Pyramid Xception network for accurate detection of abdominal abnormalities in CT scans

Abstract

Abdominal abnormalities are deviations from the normal structure or function of organs and tissues within the abdominal cavity. Effective detection and diagnosis of these abnormalities, such as tumors, infections, cysts, structural anomalies, and inflammations, are essential for proper treatment and management. Abnormalities can arise from various factors, including disease, injury, and congenital conditions, making accurate detection crucial for timely medical intervention. Hence, this paper presents the Pyramid Xception Network (PyX-Net) framework, an advanced method for detecting abdominal abnormalities using Computed Tomography images. The methodology starts with acquiring abdominal CT images from a medical database, followed by image enhancement through Anisotropic Diffusion. Organ segmentation is then performed using a Conditional Generative Adversarial Network. After segmenting the organs, features are extracted using the Gray-Level Co-occurrence Matrix and wavelet texture analysis. The final detection of abnormalities is achieved with the PyX-Net framework, which integrates Pyramid Network (PyramidNet) and the Xception model. PyX-Net achieved an accuracy of 91.269%, a True Positive Rate of 92.237%, and a True Negative Rate of 91.142% with a K-group of 9.

Introduction

Accurate diagnosis in the medical area requires classifying the medical condition by recognizing a patient’s symptoms and the outcomes from various medical imaging tests. Different medical imaging technologies, such as Ultrasound, X-rays, Magnetic Resonance Imaging (MRI), CT scans, and Nuclear Magnetic Resonance (NMR) are used for accurate diagnosis¹. Over time, diagnostic imaging using CT scans in the emergency department has contributed to rising hospital costs. The CT scans become a significant source of radiation exposure, particularly in adult patients². However, the patient-tailored approach may not fully encompass the wide spectrum of clinical presentations associated with abdominal pain³. The optimal imaging strategy for patients with abdominal pain should enable the timely identification of urgent conditions without exposing patients to unnecessary imaging⁴. Synthetic CT scans offer the potential to enhance access to radiology services while reducing radiation exposure. In recent years, there has been a development of computer-assisted technologies to support clinicians. The pixel-level semantic information provided by CT scans helps intelligent systems to understand spatial relationships and make critical decisions⁵. Abdominal pain is a prevalent symptom in children, accounting for approximately 5–10% of pediatric visits to the emergency department¹.

When the abdominal pain arises from a non-invasive cause and persists for above five days is known as acute abdominal pain. The causes of abdominal pain vary widely from self-limiting conditions to dangerous situations. The causes of abdominal pain⁶ are further classified into urgent, requiring immediate medical attention, and non-urgent, which do not rapidly escalate in severity⁴. The accurate diagnosis of abdominal pain is crucial for timely and effective management, leading to better outcomes and reducing morbidity. To develop a differential analysis for abdominal pain, a comprehensive understanding is essential for early detection. Additionally, the mechanism of abdominal pain is crucial to be identified by the person. The abdominal pain is manifested in three broad patterns: parietal, visceral, and referred pain. Visceral Nociception involves the stretching and distension of abdominal organs using torsion and contraction⁷. The visceral nociception pain, which is described as a dull ache by the patients, is transmitted through slow-conducting C-fibers. Generally, the visceral pain is localized at the mid stage due to the bilateral nature of the visceral innervation of abdominal organs. Moreover, the disease processes from organs, which are outside the abdominal cavity, can also cause abdominal pain⁸. In recent years, researchers have focused on developing automated systems for precise and timely predictions that aim to conserve time and energy.

The benefit of automatic technologies lies in their ability to evolve over time, which improves performance through the combination of various methods and contributions. The emerging technologies have shown promising results in object recognition, image classification, obstacle avoidance, facial recognition, natural language processing, material inspection, and many other applications^9–12. The radiological evaluation of diseases is primarily based on visual assessment and the interpretation that is enhanced by advanced computer analyses^13,14. Artificial Intelligence (AI) is expected to assist specialists in qualitatively interpreting diseases, including tasks like tumor volume delineation over time, biological progression estimation, clinical outcome prediction, and assessing the impact of disease and treatment on nearby organs^15,16. Deep learning (DL) models have proven highly effective in various fields like medical image segmentation, classification, and lesion detection^17–19. The accuracy of disease detection can be improved by combining the attributes of each model into a stacked ensemble learning classifier^20,21. The Convolutional Neural Network (CNN) allows deep networks to learn and recognize complex features by hierarchically categorizing and combining features from previous layers, a process known as the feature tier^22,23. This feature tier allows DL networks to manage large datasets, efficiently processing millions of inputs through nonlinear functions^24–26. The robustness of CNN in evaluating fluctuating image appearances makes it especially suitable for fully automatic segmentation in CT volumes^13,27.

The key contribution of this research is demonstrated as,

Innovative PyX-Net framework for abdominal abnormality detection The paper introduces a novel method, PyX-Net, that combines the strengths of PyramidNet and Xception models to detect the abdominal abnormalities in CT images.

The layout of the remaining manuscript is as follows: Section “Literature Survey” signifies the existing literature on relevant datasets. The PyX-Net model is detailed in Section “Proposed PyX-Net for Abdominal Abnormality Detection”. Section “Results and Discussion” presents an evaluation of PyX-Net. Section “Conclusion” discusses the conclusion.

