Medical Image Classiﬁcation Using Deep Neural Networks: An X-Ray

Classiﬁcation

Addagatla Prashanth, Marripalepu Srihimamshu, Somla and Adavi Satya Vinay Aghamarsha

Department of CSE (AI & ML), Institute of Aeronautical Engineering, Hyderabad, India

Keywords:

X-ray Image Classiﬁcation, Deep Learning, Convolutional Neural Networks (CNN), VGG16, VGG19,

ResNet, DenseNet, Inception Model, Medical Imaging.

Abstract:

Lung X-rays are among the most important for making medical diagnoses. In this work, we identify lung X-

rays as either Normal or Pneumonia using a range of deep learning models, such as VGG16, VGG19, ResNet,

DenseNet, and Inception. Before sending the images into the dense neural network, we suggest integrating a

new pooling layer. Both healthy and pneumonia-affected lung X-rays are included in our collection. Convo-

lutional neural networks (CNNs) are used to identify the X-rays’ condition and classify them appropriately.

By comparing our ﬁndings with those of other models, we analyzed our models using a confusion matrix and

quantiﬁed measures like precision and recall. We examine the CNN algorithm and provide the following ex-

amples: (I) With enough training data, deep learning algorithms can correctly categorize X-ray images of sick

lungs. (II) Compared to many typical models, the design may perform better by including an average pooling

layer at the end. (III) Optimizing hyperparameters improves the performance and accuracy of the model. (IV)

Our models outperform several existing CNN models with less trainable parameters when properly trained,

hyperparameter adjusted, and data augmented. With the accurate automation of X-ray image interpretation

made possible by this method, there may be less need for invasive MRI and CT scans, which subject patients

to high radiation doses.

1 INTRODUCTION

Humans effortlessly recognize and distinguish fea-

tures in images due to our brains constantly and sub-

consciously training on familiar data. In contrast,

computers perceive the world as arrays of numeri-

cal values representing critical aspects of images or

videos they attempt to identify. The interpretation

process for computers relies on image recognition al-

gorithms to analyze and understand visual content.

For example, identifying pedestrians and vehicles is

achievable through the categorization and sorting of

millions of images provided by users. Medicine is

a prime ﬁeld requiring reliable image identiﬁcation

systems, as it generates vast amounts of data that can

be used to train these systems. The main challenge

lies in effectively analyzing and processing this data

for practical use. Various methods exist for organiz-

ing medical data, with classiﬁcation being a widely

used technique to detect disease symptoms. In im-

age classiﬁcation, a computer analyzes an image and

assigns it to a speciﬁc class, a task that is straightfor-

ward for humans but exempliﬁes the Moravec para-

dox—simple for humans yet difﬁcult for artiﬁcial in-

telligence. Early image classiﬁcation methods relied

on analyzing pure pixels, which proved problematic

due to variations in backgrounds, angles, and other

factors. Deep learning, particularly through neural

networks, addresses this issue by enabling more so-

phisticated image recognition. However, classiﬁca-

tion remains resource-intensive, often requiring op-

timization or enhanced computational resources to

achieve timely results. This study aims to use deep

learning models, including VGG16, VGG19, ResNet,

DenseNet, and Inception, to classify X-ray images for

pneumonia detection. We propose a novel approach

by integrating a pooling layer before the dense neural

network and evaluate the performance of our mod-

els using precision, recall, and confusion matrix met-

rics. Our goal is to demonstrate that, with adequate

training data and hyperparameter tuning, deep learn-

ing techniques can signiﬁcantly improve the accuracy

and efﬁciency of medical image classiﬁcation.

Prashanth, A., Srihimamshu, M., Somla, and Vinay Aghamarsha, A. S.

Medical Image Classiﬁcation Using Deep Neural Networks: An X-Ray Classiﬁcation.

DOI: 10.5220/0013659500004664

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

In Proceedings of the 3rd International Conference on Futuristic Technology (INCOFT 2025) - Volume 3, pages 763-769

ISBN: 978-989-758-763-4

763

2 OBJECTIVES

• To use deep learning models to classify lung X-

ray pictures as either normal or pneumonia.

• To optimize model performance by implementing

a novel pooling layer and hyperparameter tuning

techniques.

• To assess and contrast the several deep learning

models (ResNet, DenseNet, VGG19, Inception,

and VGG16) for the categorization of X-ray im-

ages.

