast without losing detail in
the image.
Limitations of the Gaussian Equalization method:
Computational complexity: Calculating the Gaussian function for each pixel can
be a resource-intensive operation, especially for large images.
Parameter settings: Choosing the right values for the mean and variance is
important and can affect the result.
The result of the algorithm is shown in Figure 2:
Fig.2 Gaussian filter realization
Orest Denysiuk, Rostyslav Nakonechnyi Analysis and improvement of methods and means for
eliminating distortions in image and video signals
62
3. Bilateral equalization
Bilateral Equalization is a powerful image processing algorithm aimed at
improving contrast and correcting luminance distribution. This method combines
bilateral filtering and histogram equalization techniques to achieve the desired results.
The Bilateral Equalization method combines two key stages of image
processing: bilateral filtering and histogram equalization.
First, a bilateral filter is applied to the input image. The bilateral filter preserves
image details by taking into account both spatial and luminance information. This
helps reduce noise and improve the overall image quality. The image is passed through
a bilateral filter, where each pixel is evaluated based on its brightness and spatial
location. The filter takes into account the proximity of pixel brightness and their
distance in space.
𝐼𝑓𝑖𝑙𝑡(𝑥, 𝑦) =
1
𝑊𝑡𝑜𝑡𝑎𝑙(𝑥, 𝑦)
∑ 𝐼(𝑝)𝑊𝑠𝑝𝑎𝑐(‖𝑝 − (𝑥, 𝑦)‖
𝑝∈Ω
)𝑊𝑖𝑛𝑡𝑒𝑛(|𝐼(𝑝) − 𝐼(𝑥, 𝑦)|)
where
𝐼𝑓𝑖𝑙𝑡(𝑥, 𝑦) −new pixel value after bilateral filtering;
𝐼(𝑝) −is the pixel value at the point𝑝;
𝑊𝑠𝑝𝑎𝑐 −is a weighting function for spatial proximity;
𝑊𝑖𝑛𝑡𝑒𝑛 −is a weighting function for the difference in brightness;
Ω −is the set of all neighboring pixels;
𝑊𝑡𝑜𝑡𝑎𝑙 −is the normalization term.
After filtering, the histogram is equalized for the entire image. This ensures that
the brightness distribution is equalized.
𝐼𝑒𝑞(𝑥, 𝑦) =
𝐶𝐷𝐹[𝐼(𝑥, 𝑦)] −min(𝐶𝐷𝐹)
max(𝐶𝐷𝐹) − min(𝐶𝐷𝐹)
𝐿
where
𝐼𝑒𝑞(𝑥, 𝑦) −new pixel value after histogram equalization;
𝐶𝐷𝐹 −is a function of the cumulative brightness distribution;
𝐿 −is the number of brightness levels.
Advantages of the Bilateral Equalization method:
Contrast: The method improves the contrast of an image while preserving details
and structure.
Noise reduction: Bilateral filtering helps reduce noise in an image.
Corrects uneven lighting: Histogram equalization flattens the brightness
distribution, which can be useful for correcting uneven lighting.
Limitations of the Bilateral Equalization method:
Computational complexity: Bilateral filtering can be a resource-intensive
operation, especially for large images.
Requires parameter selection: Bilateral filter and histogram equalization
parameters need to be adjusted to achieve optimal results.
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4. Gathos thresholding
Gathos, Thresholding is an approach to image binarization that uses a local
threshold to determine which pixels in an image should be considered an object and
which should be considered a background. This method is especially useful when
processing images with uneven lighting or large contrast changes.
Firstly, the image 𝐼 is divided into small local blocks or windows 𝑊𝑖 . Each
window has its own size, for example, 3x3, 5x5, or 7x7 pixels.
For each local block 𝑊𝑖, a local binarization threshold is calculated 𝑇𝑖. This
threshold can be calculated in several ways, but the Gathos Thresholding method uses
a statistical measurement approach.
𝑇𝑖 = 𝑘𝑊𝑖𝑎𝑣𝑔 −𝑊𝑖𝑎𝑣𝑔
where
𝑊𝑖𝑎𝑣𝑔 −average value of the brightness (or intensity) of pixels in the block.
After the local thresholds are calculated, the image is binarized, meaning that
each pixel takes on the value of "object" or "background" depending on whether its
brightness exceeds the corresponding local threshold.