Literature survey

CT-based abdominal abnormality detection

Several deep learning approaches have been developed for abdominal abnormality detection using CT images. In⁵, the Two-Stage Training Scheme was introduced by Li, D., et al., for detecting kidney stones in the abdomen. The Two-Stage Training Scheme was highly capable of accurately detecting kidney stones. Moreover, the Two-Stage Training Scheme had high false positives that affected the cropping ability, which led to incorrect predictions. The scholar Park, Y.J., et al.¹⁵ introduced an AI model, which is utilized for the detection of abdominal hemorrhage lesions. The AI model increased the specificity, reduced false positives, and was also capable of detecting abdominal hemorrhage lesions that were scattered in different sizes with high precision. But the AI model did not improve the detection accuracy and also failed to improve the DL techniques. Patro, K.K., et al.¹⁷ introduced the Deep Kronecker Neural Network (DKN) for the automated detection of kidney stones. The DKN achieved high robustness and accurate detection, but the effect of Kronecker convolution on overall computational complexity was not assessed.

Abdominal organ segmentation

Accurate organ segmentation is a critical step for abdominal abnormality analysis. The ResUNet model is devised by Rahman, H., et al., in¹³ for liver and tumor segmentation. The performance of ResUNet was efficient and quick. Additionally, the ResUNet model demonstrated greater efficiency in training time, memory usage, and accuracy. However, ResUNet did not improve localization accuracy or reduce the false negative rate. In²⁸, the DL-based pipeline is introduced by Brutti, F., et al., for localizing and segmenting the thrombus. The DL-based pipeline produced consistent results and did not require prior knowledge about the lumen region. However, the DL-based pipeline was trained only on preoperative CT scans and did not extend the dataset.

DL-Based abdominal abnormality detection

Accurate organ segmentation is a critical step for abdominal abnormality analysis. Zhang, J., et al.²⁹, introduced U-net and a Graph Convolutional Neural Network (U-GCN) for automating the detection and classification of vertebral body fractures. The U-GCN was effective in producing an accurate diagnosis and achieved minimal computational complexity. But, U-GCN failed to simplify the system process. The researcher named Ogunleye, O.A., et al., devised a CNN approach in³⁰ for detecting adipose tissue in children. The CNN enhanced robustness and precision in detection. However, the CNN had included a dataset of pediatric participants who underwent repeated MRI scans and also suffered from generalization issues. The author named Alawneh, K., et al., developed the LiverNet in³¹, which was used for diagnosing liver tumors. The LiverNet was light, fast, reliable, and accurate, but was not implemented on a large clinical dataset.

Research gap and challenges

Although existing studies have reported promising results in abdominal image analysis, several challenges remain unresolved. Variations in image quality, noise, and low-contrast regions in CT images can adversely affect the accuracy of abnormality detection. In addition, precise organ segmentation remains difficult due to complex anatomical structures, overlapping boundaries, and inter-patient variability. Another major challenge is the extraction of discriminative features that effectively represent both texture and semantic information. Many existing approaches rely solely on deep learning features and fail to exploit complementary texture characteristics present in medical images. Furthermore, achieving high detection accuracy while maintaining computational efficiency remains an important requirement for practical clinical applications.

These deficiencies point toward the need for a reliable framework that can effectively enhance image quality, accurately segment abdominal organs, extract informative features, and perform reliable abnormality detection. To address these challenges, this work proposes the PyX-Net framework, which integrates Anisotropic Diffusion for image enhancement, CGAN for organ segmentation, GLCM and wavelet-based feature extraction for capturing texture information, and a hybrid PyX-Net architecture for meaningful feature representation and classification. The combination of these components enables the PyX-Net to improve detection performance while maintaining computational efficiency.

Proposed PyX-Net for abdominal abnormality detection

The proposed model follows a systematic approach, beginning with the acquisition of abdominal CT images and ending with the detection of abnormalities. The process begins by acquiring CT images of the abdomen, which provide a detailed cross-sectional view of abdominal organs. After acquisition, the CT images undergo an enhancement process that is done using Anisotropic diffusion³² to improve the image quality. The enhanced images are then subjected to segmentation, where the specific abdominal organs are delineated using CGAN³³, which is suitable for medical image segmentation. Following the segmentation of abdominal organs, features are extracted from the identified regions. GLCM³⁴ and wavelet texture features³⁵ are used for the subsequent detection of abnormalities. The workflow ends with the detection of abdominal abnormalities using the PyX-Net framework. The PyX-Net model combines the PyramidNet³⁶ and the Xception model³⁷. The detailed conceptual illustration of the proposed PyX-Net for abdominal abnormality detection is presented in Fig. 1.

Fig. 1.

The conceptual illustration of proposed PyX-Net.

Abdomen CT image acquisition

The high- resolution CT images of the abdominal region are considered from the dataset ³⁸, which consists of input images , and the total number of CT images is illustrated in the equation below.

1

Anisotropic diffusion-based image enhancement

The collected CT input image is enhanced using Anisotropic Diffusion³². The anisotropic diffusion is a technique used in image preprocessing to enhance image quality by reducing noise. The process of anisotropic diffusion is mathematically described by the following partial differential equation,

2

where, the image intensity is denoted as at iteration a, refers to the conduction coefficient, and ∇ indicates the divergence operator.