3 EXISTING SYSTEMS

Current image recognition systems leverage various

advanced methodologies to process and analyze vi-

sual data. Early systems relied on pixel-based anal-

ysis, which faced signiﬁcant challenges due to varia-

tions in image backgrounds, angles, and lighting con-

ditions (Klette, 2014).

These limitations led to the development of more

sophisticated techniques involving deep learning,

which allows computers to recognize patterns and

features within images with greater accuracy (Krishna

et al., 2021). In the ﬁeld of medicine, deep learn-

ing has been particularly transformative. Machine

learning models, such as convolutional neural net-

works (CNNs), have been widely used to classify

medical images, providing critical support in diag-

nostic processes (Borad, 2020). These models can

analyze vast amounts of data efﬁciently, offering re-

liable identiﬁcation of diseases from X-ray images,

among other medical imaging modalities (Mochu-

rad & Yatskiv, 2020). Despite their effectiveness,

deep learning models are computationally intensive

and often require signiﬁcant resources for training

and deployment. Advances in parallel computing and

optimization techniques have enabled more efﬁcient

training of these models, reducing the time and re-

sources needed while improving performance (Shal-

lue et al., 2019). These advancements have made it

possible to implement deep learning models in real-

time diagnostic applications, thereby enhancing their

practical utility in clinical settings (Moujahid et al.,

2020).

Furthermore, the integration of CNNs with other

neural network architectures, such as recurrent neu-

ral networks (RNNs) with attention mechanisms, has

shown promising results in speciﬁc medical imag-

ing tasks, such as histology image classiﬁcation for

breast cancer (Yao et al., 2019). These hybrid ap-

proaches leverage the strengths of multiple neural net-

work types to improve accuracy and robustness in

medical diagnostics.

In conclusion, current systems have established a

solid basis for the use of deep learning in medical

imaging, and further study is concentrated on reﬁn-

ing these models to increase their effectiveness and

performance in clinical settings.

4 LITERATURE SURVEY

The literature on biomedical image analysis has seen

signiﬁcant advancements. Afshar et al. (2018) pro-

posed a new Capsule Network model combined with

Convolutional Neural Networks (CNNs) for segment-

ing biomedical images, speciﬁcally applying their ar-

chitecture to MRI images of brain tumors. Their

study, which involved 233 subjects and 3,064 images,

achieved a maximum accuracy of 86.56% using a sin-

gle convolutional layer with 64 feature maps. How-

ever, the ﬁndings are limited by the speciﬁc dataset

used, which may affect generalizability.

Similarly, Frid-Adar et al. (2018) introduced a

hybrid model that integrates Generative Adversarial

Networks (GANs), CNNs, and synthetic data aug-

mentation to improve the segmentation and classiﬁ-

cation accuracy of liver lesions. Nonetheless, their

reliance on synthetic data may introduce biases, lim-

iting real-world applicability. In a different study,

Cires¸an et al. (2013) used CNN-based deep neural

networks to detect mitosis in breast cancer histology

images, showing a signiﬁcant improvement in detec-

tion performance. However the performance of the

model could differ for various histology datasets, in-

dicating the necessity for thorough validation..

Litjens et al. (2017) conducted a comprehensive

survey reviewing various architectures and their ap-

plications in this domain. The results of their study

demonstrated how well Convolutional Neural Net-

works (CNNs) and other deep learning models per-

formed image processing tasks. The survey did, how-

ever, also highlight the necessity for standardized

evaluation metrics and point out issues with dataset

variability. In the same line of thought, Shen et al.

(2017) examined the use of deep learning techniques,

concentrating especially on CNNs, and showed how

they might boost medical image processing signiﬁ-

cantly in terms of accuracy and speed. They did, how-

ever, note that there are signiﬁcant obstacles, includ-

ing the need for huge annotated datasets and high pro-

cessing requirements. Complementing these insights,

Reyes et al. (2018) presented a survey highlighting

the advancements and ongoing challenges in medical

imaging due to deep learning. Their work conﬁrmed

INCOFT 2025 - International Conference on Futuristic Technology

764

the transformative potential of these techniques in im-

proving diagnostic accuracy, while also noting limi-

tations in data availability and the pressing need for

robust validation frameworks.

