1.1 Objectives of the proposed method

1. Combining NCA and SGS: To integrate the techniques of NCA and SGS so that this integrated technique brings better accuracy in segmentation, which remains consistent across different radiology practices or sub-populations of patients.

2. Enhancing Efficiency and Ensuring Quality Control: Efficiency and quality control: The level of care and thoroughness in an automated quality control process should be maintained while maximizing computational efficiency to prevent the emergence of extra expenses.

3. Providing Radiologists with State-of-the-Art Instruments: Leverage the power of consequently highly advanced computational tools to enable radiologists with better breast cancer diagnostics.

4. Dealing with constraints on available resources: Create a universally accessible solution that can be adjusted to different healthcare settings, thereby helping to decrease healthcare inequalities.

Fig 1 depicts the block diagram of the proposed approach, which introduces multiple innovative techniques for segmenting breast tumors. The proposed model guarantees consistent accuracy in segmenting regardless of changes in medical practices or patient populations, strikes a balance between model performance and computational efficiency, improves radiologists’ diagnostic abilities, and adjusts to different healthcare settings.

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Fig 1. Flowchart of functional units.

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The organization of this document is delineated as follows: The study’s important earlier research is discussed in Section 2. Section 3 explores the techniques used to identify and separate breast abnormalities. The empirical dataset and the results are displayed in Section 4. The results, future research directions, and limitations of the study are outlined in Section 5. The concluding remarks of this paper are presented in Section 6.

2.1 A general method for segmentation in medical imaging

Medical imaging has advanced greatly with deep learning technologies, specifically deep convolutional neural networks (CNNs), making segmentation a key area of computer vision research [20]. Thresholding, clustering, edge detection, and the Lattice Boltzmann method have improved traditional segmentation methods. These methods define and classify image regions for accurate image analysis and tumor diagnosis [21].

Deep learning has been popular in this field because it can autonomously learn and identify visual features, outperforming manual segmentation [22]. The U-net architecture excels at semantic segmentation in medical imaging, improving diagnostic accuracy through precise image feature evaluation [23].

In the particular domain of mammography segmentation, several techniques have demonstrated notable efficacy:

2.2 Breast tumor segmentation based on classical method

Certain researchers have devised techniques to detect breast cancer lesions at an early stage. Utilizing the developed methodologies, masses in breast cancer images have been segmented. The approach comprises the following methods: marker-controlled watershed, threshold, active contour model, region-growing, watershed, template-matching, and level set [38, 39]. The classical segmentation method is comprised of three groups: threshold-based segmentation, edge-based segmentation, and region-based segmentation. It is based on the pixel values of an image [40]. Some studies are explained below that use threshold-based segmentation or edge-based segmentation or region-based segmentation.

The comparative analysis of segmentation algorithms for the detection of microcalcifications in mammography images was undertaken by Podgornova et al [41]. In the current study, benchmarking of three segmentation techniques has been done: watershed, mean shift, and k-means. The dataset used in the experiment consisted of 250 mammography images obtained from the Mammographic Image Analysis Society database. The results obtained from the watershed segmentation method were an accuracy rate of 18.0%, and in the detection results, 94.0% were false. The mean shift method detected the true detection rate at 39.22% and the false detection rate at 60.8%. Meanwhile, k-means segmentation showed a true detection rate of 42.8% and a false detection rate of 57.2%.

B.N. Beena et al [42] proposed a technique for segmenting mammogram images by waters idealist segmentation and classifying cancer present using the k-NN. The standard classification k-NN technique was used; the method followed to do it was the extraction of GLCMs through the Halarick texture characteristics from an available dataset of 60 mammogram images in the MIAS dataset; a Sober filter was used for noise reduction, which finally gave a segmentation of 83.33% and accuracy of 83.33.

Singh et al [43] presented the segmentation technique for breast cancer, making use of global thresholding and region merging. Wiener filtering technique was used to reduce the Gaussian noise in the present study, and in order to normalize the image, a histogram shrinkage technique was employed. Otsu’s approach for global thresholding was underpinned in the proposed to give an accuracy at 82.0% with a corresponding error rate of 18.0%, applied to a dataset of 50 images of mammography.

The research proposed by Syeda et al [44] was on automatic pectoral muscle segmentation in mammography images. This study isolates and removes the pectoral muscles in the mammograms of a breast by using global threshold and weak boundary detection techniques. A convex-hull segmentation is then performed. This technique results in an accuracy of 92.86% in segmentation from the MIAS database with a median filter for the removal of noise. Also, 4.97% of the photos received good segmentation.