The results of binarization for all local blocks are combined to obtain the final
binary image.
Advantages of the Gathos Thresholding method:
Local adaptation: The Gathos Thresholding method uses local thresholds to
binarize each block individually. This allows the method to effectively handle images
where pixel intensity varies significantly across the image area or has uneven
illumination.
Reducing the impact of noise: Local binarization helps to reduce the impact of
noise because the threshold for each block is calculated based on statistical
measurements in that block. This makes the method robust to small noise in certain
areas of the image.
Adaptability to contrast: Gathos Thresholding can effectively binarize images
even with significant contrast changes in different parts of the image.
Disadvantages of the Gathos Thresholding method:
High computational complexity: Calculating local thresholds for each block can
be computationally expensive, especially for large images and/or large block sizes.
Parameter selection: Determining the optimal values of parameters such as block
size and k in the thresholding formula can be a task that requires experimentation.
The need for debugging: Differences in image regions may require parameter
adjustments for optimal binarization.
Loss of detail: Under certain conditions, where the difference between adjacent
blocks is large, the method can lead to loss of detail.
5. Maximum entropy thresholding
Maximum Entropy Thresholding is one of the image binarization methods that
tries to choose a threshold that maximizes the entropy of the object region in the image.
Orest Denysiuk, Rostyslav Nakonechnyi Analysis and improvement of methods and means for
eliminating distortions in image and video signals
64
This method uses statistical characteristics of the image to automatically determine the
optimal binarization threshold.
First, a histogram 𝐻(𝑖) of pixel brightness is calculated, showing how many
pixels have a certain brightness value.
For each potential binarization threshold 𝑇, the entropy of the object and
background regions is calculated. Entropy is a measure of uncertainty or randomness in
a region. The threshold that maximizes the sum of the entropies of the object and
background regions is selected as the optimal binarization threshold.
Divide the histogram into two parts: 𝐻1(𝑖) for brightness values from 0 to 𝑇
and 𝐻2(𝑖) for values from 𝑇 + 1 to 𝑚𝑎𝑥𝑇. Calculate the probabilities𝑃1, 𝑃2:
𝑃1 =∑
𝐻(𝑖)
𝑁
𝑇
𝑖=0
, 𝑃2 = ∑
𝐻(𝑖)
𝑁
𝑚𝑎𝑥𝑇
𝑖=𝑇+1
Calculate the entropies of the object and background regions:
𝐸1 = −∑𝑃1 log2(𝑃1)
𝑇
𝑖=0
, 𝐸2 = − ∑ 𝑃2 log2(𝑃2)
𝑚𝑎𝑥𝑇
𝑖=𝑇+1
Calculate the total entropy for the current threshold:
𝐸(𝑇) = 𝐸1(𝑇) + 𝐸2(𝑇)
The threshold value is chosen to maximize the entropy function. The maximum
entropy method is effective for binarizing images with complex brightness
distributions and different illuminations. It allows automatic thresholding without prior
knowledge of the image structure, making it useful for a variety of image-processing
applications.
Advantages of the maximum entropy method:
Automated approach: The method requires no prior knowledge of the image
structure or threshold parameters. It automatically determines the optimal threshold
based on image statistics.
Efficiency in difficult lighting conditions: The method works effectively with
images that have complex brightness distributions and different lighting conditions.
Application in various fields: This method can be used in a variety of image-
processing applications that require automatic image binarization.
Disadvantages of the maximum entropy method:
Computational complexity: Calculating the entropy and choosing the optimal
threshold can be computationally expensive, especially for large images.
Sensitivity to noise: The method can be sensitive to random noise in the image,
which can lead to incorrect binarization.
Dependence on parameters: The method includes parameters such as T
(threshold) and a number of objects that can affect the binarization results.
6. Sauvola thresholding
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The Sauvola Thresholding method involves calculating a binarization threshold
for each pixel in the image based on local statistical characteristics. Below is a more
detailed description of this method.
The first step in the Sauvola method is to create two auxiliary "integral" images:
The first integral image is created using a square aperture covering the entire
image area. For each pixel in this image, the average luminance of the pixels within the
aperture is calculated.
The second integral image is also created using a square aperture. For each pixel
in this image, the sum of the squares of the pixel brightnesses within the aperture is
calculated, and then the square of the average pixel brightness from the first integral
image is subtracted from this sum.