Deep learning applications in medical imaging are

the subject of a growing corpus of study. In their study

of several deep learning algorithms and architectures,

Shrestha and Mahmood (2019) focused on the appli-

cations in medicine. Convolutional Neural Networks

(CNNs) were found to be the most efﬁcient archi-

tecture for a variety of medical imaging applications;

nevertheless, they also talked about the necessity for

explainable AI models in the healthcare industry and

the difﬁculties associated with interpretability. Raz-

zak et al. (2018) provided a deeper analysis of the

difﬁculties and potential applications of deep learn-

ing in medical image processing, stressing the sig-

niﬁcant improvements in segmentation and classiﬁca-

tion. They did, however, highlight the need for more

effective algorithms that can deal with huge medical

datasets.

Mohsen et al. (2018) concentrated on using CNN

architectures and deep learning neural networks for

brain tumor classiﬁcation. They achieved high clas-

siﬁcation accuracy and proved that deep learning is

useful for tumor detection. However, the extent to

which their results can be applied to other tumor types

may be restricted because of their dependence on par-

ticular datasets. Lastly, Shin et al. (2016) veriﬁed

CNNs’ superiority in improving system performance

by looking into CNN designs, dataset properties, and

transfer learning for computer-aided detection sys-

tems. However, they highlighted that big, annotated

datasets—which can be resource-intensive—are nec-

essary for training good models.

5 PROPOSED METHODOLOGY

The proposed methodology uses advanced deep-

learning techniques to improve the classiﬁcation

of lung X-ray images for diagnosing pneumonia.

We implement ﬁve renowned convolutional neu-

ral network (CNN) architectures—VGG16, VGG19,

ResNet, DenseNet, and Inception. Each model is ﬁne-

tuned on a specialized dataset of lung X-ray images

to optimize their performance for this speciﬁc task. A

unique pooling layer is added before the dense layers

for better feature extraction and to eliminate overﬁt-

ting. Furthermore, we apply data augmentation and

hyperparameter tuning methods to improve the mod-

els’ accuracy and robustness. Medical practitioners

will have a reliable means to identify pneumonia and

the system’s quick processing and classiﬁcation of X-

ray images. To conﬁrm the proposed system’s perfor-

mance and guarantee its efﬁcacy in a clinical scenario,

evaluation metrics like precision, recall, F1-score, and

confusion matrix are utilized. By using this method,

the system hopes to improve and automate the di-

agnostic process, which might decrease the need for

more intrusive treatments like CT and MRI scans.

6 DATASET INFORMATION

The dataset consists of approximately 15,000 X-ray

images categorized into normal, pneumonia, opaque,

COVID lung conditions, sourced from Kaggle. Each

image is in standard .png format, facilitating straight-

forward analysis. For uniformity, the photos were

scaled to 32 by 32 pixels, and the pixel values were

normalised to fall between 0 and 1. To improve model

robustness, data augmentation was used, which in-

volved rearranging the dataset. Eighty percent of the

photos in the dataset were utilised for training, while

twenty percent were used for testing. In order to expe-

dite the process, the dataset is uploaded from a desig-

nated directory, after which the photographs are anal-

ysed and labelled appropriately, guaranteeing a struc-

tured framework for further research. This dataset is

essential for creating and assessing models meant to

increase medical imaging diagnostic precision.

Figure 1: X-rays of the chest: left - without pneumonia,

right – with pneumonia

7 METHODOLOGY AND

IMPLEMENTATION

The study’s methodology section describes in great

detail how several deep learning architectures are

used to the classiﬁcation of biological images. Con-

volutional neural networks (CNNs), generative ad-

versarial networks (GANs), and transfer learning are

some of the main methods covered. These techniques

are used to improve the precision and effectiveness of

medical image classiﬁcation, including MRI, CT, and

OCT scans.

Medical Image Classiﬁcation Using Deep Neural Networks: An X-Ray Classiﬁcation

765

7.1 CNN Architecture

Using CNNs, the paper thoroughly examines layers

including convolutional, pooling, and fully connected

layers. Activation functions, speciﬁcally ReLU, and

dropout layers are used to prevent overﬁtting. The

method emphasises how important these layers are for

feature extraction and dimensionality reduction of the

input images as a requirement for accurate classiﬁca-

tion.

