Deep Neural Network Based Algorithm for Recognition of Static Signs of

Polish Sign Language

Wiktor Bara

nczyk

and Piotr Duch

Institute of Applied Computer Science, Lodz University of Technology, Bohdana Stefanowskiego 18, Lodz, Poland

Keywords:

Sign Language Recognition, Deep Learning, Computer Vision.

Abstract:

Developing sign language recognition algorithms is important for promoting accessibility and inclusion for

deaf and hard-of-hearing individuals, improving education, and advancing technological applications in var-

ious ﬁelds. This paper presents a novel approach for recognizing static signs of Polish Sign Language using

characteristic points and deep neural networks. As an input to the deep neural network the distances between

every landmark of hands, elbows, and shoulders were used. The study focused on exploring the effectiveness

of using deep learning techniques for sign recognition. The proposed algorithm was evaluated on two publicly

available databases (NUS and LSA16) and achieved higher or comparable accuracy to other algorithms. Ad-

ditionally, it was tested on a collected database of photographs of 24 people. The proposed algorithm achieved

96.45% accuracy, 96.15% recall, and 96.66% precision.

1 INTRODUCTION

It is estimated that in the world live about 70 million

deaf people, more than 80% of whom live in develop-

ing countries. More than 300 different sign languages

are in use

. For Deaf people, phonetic languages used

in their country are foreign to them. That situation

does not only cause problems in social life but also in

ofﬁcial matters, such as problems with understanding

documents or contracts.

In Poland, Deaf people use Polish Sign Language

(PSL). Currently, the estimated number of PSL users

is approximately 50,000. Despite its signiﬁcant di-

vergence from spoken Polish, PSL was not ofﬁcially

recognized as a natural language for many years. In

2011, the Polish Government passed a law on sign

language and other communication methods, which

granted the Deaf community the legal right to request

interpreter services when interacting with public ad-

ministration (Linde-Usiekniewicz et al., 2016).

In this work, we propose a method for recogniz-

ing static signs of Polish Sign Language using im-

age processing. The presented algorithm is an inte-

gral component of our broader research framework,

https://orcid.org/0009-0007-9377-0950

https://orcid.org/0000-0003-0656-1215

https://www.un.org/en/observances/sign-languages-

day

enabling the identiﬁcation and classiﬁcation of PSL

signs. This is an important contribution to the ﬁeld,

as there are few articles related to recognizing PSL

signs. The approach involves the use of a database

that was collected with the help of both deaf and non-

deaf people, which ensures that the database is rep-

resentative of the diverse range of signing styles and

handshapes that exist in PSL. In the conducted experi-

ments, we used a single color camera situated in front

of the signer. There is no need to wear gloves or to

use special equipment.

2 LITERATURE ANALYSIS

Sign languages are natural languages that rely on

hands and body movements, facial expressions, and

gestures rather than voice to communicate. The main

users are Deaf individuals, hearing-impaired people,

or those who are unable to speak due to physical con-

ditions.

Many hearing people think sign languages are vi-

sual representations of the spoken languages used in

a respective country, with hand movements replacing

vocalization. Another misunderstanding is the belief

that only one universal sign language exists. Both of

them are incorrect. Each sign language has its own

grammar, words, and syntax, which differs from other

languages. Of course, similarities may exist between

Bara

nczyk, W. and Duch, P.

Deep Neural Network Based Algorithm for Recognition of Static Signs of Polish Sign Language.

DOI: 10.5220/0013112400003890

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2025) - Volume 3, pages 201-208

ISBN: 978-989-758-737-5; ISSN: 2184-433X

201

different sign languages

. Moreover, due to the iso-

lated nature, sign languages have many developed re-

gional variations counted to the same language. It is

similar to the dialects or regional accents in spoken

languages

Signs can be classiﬁed into two categories based

on observable features: static and dynamic signs.

Static signs are those in which the hand position does

not change during the duration of the sign. In Pol-

ish Sign Language, static signs are used mainly to de-

scribe alphabet letters and digits. On the other hand,

dynamic signs involve hand position and ﬁnger ar-

rangement changes over time. Despite the shape of

ﬁngers, hand trajectory, orientation, and sometimes

the coordinated movement of both hands matter in

those signs.