The image-enhanced output is deliberated as E , and it is fed into segmentation.

Abdominal organ segmentation using CGAN

The Abdominal Organ Segmentation refers to the process of delineating different organs within the abdominal region from medical images. The output from image enhancement E is passed to CGAN, which is an extension of the traditional Generative Adversarial Network (GAN). Here, CGAN³³ is used for segmenting abdominal organs. The CGAN can learn both the segmentation mapping and the underlying data distribution through its generator-discriminator framework. The adversarial learning process encourages the generation of more accurate and realistic segmentation masks, particularly in cases with complex organ boundaries and variations in abdominal CT images.

CGAN architecture

The purpose of using CGAN³³ for abdominal organ segmentation is to improve training stability and also increase flexibility. A CGAN incorporates additional information to control the output of the generated data.

1. Generator

The generator creates segmentation masks, which are refined through a process involving encoding and decoding layers. Typically, a UNet architecture is used as the generator. The UNet architecture consists of an encoder, decoder, and convolutional layers. The encoder reduces the spatial dimensions, whereas the object details and the initial resolution are recovered by the decoder. The decoder also uses shortcuts that add features from the contracting encoder and expanding decoder paths. When the spatial size reduces, the network’s depth is increased. A doubling of channels occurs after every pooling layer.

• (b)Discriminator

The discriminator assesses the quality of the segmentation masks by distinguishing between real masks and synthetic masks that are generated by the generator. The Discriminator contains five convolutional layers. The input concatenates source images and either a real mask or predicted masks. Values produced by the model are bounded between 0 and 1, where higher values correspond to a greater likelihood of segmentation.

• (c)Generator loss

The loss function for the generator is a combination of Dice loss and Adversarial loss. The dice loss focuses on matching the predicted masks with the real masks, aiming to improve the overall shape prediction of the organ. The adversarial loss is the log of the discriminator’s output, which is used to refine the contours of the generated mask. The overall loss for the generator is articulated as,

3

where, the generator is denoted as I, whereas the discriminator is specified as J, μ refers to a weighting factor, the generator loss function is labeled as , denotes dice loss, ℜ defines the expectation over the data distribution, and u,v stands for predicted masks and real masks, respectively.

• (d)Discriminator loss

The discriminator loss function is implemented to maximize the likelihood of real masks and minimize the generated masks. The optimization is performed using Binary Cross Entropy (BCE), where the optimizer alternates between updating the generator and the discriminator at each batch.

The loss function for the discriminator is demonstrated in the following equation as,

4

The output from the abdominal organ segmentation is represented as O , which is passed to the feature extraction process. The block diagram of CGAN is depicted in Fig. 2.

Fig. 2.

Block Diagram of CGAN.

Feature extraction

The feature mining reduces the complexity of data while preserving essential information. Feature extraction involves transforming raw data into a feature that is used for tasks, like detection, regression, or clustering. In this paper, the GLCM³⁴ features and wavelet texture ³⁵ features are mined from the segmented organ O.

1. GLCM- based feature extraction

The GLCM ³⁴ is a statistical method used to examine the spatial relationship between pixels in an image. The extracted features are discussed in this section.

• (i)
  Energy Energy measures the uniformity of the matrix elements, and it is also high when pixel pairs are consistent or similar. The formula for calculating energy is demonstrated as,

  5

  where, pixel intensity values are indicated as c,b, and represents the probability of pixel pairs.
• (ii)
  Contrast Contrast evaluates the difference in intensity between a pixel and its neighbor. The contrast is represented in the equation below as,

  6
• (iii)
  Homogeneity Homogeneity refers to the uniformity or similarity of components or elements within a given diagonal. The higher homogeneity values show that the elements are closer to the diagonal. The formula for homogeneity is illustrated in the equation below as,

  7
• (iv)
  Entropy Entropy measures the complexity or randomness of the texture, with higher entropy indicating more complexity or variability in the texture. The entropy is expressed as,

  8
• (v)
  Correlation Correlation explains the degree to which the pixel intensities of an image are linearly related. A high correlation value indicates a strong relationship between the pixel intensities. If the intensity of one pixel increases, then the intensity of neighboring pixels tends to increase. The correlation is calculated based on the given equation,

  9

  where, the means of the pixel intensities in the rows and columns are denoted as , respectively, and refers to the standard deviations.

The overall features mined from the GLCM are demonstrated in the equation below as,

10

(b) Wavelet texture feature extraction

The wavelet transform is employed as a tool for wavelet texture feature extraction³⁵. The wavelet transform allows for the representation of textures at multiple scales by adjusting the spatial resolution. The wavelet transform differs by using wavelets instead of sinusoidal waves. The wavelet transform is commonly implemented to decompose the images into multiple scales using filter banks. The wavelet transform is determined by the following equation,

11

where, γ depicts the wavelet function, translation and scale parameters are indicated as X,Y, respectively, refers to the complex conjugate of the wavelet function, q indicates the position of an image, and the wavelet transform is designated as .

The wavelet functions are generated by translating and scaling the base atom γ that is given in the following equation as,

12

The combination of GLCM features and wavelet texture features is represented in the equation below,

13

The mined features F are subjected to abdomen abnormality detection.