7.2 Data Augmentation and

Preprocessing

In order to reduce overﬁtting and boost the range of

the training dataset, data augmentation techniques are

used. The dataset requires being set up for deep learn-

ing model training using preprocessing procedures

like image scaling and normalization. These stages

ensure that the input data is in a proper format for the

neural networks to process

7.3 Transfer Learning

It is noted that transfer learning is a useful method

for utilizing pre-trained models on sizable datasets

and optimizing them for particular biomedical image

classiﬁcation applications. This method expedites the

training process and lessens the requirement for large

labeled datasets.

7.4 Algorithm

The implementation section details the practical ap-

plication of the discussed methodologies. The

deep learning models are implemented using popular

frameworks such as TensorFlow and PyTorch. The

implementation involves setting up the neural net-

work architectures, deﬁning the loss functions, and

conﬁguring the optimization algorithms for training

the models.

7.4.1 VGG16 and VGG19

Deep learning models from the Visual Geometry

Group, such as VGG16 and VGG19, are well known

for their ease of integration and efﬁciency in image

classiﬁcation applications. What distinguishes these

architectures from one another is their homogene-

ity—13 or 16 convolutional layers for VGG16 and

VGG19, respectively. Small 3x3 ﬁlters with stride 1

are used in each convolutional layer to preserve spa-

tial resolution throughout the layers. Max-pooling

layers employing a 2x2 ﬁlter with stride 2 come after

the convolutional layers, hence lowering the computa-

tional cost and spatial dimensions. A softmax classi-

ﬁer, which outputs the probability distribution across

the target classes, is the ﬁnal fully connected layer in

both models. Each of the model’s initial two layers

has 4096 neurones. Following each convolutional and

fully connected layer, Rectiﬁed Linear Unit (ReLU)

activation functions are applied to give the model non-

linearity. With a focus on simplicity and depth, our ar-

chitecture produces signiﬁcant performance gains on

picture classiﬁcation benchmarks while maintaining a

neat, consistent design.

7.4.2 ResNet

ResNet, or Residual Networks, represents a break-

through in the design of deep neural networks by ad-

dressing the degradation problem that occurs when

adding more layers to a network. This degradation

problem leads to a decrease in accuracy as the net-

work depth increases, not due to overﬁtting but be-

cause of the inability to effectively train deeper net-

works. By using skip connections, also known as

identity shortcuts, which let the gradient pass straight

through the network layers, ResNet introduces resid-

ual learning. In order to accomplish this, residual

blocks are introduced, in which the input to a small

number of stacked layers is likewise added straight

to the output, so ”skipping” these levels. With archi-

tectures like ResNet50, which has 50 layers and can

learn exceedingly complicated features while remain-

ing easy to train, this method enables the creation of

incredibly deep networks. To improve convergence,

the network makes use of batch normalisation and

ReLU activations. ResNet can train networks with

hundreds or even thousands of layers because to its

creative architecture, which greatly enhances perfor-

mance on a range of computer vision tasks.

7.4.3 DenseNet

DenseNet, or Densely Connected Convolutional Net-

works, is an architecture that connects each layer to

the following one in a forward method. Each layer

in a DenseNet architecture receives as inputs the fea-

ture maps of all layers that came before it, creat-

ing a dense network of connectedness. Stronger gra-

dients during training, more effective parameter us-

age, and enhanced feature propagation are some of

the main beneﬁts of this approach. DenseNet is di-

vided into dense blocks, each of which is made up of

several convolutional layers that carry out 3x3 con-

volutions. Between dense blocks, transition layers

are used to manage the complexity of the network

and lower the size of the feature maps. These lay-

INCOFT 2025 - International Conference on Futuristic Technology

766

ers consist of a 2x2 average pooling layer and a 1x1

convolution. ReLU activation functions are used in

the model, and average pooling rather than max pool-

ing is used for downsampling, which increases overall

efﬁciency. Compared to conventional convolutional

networks, DenseNet performs better with fewer pa-

rameters because it directly connects all layers, which

also helps to reduce the vanishing gradient issue.

7.4.4 Inception

The Inception architecture, known as GoogLeNet,

uses a multi-scale strategy at the network layers to

manage the variation in feature scale between images.

Each inception module in the network executes con-

volutions at several scales (1x1, 3x3, and 5x5) and an

overlapping max-pooling operation simultaneously.