The paper focuses on recognizing static signs in

Polish Sign Language. Although PSL is one of the

biggest minority languages in Poland, it still remains

under-researched. In 2010, the ﬁrst academic unit

dedicated to research on PSL grammatical and lexi-

cal properties was established within the University

of Warsaw (Linde-Usiekniewicz et al., 2014).

For further experiments, 27 static signs from Pol-

ish Sign Language were selected, including only the

static characters from the manual alphabet, along with

numbers and some simple words.

2.1 Sign Language Recognition

Several methodologies are used in sign language

recognition, with the three primary approaches being

sensor-based, vision-based, and hybrid methods.

The sensor-based approach is mainly based on

special equipment, such as accelerometers (Fatmi

et al., 2019), surface electromyography (sEMG) sen-

sors (Jiang et al., 2017), gloves (Wen et al., 2021),

or even Kinect (Raghuveera et al., 2020). The recog-

nition of the signs is a two-step process. In the ﬁrst

step, the signal from the sensor is captured, and in

the second step, the data are processed using different

approaches.

Vision-based methods use cameras to capture in-

formation about speciﬁc signs. Compared to the

sensor-based techniques, this approach is less de-

manding. A user requires only a camera, which can

be found in many daily-used devices like computers

or smartphones. However, the main limitations of us-

ing only the cameras are sensitivity to the different

lighting or lack of depth perception. Sometimes the

multiple cameras approach is used (Erol et al., 2007).

https://en.wikipedia.org/wiki/Sign_language

https://www.british-sign.co.uk/what-is-british-sign-

language/

The hybrid approach combines both previous sys-

tems. The input data are collected from multiple sen-

sors, like leap motion and camera (ElBadawy et al.,

2015).

In the vision-based approach, one of the most pop-

ular methods is based on convolutional neural net-

works (CNN) in various architectures. The CNN

trained to recognize 200 different signs of Indian Sign

Language achieved an 88.98% recognition rate (Rao

et al., 2018). Another approach used DenseNet121 ar-

chitecture, achieving 80% accuracy on a dataset com-

prising 24 static signs of the American Sign Language

alphabet (Kołodziej et al., 2022).

Several studies have utilized classic CNN archi-

tectures with features extraction and classiﬁcation

parts, processing either RGB or grayscale images

(Jeny et al., 2021; Eid and Schwenker, 2023). Some

of these approaches have also used depth maps (Kang

et al., 2015) or RGB-D data (Elboushaki et al., 2020).

In other research, architectures combining detection

and recognition like You Only Look Once architec-

ture (Daniels et al., 2021; Sarma et al., 2021) and Sin-

gle Shot Detector architectures (Rastgoo et al., 2020b;

Rastgoo et al., 2020a) have been explored.

More recent advances include attention mecha-

nism (Bhaumik et al., 2023) or Vision Transformers

(Tan et al., 2023). Another vision-based approach in-

volves a multi-step process. Key characteristic points

and skeletal structures are ﬁrst extracted from images,

followed by sign recognition using classiﬁers (Jiang

et al., 2021; Bajaj and Malhotra, 2022).

2.2 Polish Sign Language Recognition

PSL is relatively understudied compared to other sign

languages like American Sign Language or British

Sign Language.Speciﬁcally, only a few articles de-

scribe algorithms for recognizing signs of PSL, high-

lighting the need for further research in this domain.

One of the ﬁrst approaches to recognizing isolated

PSL words was based on analyzing images captured

from the canonical stereo system. This method uti-

lized information on the hand position and its 3D

position relative to the face. The study employed a

database of 101 words signed by two individuals (Ka-

puscinski and Wysocki, 2005).

Another approach utilized image analysis for PSL

word recognition through a graph-based representa-

tion of hand posture. In this method, the hand was

detected using a Gaussian distribution model of skin

colour and morphological operations. The contour

of the hand was then extracted to construct a graph

for recognition. The method achieves an accuracy of

94.3% (Flasi

nski and My

sli

nski, 2010).

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

202

Another works explores also the recognition of se-

quences of PSL letters. One of the proposed approach

used input from Kinect, which was analyzed with hid-

den Markov models to classify postures correspond-

ing to speciﬁc letters by analyzing their transitions,

yielding a recognition accuracy of 75.2%. The exper-

iments were conducted with a database comprising

three individuals and 20 sequences (Warchoł et al.,

2019).