Abdomen abnormality detection using the proposed PyX-Net

Abdominal abnormality detection is very important for diagnosing a large range of medical conditions that can impact the organs and structures within the abdominal cavity. The proposed PyX-Net combines PyramidNet³⁶ and Xception³⁷ to utilize the advantages of both models. PyramidNet helps in extracting multi-scale features, while Xception efficiently captures important spatial features using depthwise separable convolutions. By combining these two networks, PyX-Net learns more informative features than a single backbone model. Hence, the PyX-Net is introduced for the early detection of these abnormalities. The output from the enhanced image E is passed to the PyramidNet model and produced , which is further passed to the PyX-Net layer. Furthermore, the extracted feature F is passed to the PyX-Net layer, in which the PyX-Net layer fuses the received extracted features F with the output of PyramidNet , where regression takes place, and the resultant output A is subjected to the Xception model, which forms the final detection output B. The pictorial representation of the proposed PyX-Net for abdomen abnormality detection is portrayed in Fig. 3.

Fig. 3.

The Pictorial representation of proposed PyX-Net.

Architecture of PyramidNet

This section presents the detailed network architecture of PyramidNets³⁶. The difference between PyramidNets and traditional networks lies in the gradual increase of channel dimensions. The other networks keep the channel dimensions constant until a residual unit with downsampling occurs. However, PyramidNets expands the channel dimensions throughout the network. The enhanced image E is fed into the PyramidNets for further processing. The Systematic diagram of PyramidNet is shown in Fig. 4. The dimension of the feature map can be calculated by using the equation below,

14

where, the residual unit is denoted as r, and w refers to the group.

Fig. 4.

Systematic Diagram of PyramidNet.

The residual units within the cluster have the same feature map size, and each cluster consists of residual units . After passing through the residual units in a group, the feature map dimensions are doubled, while the feature size is simultaneously reduced by half. The increased feature map is represented by the following equation:

15

where, α denotes the residual units, and defines the step factor.

However, to increase the channel dimension, introduces an alternative method for generating a pyramid structure. The transformation of Eq. (15) is given as,

16

In an additive network, the feature map dimensions increase linearly, whereas in a multiplicative network increase geometrically. Due to the variations in feature map dimensions in PyramidNet, mapping cannot be used as a shortcut. Therefore, zero-padded shortcuts are employed across all residual units. The zero-padded shortcut prevents overfitting as it does not introduce additional parameters and has shown significant effectiveness compared to other shortcut methods. The impact of the zero-padded mapping shortcut on the residual unit within the cluster is illustrated by the reshaped vector E , which is demonstrated as,

17

where, the output of the convolutional operations is given as for the residual function, and the dimension of the feature map before residual unit is symbolized as . In the Residual Network (ResNet), the function of the layer of the block is illustrated in the equation below,

18

The minor performance is improved after the removal of ReLU τ. The ReLUs enforce a non-negative shortcut connection that limits the network’s ability to generate negative values in the residual connections. To improve the performance, pre-activation ResNets are identified, where the ReLUs are placed before the convolutional layers. The pre-activation ResNet is deliberated in the equation below,

19

The final output obtained from the PyramidNet is represented in Eq. (19), and the output is passed to the proposed PyX-Net.

PyX-Net layer

The PyraimdNet³⁶ output and feature extracted output F are given as input for the PyX-Net. The Fractional calculus [FC]³⁹ is performed to enhance the ability and analyze systems with complex behaviors. In the proposed PyX-Net framework, the FC combines the feature representation generated by PyramidNet with the handcrafted features extracted using GLCM and wavelet analysis. The fused feature set is then processed through a regression layer before being forwarded to the Xception model for final abnormality detection. This design enables the model to utilize both deep hierarchical features and texture-based handcrafted features, resulting in a richer feature representation.

The output from the GLCM features is considered at a time period , and the obtained resultant output is M, therefore, the values of varies from 1 to 5.

20

where, defines the weight of .

The wavelet texture feature output is taken at a time period , and the obtained output , hence the values of differs from 1 to h, and differ from 1 to l.

21

The equation for FC is depicted in the below equation,

22

where, the output from the Xception model A is considered at a time interval , and the PyramidNet output is taken as the time interval .

Now, consider

23

24

25

26

Now, substitute Eqs. (23), (24), (25), (26) in Eq. (22),

27

Therefore, the final Eq. (28) is obtained by substituting (19), (20), and (21), and is represented in the following equation,

28

Architecture of Xception model

The Xception³⁷ is a CNN architecture that builds upon the concept of the Inception module, which is designed to capture cross-channel correlations and spatial relationships within the feature maps. The Xception model aims to decouple all the cross-channel correlations. This section illustrates the architecture of the Xception module. The framework of Xception is portrayed in Fig. 5.

Fig. 5.

Architecture of Xception model.

1. Role of convolutional layers

The model employs convolutional layers for identifying salient features within the input, and feature maps are subsequently generated using convolutional kernels. The newly generated feature map performs a convolution operation to extract the feature. A non-linearity is introduced into the network because of the activation function that passes the feature maps after the convolution operations. The value of the feature map function is demonstrated as,

29

where, the weight and bias vector of filter and layer are specified as and .