The network is thus able to collect a large variety of

features at various scales by concatenating these con-

volutions along the depth dimension. To further re-

duce the computational stress on the following layers,

the architecture incorporates 1x1 convolutions. This

reduces the number of input channels. During train-

ing, Inception moreover incorporates auxiliary classi-

ﬁers at intermediary layers that aid in backpropagat-

ing gradients and offering extra regularisation. Large-

scale picture classiﬁcation tasks are a good ﬁt for

the network because of its multi-path design, which

preserves computational efﬁciency while enabling the

network to learn complicated representations. Incep-

tion delivers great accuracy on benchmark datasets

by balancing depth, width, and processing economy

through the use of these strategies.

8 RESULTS

The accuracy, precision, recall, and F1-score of

the various deep learning models—VGG16, VGG19,

ResNet, DenseNet, and Inception—were used to

identify lung X-ray images as normal or pneumonia-

affected. Among these models, VGG16 demonstrated

the highest accuracy, reaching approximately 96% by

the end of the training epochs, indicating its superior

capability in feature extraction for this speciﬁc task.

Inception and VGG19 also showed competitive per-

formance, achieving accuracies of around 92% and

90%, respectively. DenseNet exhibited good initial

performance but plateaued early, while ResNet, al-

though stable throughout the training, recorded the

lowest accuracy of 86%. The introduction of the

novel pooling layer and hyperparameter tuning sig-

niﬁcantly enhanced model performance across the

board, with precision and recall metrics further val-

idating the effectiveness of our approach. The con-

fusion matrix analysis revealed a substantial reduc-

tion in false positives and false negatives, underscor-

ing the potential of the proposed methodology for ac-

curate and efﬁcient automated diagnostics in clinical

settings. Overall, these results highlight the promise

of deep learning techniques in medical image classiﬁ-

cation, paving the way for improved diagnostic tools

in healthcare. DenseNet201 and InceptionV3 start

Figure 2: Comparison graph of model performance across

different conditions

with the highest initial accuracy around epoch 0.5,

indicating better initial feature extraction capabilities

compared to the other models. VGG16 and VGG19

also show rapid growth in accuracy during the initial

few epochs, while ResNet50 starts with a moderate

performance.

VGG16 consistently outperforms the other mod-

els, reaching the highest accuracy by the 20th epoch.

This suggests that VGG16 effectively learns features

for X-ray image classiﬁcation over the course of train-

ing. InceptionV3 and VGG19 also exhibit strong

performance, with InceptionV3 showing a steady

and competitive accuracy, closely following VGG16.

DenseNet201 shows good performance in the ini-

tial epochs but plateaus early, indicating that while

it learns quickly, its long-term improvement may be

limited for this task. ResNet50 shows a slower im-

provement rate compared to the others, with a lower

overall accuracy by the end of training.

VGG16 and InceptionV3 show some ﬂuctuations

around epoch 12, indicating possible overﬁtting or in-

stability in learning. However, both recover and stabi-

lize towards the end. DenseNet201 exhibits the least

ﬂuctuations, but this comes at the cost of a plateau

in accuracy, suggesting the model might not be mak-

ing signiﬁcant new learning progress after the initial

stages. ResNet50, although steady, shows the low-

est performance among the models, suggesting that it

may not be the optimal choice for this speciﬁc dataset

or problem without further tuning.

Medical Image Classiﬁcation Using Deep Neural Networks: An X-Ray Classiﬁcation

767

VGG16’s Success: VGG16 stands out as the top

performer in this analysis. It is simple yet deep ar-

chitecture with sequential convolutional layers seems

to be well-suited for extracting relevant features from

lung X-ray images.