The following rules are applied in the main processing cycle for each image
pixel:
If the brightness of the current pixel is less than the global minimum (predefined
by the parameter), then this pixel is considered an object and is set to "1" in the binary
image.
If the brightness of the current pixel is greater than the global maximum (also set
by the parameter), then this pixel is considered the background and is set to "0" in the
binary image.
If the brightness of the pixel remains between the global minimum and
maximum, the formula that determines the binarization threshold for the current pixel
is applied.
For a pixel that lies between the global minimum and maximum, the binarization
threshold is determined:
𝑡(𝑥, 𝑦) = 𝜇(𝑥, 𝑦) [1 + 𝑘 (
𝑆(𝑥, 𝑦)
𝑅
− 1)]
where
𝑡(𝑥, 𝑦) −is the binarization threshold for a pixel;
𝜇(𝑥, 𝑦) −is the average value of pixel brightness within the square aperture for a pixel;
𝑆(𝑥, 𝑦) −is the sum of the squared brightness of pixels within a square aperture for a
pixel;
𝑘 −is a parameter that can be adjusted to adjust the threshold value;
𝑅 −is the maximum possible value of the sum of squared brightness in a square
aperture.
The Sauvola Thresholding method automatically determines the binarization
threshold for each pixel based on local statistical characteristics, making it effective for
images with variable lighting and noise.
Advantages of the Sauvola Thresholding method:
Automated approach: The method automatically determines the binarization
threshold for each pixel based on local image properties, making it effective in variable
lighting and noise conditions.
Orest Denysiuk, Rostyslav Nakonechnyi Analysis and improvement of methods and means for
eliminating distortions in image and video signals
66
Contrast consideration: The method takes into account local contrast, which
improves the quality of binarization in images with different lighting conditions and
large contrast changes.
Parameterized approach: The method includes parameters, such as k, that can be
adjusted to achieve optimal results in specific conditions.
Disadvantages of the Sauvola Thresholding method:
Computational complexity: Calculating local statistical characteristics for each
pixel can be computationally expensive, especially for large images.
Sensitivity to parameters: Properly tuning parameters such as k and R is
important to achieve the best results, and this may require experimentation.
Parameter dependence: Although the method automatically determines the
binarization threshold, it still depends on manually defined parameter.
7. Bernsen thresholding
Bernsen Thresholding is an image binarization method that uses the local
statistical characteristics of each point in an image to determine the binarization
threshold. The basic idea of this method is to compare the brightness of points within a
square aperture and determine whether the current pixel is part of an object or
background in the image.
First, you select a square aperture around the current pixel in the image. This
aperture is usually an odd size and is placed around the pixel. The aperture moves
across the image, starting at the top left corner and ending at the bottom right corner.
For each aperture, the brightness values of the pixels inside it are found. The
minimum brightness value 𝑀𝑖𝑛 and maximum brightness value 𝑀𝑎𝑥 among these
pixels are found.
The average value 𝐴𝑣𝑔 is calculated as the arithmetic mean between 𝑀𝑖𝑛 and :
𝐴𝑣𝑔 =
𝑀𝑖𝑛 + 𝑀𝑎𝑥
2
For each pixel in the image, its brightness is calculated, and this brightness is
compared with the value. If the brightness of a pixel is greater than plus a certain
constant (set by the user), the result of binarization of this pixel is "0" (background);
otherwise, it becomes "1" (object).
However, if 𝐴𝑣𝑔 is less than the contrast threshold (which is also set at the
beginning of the algorithm), the current pixel becomes the one selected for the
"unspecified pixel". This means that in this case, it can take the value of the
background or object, depending on the selected mode for ambiguous pixels.
The result of the algorithm is shown in Figure 3:
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Fig.3 Bernsen method realization
Advantages of the Bernsen Thresholding method:
Simplicity: The method is relatively simple to implement and easy to understand
in terms of concept. It does not require complex calculations or many parameters.
Local adaptation: The method uses a local approach to binarization, which
allows it to work well on images with variable illumination and contrast.
User-controlled sensitivity: The user can adjust the E constant to achieve the
desired level of sensitivity to luminance differences.
Disadvantages of the Bernsen Thresholding method:
Dependence on the E parameter: To obtain optimal results, the user must adjust
the E parameter, and an incorrectly selected E can lead to unsatisfactory results.