Additionally, for the PSL letter recognition, a pro-

totype of a glove employing textronic elements was

proposed, achieving an accuracy of 86.5% (Korze-

niewska et al., 2022).

3 PROPOSED ALGORITHM

Three crucial problems must be addressed when eval-

uating sign language recognition methods.

The ﬁrst issue concerns the division of data into

training and testing sets. Neural networks can eas-

ily adapt to the shape and proportions of the hands

presented in the training. The dataset should be parti-

tioned based on individuals rather than the number of

images to ensure reliable testing. This means that im-

ages of individuals present in the training set should

not appear in the testing set.

The second problem is related to capturing the

spatial positioning of the hands in relation to the

signer and their surroundings, which is crucial for

many words in sign languages. CNNs also need ex-

tensive labelled data to achieve the best performance.

Obtaining a database that is large enough to contain

diverse PSL signs is difﬁcult due to the limited avail-

ability of data, expert labelling requirements, and in-

dividual differences among users in signing styles.

PSL signs exhibit signiﬁcant intra-class variations,

where different individuals may show the same sign

in distinct ways due to personal preferences. CNNs

perform better on tasks that are characterized by rel-

atively stable and consistent visual patterns — intr-

aclass variations might greatly impact their perfor-

mance. A promising approach may involve using

characteristic points and skeleton structures or CNN-

like architectures combined with these features.

The third challenge is that the limited of available

Deaf individuals for dataset collection is limited. A

diversity of hand shapes is essential for good gener-

alization of the problem, but only a few PSL users

are willing to help collect the dataset. Additionally,

variations and differences in signs between PSL users

further complicate the task.

3.1 Database

No PSL sign database fulﬁlled the conditions required

for this study. Many sign language databases only

contain images of hands, which do not allow for eval-

uating the hand’s position relative to the signer and

do not reﬂect typical Deaf communication. As a re-

sult, a new database was self-collected. However, this

dataset will not be publicly available due to the lack

of participant consent.

It is important to note that the dataset mostly con-

tains photos of hearing individuals. Since hearing in-

dividuals were generally unfamiliar with PSL, they

were conducted by someone who knew the signs.

This approach was adopted to try to solve the third

problem - data scarcity and diversity. Using hearing

individuals presents an advantage, as their availabil-

ity is almost unlimited, making it easier to collect a

proper amount of data.

Each individual was photographed on three dif-

ferent backgrounds. For each background, 27 pho-

tos were taken - one for each sign. In the summary,

81 images. The subjects were visible from at least the

knees to the top of the head, and both hands were fully

visible. Images where all critical hand points were not

detected were excluded from the dataset.

The database contains photos of 24 people – 3

Deaf and 21 hearing. Images of Deaf individuals were

extracted from videos ﬁlmed with the help of the Pol-

ish Deaf Association in Lodz. The images were cat-

egorized into 27 groups, each corresponding to one

speciﬁc word. Augmentation techniques applied to

the images were:

• Mirror reﬂection (signs used in the research were

"hand invariant"),

• Resizing hearing individuals’s photos to 80%,

60%, 40%, and 20% of the original size,

• Framing Deaf individuals’ images to the same 4:3

proportions as those of hearing participants

• Rotating each image by 1 or 2 degrees, both

clockwise and counterclockwise.

Images of Deaf individuals were extracted from

video, which has a lower resolution compared to the

photos of hearing participants. Therefore, further re-

sizing them was avoided to maintain data quality. The

ﬁnal database contained 90549 images. However, af-

ter excluding images where not every key point was

detected, 77933 photos were used for training and

testing.

Deep Neural Network Based Algorithm for Recognition of Static Signs of Polish Sign Language

203

3.2 Algorithm Description

The proposed algorithm comprises several stages. Ini-

tially, characteristic points of the human posture are

detected, after which those relevant to the approach

are selected. Distances between the selected points

are calculated and normalized. These distances are

the input to the neural network, which outputs infor-

mation about recognized sign (Figure 1).