• (b) Depthwise separable convolutional block of Xception

Depth-wise separable convolution is a technique used in CNNs to reduce the computational cost and model complexity while maintaining performance. Unlike conventional convolution, which operates across all input channels simultaneously, depthwise convolution applies an individual filter to each channel separately. Following this, a point-wise convolution is applied across all channels to combine the features extracted from each channel and learn correlations between different channels. A max-pooling operation is applied to the feature maps to decrease the spatial resolution.

• (c) Residual connections

Within the Xception framework, residual links contribute to improved performance and more efficient information flow. The residual connections are an essential feature as they allow the network to pass certain layers, thus helping to avoid the gradient problem and enabling the training of deeper networks. The abdominal abnormality detection output is deliberated as B.

Results and discussion

This section presents the image outcomes and performance evaluation obtained by the PyX-Net.

Experimental setup

The proposed PyX-Net framework is implemented in the Python programming environment for abdominal abnormality detection from CT images. The deep learning architecture is developed using TensorFlow and Keras, while image preprocessing and enhancement are performed using OpenCV and Scikit-image. Scikit-learn is used for performance evaluation, and NumPy, Pandas, and SciPy are employed for numerical computations and data handling. Visualization of results is carried out using Matplotlib and Seaborn.

The detailed training configuration, hyperparameters, optimization settings, hardware and software specifications used for implementation are presented in Appendix.

Dataset description

The experiments in this study are conducted using the MICCAI FLARE22 Challenge Dataset²⁰, which contains 50 labeled abdominal CT scans collected for the MICCAI FLARE 2022 Challenge. Among the 50 CT scans, 22 represent normal cases, while 28 correspond to abnormal cases. The dataset comprises high-resolution abdominal CT images covering multiple organs and anatomical structures, providing diverse samples for training and evaluating the proposed segmentation and abnormality detection framework.

Evaluation metrics

(i) Accuracy: Accuracy H denotes the ratio of absolute predictions to the total number of predictions and is mathematically illustrated in the equation below as,

30

where, N denotes the true positives, R represents true true negative, T signifies true false positives, and U indicates true false negatives.

(ii) TPR: The TPR ϑ defines the distribution of actual positive cases that the PyX-Net framework correctly detects, and it is demonstrated as,

31

(iii) TNR: The TNR ρ represents the percentage of actual negative instances that the PyX-Net correctly classifies as negative, and it is represented in the equation below.

32

Image results

The detected abdomen abnormality image outcomes obtained from the PyX-Net are depicted using the MICCAI FLARE22 Challenge Dataset.

• (i) For Image 1

The image results for image 1 are shown in Fig. 6. Specifically, the input image is displayed in Fig. 6a, and an enhanced image is pictured in Fig. 6b. The segmented image is presented in Fig. 6c. The horizontal histogram image is depicted in Fig. 6d, the vertical histogram image in Fig. 6e, the diagonal histogram image in Fig. 6f, and the approximated histogram image in Fig. 6g.

Fig. 6.

Image 1 outcomes: (a) input image, (b) enhanced image, (c) segmented image, (d) histogram of horizontal image, (e) histogram of vertical image, (f) histogram of diagonal image, (g) histogram of approximate image.

• (ii) For Image 2

The image results for image 2 are delineated in Fig. 7. In detail, Fig. 7a displays the input image, and the enhanced image in Fig. 7b. The segmented image is specified in Fig. 7c. The horizontal histogram image is shown in Fig. 7d, the vertical histogram image in Fig. 7e, the diagonal histogram image in Fig. 7f, and the approximated histogram image in Fig. 7g.

Fig. 7.

Image 2 outcomes: (a) input image, (b) enhanced image, (c) segmented image, (d) histogram of horizontal image, (e) histogram of vertical image, (f) histogram of diagonal image, (g) histogram of approximated image.

• (iii) For Image 3

The image results for image 3 are illustrated in Fig. 8. Specifically, Fig. 8a displays the input image, and the enhanced image is portrayed in Fig. 8b. The segmented image is presented in Fig. 8c. The horizontal histogram image in Fig. 8d, vertical histogram image in Fig. 8e, diagonal histogram image in Fig. 8f, and approximated histogram image in Fig. 8g.

Fig. 8.

Image 3 outcomes: (a) input image, (b) enhanced image, (c) segmented image, (d) histogram of horizontal image, (e) histogram of vertical image, (f) histogram of diagonal image, (g) histogram of approximated image.

Performance evaluation

The performance of the proposed hybrid model, PyX-Net is evaluated by varying the epochs and layers based on learning samples. To assess the effect of sample allocation, the dataset is divided into multiple training–testing ratios, including 60:40, 70:30, 80:20, and 90:10.

Learning samples by altering epochs

The performance analysis of PyX-Net with varying epochs, like 10, 20, 40, and 80 based on learning samples is delineated in Fig. 9. The accuracy obtained by PyX-Net across various epochs is illustrated in Fig. 9a. With 90% of the complete learning samples, PyX-Net achieved accuracies of 84.457% at epoch 10, 86.086% at epoch 20, 88.006% at epoch 40, and 90.944% at epoch 80. The TPR for different epochs using PyX-Net is shown in Fig. 9b. PyX-Net recorded a TPR of 85.583% for epoch 10, 87.004% for epoch 20, 88.969% for epoch 40, and 91.997% for epoch 80, which occurred at learning samples 90%. Figure 9c presents the TNR analysis acquired by PyX-Net. The TNR records 84.766%, 86.766%, 88.375%, and 90.366% for epochs 10, 20, 40, and 80, respectively, at 90% learning samples.