Aperture shape limitation: The method uses a square aperture, which may be
insufficient for some types of objects in the image.
Computational complexity: If the aperture value is large or the image is large, it
may result in a high computational load.
8. Niblack thresholding
The Niblack binarization method is a method that uses local statistical
characteristics to determine the binarization threshold for each pixel in an image. The
basic idea behind the method is to vary the brightness threshold from point to point
based on the local standard deviation of a sample of pixels in the surrounding area.
First, you select the size of the square aperture around the current pixel in the
image. The aperture size should be chosen so that it preserves local image details while
reducing the effects of noise.
For each image point in the aperture, the average brightness 𝜇 and standard
deviation 𝑠 of the pixels within the aperture are calculated. The average μ and standard
deviation s are calculated using the following formulas:
𝜇(𝑥, 𝑦) =
1
𝑁
∑𝐼(𝑥𝑖, 𝑦𝑖)
𝑁
𝑖=1
where
Orest Denysiuk, Rostyslav Nakonechnyi Analysis and improvement of methods and means for
eliminating distortions in image and video signals
68
𝑁 −number of pixels in the aperture;
𝐼(𝑥𝑖, 𝑦𝑖) −pixel brightness.
𝑠(𝑥, 𝑦) = √
1
𝑁
∑(𝐼(𝑥𝑖 , 𝑦𝑖) − 𝜇(𝑥, 𝑦))
2
𝑁
𝑖=1
The brightness threshold for each point is calculated using the formula:
𝐵(𝑥, 𝑦) = 𝜇(𝑥, 𝑦) + 𝑘𝑠(𝑥, 𝑦)
Based on the calculated threshold 𝐵, each pixel is determined to be part of an
object or background. If the brightness of the pixel is greater than or equal to the
threshold, it is considered part of the object (value "1"); otherwise, if the brightness is
less than the threshold, it is considered background (value "0").
Advantages of the Niblack Thresholding method:
Local adaptation: The method uses a local approach to binarization, which
allows it to take into account changes in contrast and illumination in an image. This
makes it effective for images with uneven lighting.
Reducing the impact of noise: The use of standard deviation allows the method
to be less sensitive to noise in the image.
Adaptable aperture: The size of the square aperture can be selected to preserve
local image details.
Disadvantages of the Niblack Thresholding method:
Dependence on the k parameter: To achieve optimal results, the user must adjust
the k parameter, and an incorrectly selected k can lead to unsatisfactory results.
Limited performance on images with complex textures: The method may
produce inconclusive results on images with complex textures or details.
Computational resource requirements: The large aperture size and high image
dimensionality can result in a high computational load.
9. Improved adaptive thresholding algorithm
Traditional binarization methods do not always provide the required quality of
blood cell isolation with high accuracy and low noise. The new algorithm aims to
reduce noise and improve object separation.
First, the size of the square aperture used for image processing is determined.
This aperture size is fixed for the entire algorithm.
An additional image is created that reflects the intermediate result of binarization
of the main image. This intermediate binarization step is performed based on a pre-
selected binarization method, such as a gradient binarization algorithm.
For each point of the source image, an aperture with the dimensions determined
earlier is selected again. For each specific aperture, all values of the P parameter are
selected that correspond to the gradient between any two points in the aperture and are
less than the specified value of the binarization parameter B. All these values of the P
parameter are adjusted upward based on the inverse normal distribution for the discrete
area.
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The values of P that have been adjusted to be greater than the binarization
parameter B mark points on the supplementary image. This adds new boundary points
to the supplementary image that were not previously selected.
The correction operation of the P parameter values can be performed several
times, depending on the image characteristics and the required binarization quality.
This approach allows us to improve the binarization result and highlight the boundaries
of objects more accurately.
The algorithm takes into account the specifics of object boundaries, providing
selective processing of individual boundary areas and reducing the requirements for
points that have not been binarized but are close to the defined boundary points.
The result of the algorithm is shown in Figure 4:
Fig.4 Adaptive method realization
10. Comparison of image processing quality using PSNR and SSIM metrics
PSNR (Peak Signal-to-Noise Ratio) is a metric used to measure the quality of a
recovered signal or image after processing compared to the original signal. It expresses
the ratio between the peak of the signal (the maximum possible value) and the noise in
the signal. PSNR is measured in decibels (dB) and provides information about how
much the recovered signal differs from the original. A high PSNR value indicates a
high quality of the recovered signal, since the noise in the signal is insignificant
compared to the signal.