The ﬁrst stage of the algorithm involves detecting

key body landmarks. For this purpose, the Holistic

MediaPipe Solution

is used, which detects 75 land-

marks—33 pose landmarks and 21 hand landmarks

for each hand). Therefore, from the 75 detected land-

marks, 46 are selected for further processing: 42 rep-

resenting hand poses and 4 representing the positions

of the shoulders and elbows.

Following this, 1035 Euclidean distances between

each point, based on their x and y coordinates, are

computed and normalized using the following equa-

tion:

value

scaled

value − value

min

value

max

− value

min

(1)

where:

• value - currently scaled value,

• value

max

- maximum value in a column to which

belongs scaled value,

• value

min

- minimum value in a column to which

belongs scaled value.

It is worth noting that using distances between key

hand and body points in sign language recognition

has not been previously presented in the literature re-

viewed by the authors.

3.3 Neural Network Architecture

A deep neural network (DNN) was used to recognize

the selected signs. The input to the network consists

of the distances between the characteristic points.

The optimal architecture, learning rate, and optimizer

were selected using grid search algorithm. In the re-

sult proposed model comprises six fully connected

layers with 1035, 512, 256, 128, 64, and 27 neurons,

respectively. Each layer, except the ﬁnal one, utilizes

the LeakyReLU activation function, while the output

layer uses the softmax function. Categorical cross-

entropy is used as a loss function, and Adamax is used

as an optimizer with a learning rate of 1e-4. The neu-

ral network was trained for 1000 epochs. This number

of epochs was chosen because the algorithm initially

learned quickly, reaching approximately 90% accu-

racy. However, the model appeared to struggle with

https://google.github.io/mediapipe/solutions/holistic

Table 1: Performance of the proposed pipeline and selected

approaches from the literature on the NUS dataset.

Model Accuracy

(Eid and Schwenker, 2023) 93.5%

(Tan et al., 2021) 96.75%

(Bhaumik et al., 2023) 97.78%

Our 97.87%

(Tan et al., 2023) 99.85%

the details of the signs. Prolonged training allows the

model to focus on details, leading to improved perfor-

mance.

4 RESULTS

The research was divided into three parts. The ﬁrst

part focused on ﬁnding the best architecture and hy-

perparameters, which provided the foundation for the

next experiments. The second part involved compar-

ing the proposed algorithm with other approaches.

Lastly, a detailed analysis of the results on the col-

lected dataset was conducted.

4.1 Comparing with Other Approaches

To better demonstrate the effectiveness of the pro-

posed approach, the algorithm was evaluated on pub-

licly available datasets and compared with models de-

scribed in the literature.

4.1.1 Results on NUS Hand Posture Dataset

The NUS hand posture dataset was used to better

compare with other approaches. This dataset includes

images of 10 different hand shapes captured from 40

individuals. Each hand shape was captured ﬁve times

for every subject, resulting in 200 images per class

and a total of 2000 images in the dataset. The dataset

does not provide user independence.

Due to the relatively small sample size, the batch

size was reduced to 512 for training. The model

was evaluated using 5-fold cross-validation. The

model achieved 97.47%, 97.97%, 97.97%, 98.73%

and 97.22% accuracy across the folds, with an aver-

age of 97.87%. A comparison with other approaches

on this dataset is presented in Table 1.

The proposed model demonstrates excellent per-

formance compared to other models. While the model

presented in (Tan et al., 2023) achieves signiﬁcantly

better accuracy, it utilizes Vision Transformer archi-

tecture. The Transformer model has 86 million pa-

rameters, which is more than nine times the number of

parameters in the proposed pipeline. This large num-

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204

Figure 1: Diagram of the algorithm for the recognition of static signs in Polish Sign Language.

ber of parameters may make the Transformer model

unsuitable for mobile devices.

4.1.2 Results on LSA16 Dataset

The LSA16 dataset contains images of 16 hand

shapes taken from 10 subjects, with each hand shape

performed ﬁve times, resulting in a total of 800 im-

ages. This dataset ensure user-independence. Sev-

eral models were evaluated in (Quiroga et al., 2017),

from which citation is provided. The authors focused

only on the right hand for recognition; thus, for a

fair comparison, only distances between characteris-

tic points detected on the right hand were utilized.