In addition, Andrik et al [45] and his research group presented a methodology for fully automatic breast boundary and pectoral muscle segmentation in mammography. In the present study, the contour boundaries of the pectoral muscle were identified using Canny edge detection. In order to remove the noise, median and anisotropic diffusion filters were also performed. The method as described above returned Dice similarity coefficients within the range of 97.8% to 99.2% with the use of datasets based on the MIAS, INbreast, and the Breast Cancer Digital Repository databases.

Another comprehensive framework for the enhancement, mass segmentation, and classification of mammography images was proposed by Al-Najdawi et al. [46]in which the methodology that the researchers used incorporated a number of enhancement techniques such as Clare and median filters, among others, in order to improve the performance of breast ROI detection. On a dataset of 1300 mammogram images acquired from King Hussein Cancer Center and Jordan Hospital, it achieved sensitivities and specificity rates of 96.2% and 94.4%, respectively. On a separate note, the classifier achieved accuracies for mammogram mass calcification of between 81.4% and 94.1%, with a segmentation accuracy of 90.7%.

2.3 Breast tumor segmentation based on deep learning approaches

The process of segmenting breast cancers was accomplished by using deep learning methodologies implemented on diverse neural networks. ome models, on the other hand, use deep learning techniques for breast tumor segmentation, such as U-Net [47], SegResNetVAE [48], DynUNet [3], UNETR [49], RF-Net [50], and MDA-Net [51]. Such models have shown impressive effectiveness with regard to their ability to accurately obtain segmentation results.

The architecture of U-Net incorporates an encoder to acquire comprehensive contextual representations and a decoder to make semantic predictions. Skip connections are used to retrieve incomplete spatial data. A dice score of 86.60% and an accuracy of 90.73% were attained [47]. A modified U-Net with residual connections, autoencoder regularization, and unique Encoder Block and Variational Autoencoder Branch outperforms the standard version. The Autoencoder Truncation branch boosts the dice score to 89.36% and accuracy to 92.78% as per published data. [48].

The DynUNet, a dynamic variant of the U-Net paradigm, outperforms both U-Net and SegResNetVAE models with 93% accuracy and 89.57% dice score [3]. UNETR, incorporating multi-head self-attention instead of 3D convolutions, achieves 90.73% accuracy and 89.59% dice score but falls short compared to DynUNet [49].

The RF-Net design uses an encoder-decoder architecture to enhance pixel predictions by feeding challenging pixel residual representations into encoder blocks. Achieving 92.92% accuracy and a dice score of 89.56%, this method is highly proficient in segmenting breast lesions [50].

MDA-Net features a multiscale fusion block with 1 × 1, 3x3, and 5x5 convolutions, addressing fixed receptive field issues and facilitating semantic feature extraction. MDA-Net enhances brain tumor segmentation by achieving 93.48% accuracy and a 90.25% dice score [51]. Deep learning methods, like ECNN with optimized loss functions, 3 × 3 filters, and BAT algorithm for binary segmentation, improve efficiency. A novel approach, sequential U-Nets, automates 3D brain tumor detection using a stacked U-Net design. ARU-GD method enhances computer learning with performance metrics [52]. Pan et al. [53] study introduces three new modules (PEM, SGA, and CSA) to enhance medical image segmentation in EG-TransUNet, a Transformer-based architecture.

Utilising MDU-Net, a Multi-Scale Densely Connected U-Net, to segment biomedical images. By incorporating novel multi-scale dense connections (MDC), their model successfully amalgamates adjacent feature maps, resulting in a 3.5% enhancement in segmentation performance. In liver tumor diagnosis from CT images, a novel approach combines U-Net with GW-CTO algorithm, outperforming alternatives by 4.3%-5.2%, with 85% learning efficiency [54, 55]. In eye tracking, Eye-UNet, incorporating an attention mechanism, excels in segmenting low-quality human eye images, outperforming other methods [56]. A compilation of conventional methodologies pertaining to the segmentation of breast tumors is presented in Table 1.

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Table 1. Understanding the limitations of convention studies.

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3.1 Rationale for using a 3D model for 2D data

This study is set to investigate the use of a three-dimensional model in analyzing two-dimensional image datasets for better feature extraction, boundary delineation, and accuracy on segmentation tasks. Clearly, the depth and contextual information in multiple planes are very important for accurate breast tumor segmentation. The approach will make use of 3D convolutions and 3D batch normalization to capture features that span along slices, which assist in improving the consistency of segmentation. It helps to stabilize the process of learning and decrease the effect of internal covariate shifts, improving the ability to generalize learned knowledge to new situations.

The 3D model brings the added functionality of handling multi-channel data, in which case correlation and interaction among different image channels help to derive accurate and reliable segmentation. The M3D-NCA framework efficiently utilizes the spatial context and manages data to produce high-quality segmentation results.