Fig. 9.

Performance evaluation of PyX-Net by altering epochs (a) accuracy (b) TPR (c) TNR.

Learning samples by altering layers

The improved performance of PyX-Net with altering layers 2, 4, 6, and 8, depending on learning samples are illustrated in Fig. 10. Figure 10a presents an accuracy-based evaluation of PyX-Net. With a learning sample of 90%, the PyX-Net achieved accuracies of 85.697%, 87.877%, 90.173%, and 91.269% for layers 2, 4, 6, and 8. In Fig. 10b, the TPR-based evaluation of PyX-Net is shown relative to learning samples. With 90% of learning samples and layer 2, the PyX-Net attained a TPR of 86.233%, while layers 4, 6, and 8 yielded the TPR of 88.233%, 90.686%, and 92.237%, respectively. Figure 10c highlights the TNR performance for PyX-Net, in which the PyX-Net achieved a TNR of 85.576%, 87.646%, 89.968%, and 91.142% for learning samples of 90% at layers 2,4,6, and 8 correspondingly.

Fig. 10.

Performance evaluation of PyX-Net by varying layers (a) accuracy (b) TPR (c) TNR.

Comparative methods

The proposed PyX-Net approach is compared against other techniques, including CNN³⁰, ResUNet¹³, DL-pipeline²⁸, and DKN¹⁷. The comparative methods considered in this study were implemented and evaluated under the same experimental conditions as the proposed PyX-Net framework.

Comparative analysis

The comparative assessment of the PyX-Net method against various prevailing approaches is demonstrated by varying the learning samples as well as the K group. The K-group analysis refers to k-fold cross-validation, where the dataset is divided into k subsets and each subset is used once for testing while the remaining subsets are used for training. During both the training–testing split analysis and k-fold cross-validation, the training and testing sets are kept completely separate to avoid any overlap between samples. Therefore, the data used for testing are not involved in the training process.

• (i) By altering learning samples

The comparative validation of PyX-Net and other prior models is attained by changing the learning samples, as outlined in Fig. 11. The comparison of PyX-Net with other prevailing models based on accuracy is shown in Fig. 11a. The PyX-Net achieved an accuracy of 90.944% with learning samples 90%, while CNN, ResUNet, DL-pipeline, and DKN, attained an accuracy of 82.187%, 84.786%, 86.273%, and 88.179%, respectively. This demonstrates that the PyX-Net model’s accuracy is 3.040% higher than DKN. Figure 11b presents the TPR of PyX-Net and various approaches, where PyX-Net achieved a TPR of 91.997% for 90% of learning samples. In comparison, CNN, ResUNet, DL-pipeline, and DKN obtained TPR of 83.237%, 86.194%, 87.858%, and 89.238%, respectively. PyX-Net outperformed DL-pipeline by 4.498% in TPR. Figure 11c illustrates the evaluation of TNR for PyX-Net across different methods. For the 90% learning samples, PyX-Net achieved a TNR of 90.366%. In contrast, CNN also attained 80.959%, ResUNet gained 83.237%, DL-pipeline reached 85.237%, and DKN achieved 88.236%. The performance of PyX-Net surpassed CNN by 10.409% in TNR.

Fig. 11.

Comparative analysis of PyX-Net by varying learning samples (a) accuracy (b) TPR (c) TNR.

• (ii) By altering K-group

The performance of PyX-Net by varying the K-group is compared with prior models, as shown in Fig. 12. Figure 12a illustrates the accuracy of PyX-Net and other prevailing methods for the K-group. For K-group 9, PyX-Net achieved an accuracy of 91.269%, while CNN reached 83.238%, ResUNet obtained 85.005%, DL-pipeline produced 86.576%, and DKN acquired 88.887%. This indicates that PyX-Net’s accuracy is 6.863% higher than that of ResUNet. Figure 12b presents the TPR of various methods with different K-groups. PyX-Net achieved a TPR of 84.877% for K-group 9, whereas CNN, ResUNet, DL-pipeline, and DKN obtained TPRs of 84.877%, 86.877%, 88.997%, and 90.283%, respectively. The PyX-Net outperformed the CNN by 7.979% in TPR. Figure 12c presents the comparative analysis of TNR for PyX-Net and prevailing techniques. With a K-group of 9, PyX-Net achieved a TNR of 91.142%. In comparison, CNN, ResUNet, DL-pipeline, and DKN recorded TNR of 82.996%, 85.997%, 87.655%, and 89.222%, respectively. PyX-Net’s performance surpassed DKN by 2.106% in TNR.

Fig. 12.

Comparative analysis of PyX-Net by altering k-group (a) accuracy (b) TPR (c) TNR.

Analysis based on region of convergence (ROC)

To determine the optimal threshold value, the ROC curve is used to enhance the detection performance. In ROC space, each point on the curve represents the prediction outcome. Figure 13 illustrates the plot of False Positive Rate (FPR) against TPR. When the FPR is 0.8%, then the TPR values recorded by CNN is 0.932%, ResUNet is 0.947%, DL-pipeline is 0.968%, DKN is 0.979%, and Proposed PyXNet is 0.995%.

Fig. 13.

ROC Analysis of TPR.