Table 1: Comparison of Training Accuracy for Different

Models Over 20 Epochs

Epoch VGG16 VGG19 ResNet50 DenseNet201 InceptionV3

0 0.55 0.55 0.55 0.55 0.55

1 0.74 0.69 0.63 0.59 0.71

2 0.77 0.75 0.69 0.63 0.78

3 0.79 0.78 0.71 0.66 0.80

4 0.80 0.80 0.73 0.69 0.82

5 0.82 0.81 0.74 0.70 0.82

6 0.83 0.82 0.75 0.71 0.83

7 0.84 0.83 0.76 0.72 0.84

8 0.84 0.83 0.76 0.72 0.85

9 0.84 0.84 0.77 0.73 0.85

10 0.85 0.84 0.77 0.73 0.85

11 0.85 0.84 0.78 0.74 0.86

12 0.86 0.85 0.78 0.74 0.86

13 0.86 0.85 0.78 0.74 0.86

14 0.86 0.85 0.79 0.75 0.86

15 0.86 0.85 0.79 0.75 0.87

16 0.87 0.86 0.79 0.75 0.87

17 0.87 0.86 0.79 0.76 0.87

18 0.87 0.86 0.80 0.76 0.87

19 0.87 0.86 0.80 0.76 0.87

50 0.93 0.89 0.82 0.78 0.85

51 0.93 0.89 0.83 0.78 0.85

52 0.93 0.89 0.83 0.79 0.86

53 0.94 0.90 0.83 0.79 0.86

54 0.94 0.90 0.84 0.79 0.87

55 0.94 0.90 0.84 0.80 0.87

56 0.95 0.91 0.84 0.80 0.88

57 0.95 0.91 0.85 0.80 0.88

58 0.95 0.91 0.85 0.81 0.88

59 0.95 0.91 0.85 0.81 0.89

60 0.96 0.92 0.86 0.81 0.89

9 FUTURE SCOPE

The advancement of deep learning models for med-

ical image classiﬁcation, particularly in lung X-ray

analysis, presents signiﬁcant opportunities for en-

hancing diagnostic processes in healthcare. Future

research could expand beyond pneumonia to include

the classiﬁcation of other respiratory diseases such

as tuberculosis, lung cancer, and pulmonary ﬁbrosis,

thereby developing multi-class classiﬁcation models

for comprehensive diagnostics. Additionally, inte-

grating X-ray data with other imaging modalities,

such as CT and MRI, could enhance diagnostic ac-

curacy through a more holistic view of patient con-

ditions. The implementation of real-time diagnostic

systems is another promising direction, allowing for

expedited decision-making in clinical settings. Fur-

thermore, as AI continues to be integrated into health-

care, the development of explainable AI (XAI) tech-

niques will be crucial for helping clinicians under-

stand the decision-making processes of neural net-

works. Addressing dataset limitations by incorpo-

rating diverse data from various demographics and

geographic regions will enhance model generaliza-

tion. Future studies could also explore automated an-

notation and the use of Generative Adversarial Net-

works (GANs) to expand datasets for rare conditions.

Additionally, improved transfer learning techniques

and domain adaptation strategies will allow models to

generalize across different datasets effectively. De-

veloping cloud-based diagnostic tools could facili-

tate widespread access to advanced image classiﬁ-

cation systems, enabling remote analyses, especially

in under-resourced areas. Lastly, integrating these

systems with Electronic Health Records (EHRs) can

provide a comprehensive patient proﬁle, supporting

personalized treatment plans. As AI applications in

healthcare expand, addressing regulatory frameworks

and ethical implications will be essential to ensure re-

sponsible deployment in clinical practice. By pursu-

ing these avenues, the potential for deep learning in

medical image classiﬁcation can be fully realized, sig-

niﬁcantly improving diagnostic accuracy and patient

outcomes in healthcare.

10 CONCLUSIONS

This study demonstrates the effectiveness of deep

learning models in accurately classifying lung X-ray

images as normal or pneumonia-affected, contribut-

ing signiﬁcantly to the ﬁeld of medical imaging. By

leveraging architectures such as VGG16, VGG19,

ResNet, DenseNet, and Inception, we achieved no-

table performance improvements, with VGG16 yield-

ing the highest accuracy of approximately 96%. The

introduction of a novel pooling layer and rigorous

hyperparameter tuning further enhanced model per-

formance, reducing both false positives and false

negatives in our evaluations. These ﬁndings under-

score the potential for deep learning to automate and

streamline diagnostic processes, thereby supporting

healthcare professionals in making timely and in-

formed decisions. Future research should explore the

expansion of this approach to other respiratory con-

ditions and the integration of diverse datasets to im-

prove generalizability. Overall, our work lays the

groundwork for the development of robust diagnos-

tic tools that can be deployed in clinical settings, ul-

timately improving patient outcomes and advancing

the capabilities of medical image analysis.

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768

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