𝑃𝑆𝑁𝑅 = 10 log10
𝑀2
𝑀𝑆𝐸
where
𝑀 −maximum possible pixel intensity (usually 255 for 8-bit images);
𝑀𝑆𝐸 −the average square deviation between the original and processed images, and it
is calculated as the sum of the squares of the difference between the corresponding
pixels of the two images divided by the number of pixels.
SSIM (Structural Similarity Index) is a metric used to measure the similarity
between two images. It takes into account the structural similarity between the pixels
of the images, not just their brightness and contrast. SSIM generates a value between -
Orest Denysiuk, Rostyslav Nakonechnyi Analysis and improvement of methods and means for
eliminating distortions in image and video signals
70
1 and 1, where 1 indicates that the two images are identical. A high SSIM value means
that the images are highly similar.
𝑆𝑆𝐼𝑀 =
(2𝜇𝑥𝜇𝑦 + 𝑐1)(2𝜎𝑥𝑦 + 𝑐2)
(𝜇𝑥2 + 𝜇𝑦2 + 𝑐1)(𝜎𝑥
2 + 𝜎𝑦2 + 𝑐2)
where 𝜇𝑥𝜇𝑦 −represent the average luminance values (mean luminance) of the two
images being compared;
𝜎𝑥𝑦 −is the covariance between the pixel brightness of the two images;
𝑐1, 𝑐2 −constants introduced to prevent division by zero. They are used to smooth the
numerator and denominator of the formula.
In this research paper, PSNR and SSIM metrics were used simultaneously to
analyze the image processing quality assessment (see Table 1, Table 2). PSNR
measures the noise level, while SSIM considers structural similarity, helping to find
out how well the details and structure of the image are preserved. Combining these two
metrics will provide a more objective assessment of image processing quality.
Table 1
Results of comparing algorithms for PSNR-metric
Algorithm name PSNR
Median filter 10.5941
Gaussian filter 11.7413
Bilateral filter 14.7256
Gatos 9.4192
Max entropy 8.6929
Niblack 16.7198
Bernsen 15.2910
Sauvola 16.6869
Adaptive 16.8234
Table 2
Results of comparing algorithms for SSIN-metric
Algorithm name SSIN
Median filter 0.7027
Gaussian filter 1.9965
Bilateral filter 2.5834
Gatos 0.9950
Max entropy 1.6929
Niblack 1.1081
Bernsen 1.0005
Sauvola 1.2749
Adaptive 3.040
As can be seen from the comparison results, the adaptive image processing
method produces the best results among the considered methods. With higher PSNR
values and improved structural similarity to the original images, the adaptive method
proved to be the most effective in providing high-quality image processing. Its ability
to adapt to different conditions and highlight details makes it an ideal choice for image-
processing tasks.
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Conclusions.Several methods and algorithms are intensively used in the field of image
processing to optimize and improve visual information. These techniques have a wide
range of applications, including document identification, medical image analysis, and
many other fields. However, one of the key problems is the presence of noise in the
images, which can significantly complicate the analysis and processing. In this study,
various image processing techniques aimed at reducing noise and performing adaptive
thresholding were thoroughly reviewed. One of the goals of this paper is not only to
present and analyze these methods but also to develop an improved adaptive
thresholding algorithm that can be an important contribution to the field of image
processing. Adaptive thresholding algorithm has 3.040 for SSIN-metric and 16.8234
for PSNR-metric. Which is the best among others algorithms. Each of the methods was
carefully considered in the paper, their advantages and limitations were determined,
and the details of the improved adaptive threshold algorithm were considered.
Considering the characteristics of specific images and the desired level of accuracy, the
most suitable method of image processing for specific tasks was selected.