One of the advantages of using a 3D model is that it gives contextual information necessary for the accurate segmentation of structures in images. It can capture fine structures better, maintain consistent boundaries, and enhance learning ability. The ability of the 3D model to process volumetric data better enables it to learn and generalize from the data and hence perform better than models operating in 2D.

By integrating the sophisticated methods of SGS with 3D models, RUNet can include shape priors or other contextual information in a more comprehensive fashion. This can greatly boost the model’s ability to generate precise and dependable segmentation outcomes. On its own, the advantages brought by the 3D model are adequate for it to be utilized even when the input data is in the format of 2D slices.

3.2 M3D-neural cellular automata (M3D-NCA)

M3D-NCA represents a three-dimensional cellular automata model designed especially for medical imaging data. The software models the proliferation and interaction of cells in the three-dimensional grid by using cellular automata principles, and it is able to segment a breast tumor very efficiently. This process is started by the model through the generation of a grid of cells representing the three-dimensional volume of breast tissue. Following that, each cell updates its state according to the states of its neighbors based on the learned rules. The latter makes it possible for the model to iterate toward better segmentation of the tumor. The approach will ensure both an optimal usage of computational resources and high accuracy in tracing all fine details of breast tumor boundaries. The training process uses a combination of Dice Loss and Binary Cross-Entropy to drive better segmentation performance. Inherent adaptive learning of the evolution rules for cell states in M3D-NCA reinforces its strength toward robustness across variations in tumor appearance among different patients.

3.3 Shape-guided segmentation (SGS)

Shape-guided segmentation is one of the approaches that increases the accuracy of segmentation by making good use of tumor shape data available in advance. It is particularly efficient in medical imaging, especially when dealing with anatomic structures with consistent shapes. It uses advanced methods, such as SLIC over-segmentation techniques, to generate superpixels that may later be used as guides in order to further segment any given image. SGS enhances the accuracy of segmentations by shape information embedded within the segmentation model, ensuring that the result of the segmentations fits very tightly to the true anatomical boundaries. In this work, they introduce SGS into the M3D-NCA framework, which they refer to as the Shape-Guided Block (SGB). Then, the SGB consists of modules like Shape-Shared Unpooling, represented as SPM, and Superpixel Pooling as SUM. These modules correct deviations from the anticipated tumor shapes and thus improve the segmentation iteratively. This step-by-step integration will improve the accuracy of segmentation and enhance the model’s capability in handling indistinct or uncertain boundaries in medical images.

3.4 The proposed architecture of the model

This model architecture is configured to deliver an accurate breast tumor segmentation using sophisticated methodologies. Due to M3D-NCA and SGS, this method improves the accuracy and computational efficiency of segmentation. It exploits this advantage by using the rule-based evolution of cellular automata from M3D-NCA and uses it with accurate, shape-constrained guidance from SGS. This collaboration enhances the performance of the model in order to ensure its preciseness for the outlining of tumors and efficient computation within the bounds of the available resources. It has critical constituents in the architecture to assure dependable segmentation results. Algorithm-driven development in M3D-NCA with an accurate, shape-informed direction of SGS builds on the overall effectiveness to guarantee precise identification of tumor boundaries.

3.4.3 Shape-guided segmentation (SGS) integration.

SGS is a technique enhancing the accuracy of tumor segmentation by integrating their shape characteristics. This approach combines dividing an image into small sub-images and turning on features based on the shape of the objects, improving boundary detection accuracy and making the segmentation of an image into different parts better. SGS uses sophisticated methods to apply advanced methods apart from SLIC over-segmentation, Shape-Shared Unpooling, and Superpixel Pooling modules to ensure that the segmented output perfectly corresponds to the actual anatomical structure of the tumors depicted in Fig 3.

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Fig 3. To visualize the combination of localized and globalized learning for enhanced performance, model integration using hybrid MLP and transformer layers is utilized.

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• SLIC Over-segmentation:
  SLIC over-segmentation iteratively breaks down a given image into superpixels, which retain the structural details of the objects in an image. Hence, boundaries of tumors can be correctly delimitated. Shape-Guided Block combines the Share-Shared Unpooling module with the Superpixel Pooling module, using shape information generated from the SLIC over-segmentation.
  SPM makes use of shape information extracted from SLIC superpixels to guide the unpooling process, ensuring that the upsampled feature maps retain the shape features of the segmented objects. The SUM pooling approach utilizes information derived from SLIC-generated superpixels that help boost feature representation by highlighting those regions that are shape-guided.
• Shape-Guided Block (SGB): Now, how incorporation of SGB within the SGS framework works: First of all, an SLIC Oversegmentation algorithm generates superpixels from the image. After that, feature maps are upsampled using the shape-shared unpooling technique by the SPM module. At last, the SUM module involves the aggregation of features within each superpixel, hence taking a shape-guided region into consideration in order to enhance feature representation.
  It is in using these very components that SGS utilizes the shape information extracted from tumors to improve segmentation in the accurate definition of tumor boundaries and hence improves the refinement of overall segmentation. This will ensure that expected segmentation maps are both accurate and representative of the actual shape of the tumors.