The batch size was reduced to 128 due to the lim-

ited number of samples. The model was tested using

5-fold cross-validation, with each testing pair com-

prising one male and one female subject. In (Quiroga

et al., 2017) 100 runs of stratiﬁed randomized sub-

sampling cross-validation were conducted. However,

it is important to note that some runs may not guar-

antee user independence, making the task easier in

that paper compared to the current approach. The

proposed model achieved 97.64%, 98.39%, 96.06%,

94.78% and 94.44% accuracy, which is 96.26% on

average. Comparison with other approaches on this

dataset is shown in Table 2.

Table 2: Performance of the proposed pipeline and selected

models on LSA16 dataset.

Model Accuracy

Inception

(Szegedy et al., 2015)

91.98%

ResNet (He et al., 2016) 93.49%

AllConvolutional

(Springenberg et al., 2014)

94.56%

LeNet (LeCun et al., 1998) 95.78%

VGG16

(Simonyan and Zisserman, 2014)

95.92%

Our 96.26%

4.2 The Detailed Analyze of Result on

Collected Dataset

The proposed algorithm was evaluated in two dif-

ferent scenarios: performance for "known" and "un-

known" hands. Three metrics were used for evalu-

ation: accuracy, recall, and precision. These met-

rics help evaluate the performance of a neural net-

work in classiﬁcation tasks, as they provide insights

into different aspects of the network’s performance

and help identify areas where the network can be im-

proved. Additionally, a confusion matrix was pre-

sented to provide more detailed information about the

algorithm’s behaviour and classiﬁcation outcomes.

4.2.1 Model Performance for "known" Hand

The ﬁrst experiment focus on comparing the per-

formance of the proposed algorithm tested on the

"known" and "unknown" hands. Two models with

the same architecture and learning rate (1e-4) were

trained for 100 epochs. The ﬁrst model, tested on

"known" hands, was trained using the entire dataset

and randomly split into training and testing groups.

The training group contained 61383 images, while the

remaining images were used for testing. It is the same

distribution as in the "unknown" hand scenario. In the

second model, the data were split according to the in-

dividuals performing the signs, ensuring that the indi-

viduals in the training set were distinct from those in

the testing set.

The model tested on "known" hands achieved

97.35% accuracy, 96.82% recall, and 97.98% preci-

sion. In contrast, the model tested on "unknown"

hands produced results of 94.64% accuracy, 93.60%

recall, and 95.51% precision. The results highlight

the impact of using different individuals’ images in

the training and testing set. Using the same "hands"

for training and testing can lead to an increase in per-

formance of nearly three percentage points.

4.2.2 Test with only Deaf’s Images and Hearing

Images

Due to different methods of photo collection, it is im-

portant to evaluate the model’s performance on im-

ages of Deaf individuals separately from those of

hearing individuals. For the Deaf participants’ im-

ages, the model achieved 78.96% accuracy, 78.10%

recall and 79.71% precision. In contrast, for the hear-

ing participants’ images, the model achieved 96.95%

Deep Neural Network Based Algorithm for Recognition of Static Signs of Polish Sign Language

205

Table 3: Confusion matrix fragment which shows results for signs which are the most likely to be mistaken. "0$o" is a label

of sign which means "0" or "o".

Actual

0$o 3 4 5 a ja n s t ty

0$o 664 0 0 0 0 0 0 78 13 0

3 0 558 1 0 0 0 55 0 0 0

4 0 18 465 31 0 0 0 5 65 2

5 0 2 58 519 0 0 0 2 10 0

a 0 0 0 0 587 0 0 0 0 0

ja 0 0 0 0 0 501 0 0 0 0

n 0 59 3 0 0 0 537 0 0 20

s 57 0 0 0 1 0 0 550 23 0

t 55 0 0 0 0 0 0 21 558 0

ty 43 0 0 0 83 62 0 0 0 491

Predicted

accuracy, 96.66% recall and 97.14% precision. The

observed differences in results are caused by variabil-

ity in the Deaf individuals’ photos, which were ex-

tracted as frames from videos. This led to situations

where the subjects were not centred in the frame, un-

like the individuals in the training set. Additionally,

sometimes the Deaf people were seated, which was

not presented in training data. This highlights a lim-

itation of the current model, which can probably be

overcome by adding more varied data in the training

phase.