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Аналіз та удосконалення методів та засобів усунення
спотворень в сигналах зображень та відео
Орест Денисюк, Ростислав Наконечний
Основною метою цієї статті було дослідження існуючих методів обробки
зображень, бінаризації та шумозаглушення, а також розробка вдосконаленого
адаптивного алгоритму порогової обробки. Аналіз методів та інструментів для
усунення спотворень у зображеннях і відеосигналах є актуальним завданням у
багатьох галузях, зокрема в медицині, комп'ютерному зорі та
документознавстві. У статті детально розглянуто існуючі методи бінаризації
та шумозаглушення, виокремлено їхні переваги та обмеження. Однак головним
досягненням є розробка та реалізація вдосконаленого адаптивного алгоритму
порогової обробки. Цей алгоритм враховує особливості зображення та
автоматично адаптує поріг бінаризації для кращої якості обробки. Він є значним
внеском в область обробки зображень і може бути використаний в різних сферах,
включаючи медичну діагностику та візуальне виявлення об'єктів на зображеннях.
Ключові слова: адаптивне порогове визначення, аналіз методів обробки
зображень, бінаризація зображення, вдосконалений алгоритм адаптивного
порогового визначення, зменшення шуму в зображеннях.
Отримано: 15.11.2023.
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| institution | Physico-mathematical modeling and informational technologies |
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| language | English |
| last_indexed | 2026-06-09T01:10:31Z |
| publishDate | 2023 |
| publisher | Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України |
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| spelling | oai:ojs2.www.fmmit.lviv.ua:article-3392024-10-19T19:01:15Z Analysis and improvement of methods and means for eliminating distortions in image and video signals Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео Денисюк, Орест Наконечний, Ростислав Adaptive thresholding, Analysis of image processing methods, Image binarization, improved adaptive thresholding algorithm, Reducing noise in images. The main purpose of this article was to study existing image processing methods, binarization and noise reduction, and to develop an improved adaptive thresholding algorithm. The analysis of methods and tools for eliminating distortions in image and video signals is an urgent task in numerous fields, including medicine, computer vision, and document science. The article discusses in detail the existing binarization and noise reduction methods, highlighting their advantages and limitations. However, the main achievement is the development and implementation of an improved adaptive thresholding algorithm. This algorithm considers the specific features of the image and automatically adapts the binarization threshold for better processing quality. It is a significant contribution to the field of image processing and can be used in various fields, including medical diagnostics and visual object detection in images. Основною метою цієї статті було дослідження існуючих методів обробки зображень, бінаризації та шумозаглушення, а також розробка вдосконаленого адаптивного алгоритму порогової обробки. Аналіз методів та інструментів для усунення спотворень у зображеннях і відеосигналах є актуальним завданням у багатьох галузях, зокрема в медицині, комп'ютерному зорі та документознавстві. У статті детально розглянуто існуючі методи бінаризації та шумозаглушення, виокремлено їхні переваги та обмеження. Однак головним досягненням є розробка та реалізація вдосконаленого адаптивного алгоритму порогової обробки. Цей алгоритм враховує особливості зображення та автоматично адаптує поріг бінаризації для кращої якості обробки. Він є значним внеском в область обробки зображень і може бути використаний в різних сферах, включаючи медичну діагностику та візуальне виявлення об'єктів на зображеннях. Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2023-12-24 Article Article application/pdf https://www.fmmit.lviv.ua/index.php/fmmit/article/view/339 10.15407/fmmit2023.38.058 PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES; No. 38 (2023): PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES; 58-72 ФІЗИКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТА ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ; № 38 (2023): ФІЗИКО-МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ТА ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ; 58-72 2617-5258 1816-1545 10.15407/fmmit2023.38 en https://www.fmmit.lviv.ua/index.php/fmmit/article/view/339/299 Авторське право (c) 2023 Орест Денисюк, Ростислав Наконечний (Автор) |
| spellingShingle | Adaptive thresholding Analysis of image processing methods Image binarization improved adaptive thresholding algorithm Reducing noise in images. Денисюк, Орест Наконечний, Ростислав Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| title | Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| title_alt | Analysis and improvement of methods and means for eliminating distortions in image and video signals |
| title_full | Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| title_fullStr | Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| title_full_unstemmed | Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| title_short | Аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| title_sort | аналіз та удосконалення методів та засобів усунення спотворень в сигналах зображень та відео |
| topic | Adaptive thresholding Analysis of image processing methods Image binarization improved adaptive thresholding algorithm Reducing noise in images. |
| topic_facet | Adaptive thresholding Analysis of image processing methods Image binarization improved adaptive thresholding algorithm Reducing noise in images. |
| url | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/339 |
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