Ablation study

An ablation study is conducted to examine the impact of each component of the PyX-Net architecture and the result is given in Fig. 14. Figure 14a–c present the accuracy, TPR, and TNR analyses, respectively. At a k-fold value of 9, the PyX-Net without Anisotropic Diffusion, PyX-Net without CGAN, PyX-Net without feature extraction, PyramidNet, Xception, and the proposed PyX-Net achieved accuracies of 86.89%, 88.99%, 89.56%, 90.13%, 90.78%, and 91.27%, respectively. Similarly, the corresponding TPR values are 86.89%, 88.99%, 89.68%, 91.10%, 91.56%, and 92.24%, while the TNR values are 85.10%, 86.10%, 88.67%, 89.68%, 90.26%, and 91.14%. These results indicate that each module contributes to the overall performance improvement, with the complete PyX-Net framework achieving the highest accuracy, TPR, and TNR among all evaluated configurations.

Fig. 14.

Ablation study (a) accuracy (b) TPR (c) TNR.

Analysis based on fusion techniques

Figure 15 presents the performance analysis of different fusion techniques used in the PyX-Net model. Figure 15a illustrates the accuracy comparison. For k-fold = 9, the PyX-Net with concatenation, attention-based fusion, weighted averaging, fully connected fusion, and the proposed FC-based fusion achieved accuracies of 87.88%, 88.46%, 89.68%, 90.55%, and 91.27%, respectively. The TPR comparison is shown in Fig. 15b. The PyX-Net with concatenation, attention-based fusion, weighted averaging, fully connected fusion, and the proposed FC-based fusion attained TPR values of 88.57%, 89.35%, 90.45%, 91.35%, and 92.24%, respectively. Figure 15c presents the TNR analysis. The corresponding TNR values obtained by the PyX-Net with concatenation, attention-based fusion, weighted averaging, fully connected fusion, and the proposed FC-based fusion were 86.77%, 87.79%, 89.00%, 90.12%, and 91.14%, respectively. The results demonstrate that the proposed FC-based fusion strategy achieves the highest accuracy, TPR, and TNR among all evaluated fusion techniques.

Fig. 15.

Ablation study (a) accuracy (b) TPR (c) TNR.

Segmentation analysis

The segmentation performance of the proposed CGAN is compared with existing segmentation methods, namely U-Net⁴⁰ and Detectron2⁴⁰. Figure 16a–c present the comparative analysis based on Dice coefficient, Intersection over Union (IoU), and Hausdorff distance, respectively. For an image size of 512 × 512, U-Net, Detectron2, and CGAN achieved Dice coefficient values of 88.99%, 90.89%, and 93.00%, respectively. Similarly, the corresponding IoU values are 91.23%, 92.55%, and 93.67%. In terms of Hausdorff distance, U-Net, Detectron2, and CGAN recorded values of 3.340 mm, 2.990 mm, and 2.589 mm, respectively. The results demonstrate that the proposed CGAN outperforms the compared segmentation methods by achieving the highest Dice coefficient and IoU, while obtaining the lowest Hausdorff distance.

Fig. 16.

Segmentation analysis (a) Dice coefficient (b) IoU (c) Hausdorff distance.

Comparative discussion

The comparative evaluation of performance metrics with varying learning samples and K-group is detailed in Table 1. For a K-group of 9, PyX-Net attained an accuracy of 91.269%, TPR of 92.237%, and TNR of 91.142%. In contrast, existing approaches reported the following results: CNN with 83.238% accuracy, ResUNet with 85.005%, DL-pipeline with 86.576%, and DKN with 88.887%. Similarly, the TPR for CNN reached 84.877%, ResUNet attained 86.877%, DL-pipeline occurred 88.997%, and DKN obtained 90.283%. For TNR, CNN reached 82.996%, ResUNet yielded 85.997%, DL-pipeline acquired 87.655%, and DKN secured 89.222%. In the proposed framework, each stage contributes to improving the quality of the input for the subsequent stage. Anisotropic Diffusion reduces noise while preserving important boundaries, enabling more accurate organ segmentation. The CGAN-based segmentation stage isolates the relevant organ regions, reducing the influence of background structures during feature extraction. Subsequently, GLCM and wavelet-based features are extracted from the segmented regions, providing discriminative texture information for classification. Finally, the PyX-Net classifier combines handcrafted and deep features to improve robustness against minor errors introduced in previous stages.

Table 1.

Comparative discussion of PyX-Net.

Alterations	Metrics	Existing methods				Proposed PyX-Net
		CNN	ResUNet	DL-pipeline	DKN
Learning samples of 90%	Accuracy (%)	82.187	84.786	86.273	88.179	90.944
	TPR (%)	83.237	86.194	87.858	89.238	91.997
	TNR (%)	80.959	83.237	85.766	88.236	90.366
K-group of 9	Accuracy (%)	83.238	85.005	86.576	88.887	91.269
	TPR (%)	84.877	86.877	88.997	90.283	92.237
	TNR (%)	82.996	85.997	87.655	89.222	91.142

Computational complexity evaluation

The computational complexity of the proposed PyX-Net is evaluated and compared with CNN, ResUNet, DL-pipeline, and DKN in terms of computational time, training time, inference time, and memory consumption. The results are presented in Table 2. Among all the methods, the proposed PyX-Net achieved the lowest computational time of 26.999 s, compared to 43.999 s for CNN, 37.091 s for ResUNet, 33.990 s for DL-pipeline, and 29.990 s for DKN. Similarly, PyX-Net required the least training time of 21.888 s and inference time of 1.489 s. In terms of memory usage, PyX-Net consumed 12.600 MB, which is considerably lower than other models. These results indicate that the proposed PyX-Net offers superior computational efficiency while maintaining lower memory requirements, making it suitable for real-time abdominal abnormality detection applications.