4.2.3 Confusion Matrix

A confusion matrix was generated to analyze the re-

sults better. Based on the analysis of this matrix, it

can be noticed that the model struggles with certain

signs. A fragment of the confusion matrix showing

the most interesting cases is presented in Table 3.

It can be seen that the algorithm has the most dif-

ﬁculty with the following groups of signs: “0$o”, “s”,

“t” and "ty" (you in Polish) "3" and "n", "4" and "5",

"a" and "ty", and "ja" (I in Polish) and "ty". It is

caused by the similarity of these signs and the lack

of depth information in the photos.

The model has problems with differentiating be-

tween signs “0$o”, “s”, “t” and "ty". These signs are

shown in Figure 2. Although the algorithm correctly

recognizes the actual signs in most cases, it makes er-

rors in about 10% of them. The confusion between

the ﬁrst three signs occurs because they only differ

in the position of the index ﬁnger’s tip relative to the

thumb. Mistakes between "0$o" and "ty" are probably

caused by a lack of depth.

Another common error is between signs “3” and

“n”. The algorithm makes mistakes in about 10%.

The signs have an almost identical hand shape; in the

sign “3”, the ﬁngers are apart from each other, while

in the sign “n” they are joined together.

An unusual situation arises between signs "4"

and "5". These signs differ by only one ﬁnger; in

"4", the person shows 4 ﬁngers, and in "5", shows

ﬁve ﬁngers. Occasionally, during testing, individuals

present an alternative hand shape for "4" that was not

present in the training set. During training, the num-

ber "4" is represented without the little ﬁnger, while

some examples in the test set represent it without the

thumb.Despite this, the model performs well on "4"

and "5".

The confusion between the signs "a" and "ty" and

the signs "ja" and "ty" is mainly due to a lack of

depth information, even though these signs are visu-

ally quite different. These signs involve a clenched

hand and differ primarily in orientation.

Based on this, it can be concluded that the model

has the most difﬁculty with signs that differ only in

distances between ﬁngers and when the signs are vi-

sually similar in situations where depth information is

lacking.

5 CONCLUSION

In the paper, we presented a method for recognizing

static signs in Polish Sign Language. The proposed

method is based on image processing and does not re-

quire any specialized equipment but can be used with

a simple camera. The deep neural network recognizes

presented signs based on the detected hands’ land-

marks. We used our dataset, containing signs pre-

sented by Deaf people, for whom it is the primary

means of communication with the world, and by peo-

ple not experienced with PSL. For the experiments,

27 signs were selected and presented by 24 individu-

als. The proposed method achieved high recognition

rates, comparable to the best results in the literature.

Our algorithm was further tested against other ap-

proaches using two publicly available datasets: NUS

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

206

Figure 2: Respectively sign "0$o", sign "s", sign "t" and sign "ty".

and LSA16. The comparison results show that our

solution performs similarly or better than those pre-

sented in the literature. Notably, our model has sig-

niﬁcantly fewer parameters than proposed in articles,

making it more suitable for deployment on mobile de-

vices.

Sign language recognition is a challenging topic.

Even recognizing simple PSL signs from pictures is

difﬁcult. However, this research presents the ﬁrst step

in developing a proper translator for sign languages.

Sign languages typically construct sentences through

simultaneous combinations of signs, not just sequen-

tial gestures. Furthermore, the complexity of sign

language interpretation also includes the relative posi-

tioning of the hands and spatial conﬁgurations. Future

work will explore using recursive networks or trans-

formers to recognize sequences of movements that

form signs.

The results obtained from the proposed algorithm

serve as a foundation for the subsequent phase of

our research, which focused on the recognition of

dynamic gestures. Ultimately, we aim to use dy-

namic gesture recognition for an algorithm designed

to translate between PSL and spoken Polish.

ETHICS

Data collection was conducted following informed

consent procedures, with access to the data restricted

solely to the authors. Third-party access is limited

to ﬁles containing coordinates and distances, while

anonymity of individuals involved in the data collec-

tion is maintained after contact with the authors. The

images generated or analyzed during this study are

not publicly available to ensure the protection of per-

sonal data.

ACKNOWLEDGEMENTS

This work was ﬁnanced by the Lodz University of

Technology, Faculty of Electrical, Electronic, Com-

puter and Control Engineering as a part of statutory

activity (project no. 501/2-24-1-2).

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