Table 2.

Computational complexity evaluation.

Metrics	CNN	ResUNet	DL-pipeline	DKN	Proposed PyX-Net
Computational time (sec)	43.999	37.091	33.990	29.990	26.999
Training time (sec)	35.670	30.070	27.556	24.313	21.888
Inference time (sec)	5.001	3.800	2.689	1.990	1.489
Memory (MB)	25.700	23.600	18.700	16.700	12.600

Conclusion

The PyX-Net framework shows a significant advancement in the detection of abdominal abnormalities using CT images. By integrating PyramidNet and Xception models, PyX-Net shows the strength of both architectures to enhance detection accuracy and efficiency. The combination of advanced image processing techniques with powerful DL models in PyX-Net produces a better performance rate than other prior methods. The proposed PyX-Net methodologies include crucial steps: acquisition of abdominal CT images, image enhancement with Anisotropic Diffusion, Segmentation using CGAN, and feature extraction through GLCM and wavelet texture analysis. The PyX-Net framework demonstrates superior performance compared to existing methods by improving accuracy and reliability in detecting and diagnosing abdominal abnormalities. PyX-Net has demonstrated significant advancements in performance across various performance metrics, including accuracy, TPR, and TNR. With a K-Group of 9, the model achieved an accuracy of 91.269%, a TPR of 92.237%, and a TNR of 91.142%. The PyX-Net framework has shown promising results in the detection of abdominal abnormalities using CT images. However, the PyX-Net will be further refined and expanded with a database to offer more comprehensive and effective solutions for detecting and diagnosing abdominal abnormalities.

A. Training configuration and experimental settings

To ensure reproducibility and fair evaluation, the proposed Pyramid PyX-Net framework is implemented under a fixed and controlled training configuration. The implementation is carried out in Python 3.9.11 using TensorFlow and Keras for deep learning model development. Image preprocessing and enhancement are performed using OpenCV and Scikit-image, while Scikit-learn is used for performance evaluation. Numerical computations are supported using NumPy, Pandas, and SciPy. Visualization is performed using Matplotlib and Seaborn. The complete training hyperparameters and optimization settings used in the PyX-Net framework are summarized in Table 3.

Table 3.

Training hyperparameters and optimization settings of PyX-Net.

Parameter	Value	Description
Epochs	80	Total number of training iterations
Batch size	32	Number of samples per gradient update
Optimizer	Adam	Adaptive optimization algorithm
Learning rate	0.01	Initial step size for weight updates
β1	0.99	Exponential decay rate for first moment estimates
β2	0.999	Exponential decay rate for second moment estimates
Epsilon	1e-4	Numerical stability constant
Dropout rate	0.2	Regularization to prevent overfitting
Kernel size	(3, 3)	Convolution filter size
Activation function	Sigmoid	Output layer activation function
Random seed	42	Ensures reproducibility

B. Hardware and software environment

All experiments are conducted using a standardized hardware and software environment to ensure computational consistency and reproducibility. The hardware configuration employed for the implementation and evaluation of the proposed PyX-Net framework is summarized in Table 4. The corresponding software environment, including the programming language, deep learning frameworks, and supporting libraries, is presented in Table 5.

Table 4.

Hardware configuration used for PyX-Net experiments.

Component	Specification	Description
Operating System	Windows 11	Development and execution platform
CPU	1.7 GHz processor	Handles preprocessing and CPU-based computation
RAM	8 GB	Supports memory-intensive operations
GPU	CUDA-enabled GPU	Accelerates deep learning training
Storage	> 100 GB	Stores datasets, models, and outputs

Table 5.

Software and framework configuration.

Component	Version/tool	Purpose
Programming language	Python 3.9.11	Core implementation language
Deep learning framework	TensorFlow, Keras	Model design and training
Image processing	OpenCV, Scikit-image	Preprocessing and enhancement
Evaluation tools	Scikit-learn	Performance metrics computation
Numerical libraries	NumPy, Pandas, SciPy	Data processing and analysis
Visualization	Matplotlib, Seaborn	Result plotting and analysis

Author contributions

Ramesh Kumar Ramaswamy designed the model and the computational framework and analysed the data. Ramesh Kumar Ramaswamy, Gopika Gopinathan Nair Santhini, Rajasree Rajendran Nair Sivakumari and Santhosh Kumar Balan carried out the implementation. All authors performed the calculations. All authors wrote the manuscript with input from all authors. All authors conceived the study and were in charge of overall direction and planning.

Funding

This research did not receive any specific funding.

Data availability

The datasets generated during and/or analysed during the current study are available in the MICCAI FLARE22 Challenge repository, https://flare22.grand-challenge.org/.

Code availability

The source code developed for the proposed PyX-Net framework is publicly available at https://github.com/ramesh4477/PyX-Net.git.

Declarations

Competing interests

The authors declare no competing interests.