3.5 Training pipeline

The M3D-NCA+SGS architecture presents an end-to-end neural network for segmenting breast tumors, only taking images as input and returning the segmentation maps without any intermediate operation carried out by the user outside the network on its output. This representation integrates SGS into the M3D-NCA framework to process 2D mammographic slices and 3D volumetric data directly, hence ensuring an end-to-end workflow from input to output.

The methodology proposed in the following enhances the performance of M3D-NCA by processing very extensive three-dimensional medical images efficiently. It exploits a well-customized training pipeline that helps reduce V-RAM usage by implementing a careful downscaling strategy, guided by several aspects. On this regard, training was done at multiple scales with a scale factor of 5, which deals efficiently with high-resolution images without consuming much V-RAM during training. For example, taking an image with a dimension of [640, 640, 48], a reduction factor of d = 2 and iteration times for downsampling of n = 4, it will reduce to [40, 40, 3] as seen through an Eq 2.

The study uses shape-guided segmentation (SGS) to improve segmentation and detect hazy edges. Instead of using all convolutional layers in M3D-NCA, it substitutes some with SGS, helping the proposed method discover unclear borders and improve segmentation precision. To initialize segmentation at the smallest scale s, the suggested initial NCA model m1 iterates for a predetermined number of steps based on the core architecture and SGS. The patchification technique is repeated n − 1 times to obtain maximum resolution using an Eq 9, and dice focus loss is applied to the remaining and ground truth patches. (9) resulting in the final output after s iterations: (10) where:

• I₀ is the initial input to the model.
• M_x(I_n) represents the application of model M_x to the input I_n.
• I_s is the output after s applications of M_x.
• denotes the s-fold application of M_x on I₀.

Batch duplication is employed to mitigate training instability, as NCA models exhibit greater instability compared to conventional machine learning models due to patchification and stochastic cell activation fluctuations. Duplicating input photos several times in a batch improves convergence stability. The Pseudo Ensemble technique is used to exploit NCAs’ probabilistic nature, running the trained model ′n_epoch′ = 3000 times with the same data sample mathematically expressed in Eq 11. (11) Where:

• n_epoch = 3000 represents the number of iterations for averaging model outputs.

Early-stopping in model training is also used to reduce unnecessary calculations and ensure model convergence after 20 epochs.

3.6 Inherent quality assurance

The Neural Cellular Automata quality metric (NQM) is introduced to assess the accuracy and reliability of segmentation predictions within the context of this study. The degree of deviation of each of the ten predictions produced by the model from the training model was determined. (12)

Algorithm 1 Tumor Segmentation

for i = 0 to N do    ▷ M3D-NCA

 perform_convolution(), apply_dense_layer(), apply_3D_batch_normalization(), apply_ReLU_activation(), adjust_scaling_factors()

end for

over_segmented_image = SLIC_method(image)    ▷ SGS

for superpixel in over_segmented_image do

 pooled_superpixel = superpixel_pooling_module(superpixel)

 unpool_shape = shape_shared_unpooling_module(pooled_superpixel)

end for

segmentation_result = shared_classification_layer(unpool_shape)

for (prediction, target) in zip(predictions, targets) do    ▷ Loss

 bce_loss, dice_loss = calculate_BCE_and_dice_loss(prediction, target)

 total_loss = bce_loss + dice_loss

end for

for layer in model_layers do          ▷ Transformer

 if layer.type == ′Transformer′ then

  apply_transformer_layer(layer)

 end if

end for

4.1 Datasets

This study evaluates a proposed methodology for segmenting breast tumors using three publicly accessible datasets. The INbreast dataset [59] consists of 115 cases and 410 images. These images depict a range of abnormalities, including asymmetries, calcifications, tumors, and deformities. Out of these, 89 tumor images were accurately labeled, with 62 chosen randomly for teaching purposes and the remaining ones assigned to the validation set [59].

The DBT dataset [60] includes data from individuals who underwent digital breast tomosynthesis (DBT) evaluations between 2014 and 2018. The dataset, which includes 5,610 patients and 22,032 reconstructed volumes from 5,610 trials involving 5,060 participants [60], is categorized into benign, actionable, normal, and malignant groups.

The CBIS-DDSM dataset [61, 62], which is an enhanced version of the DDSM mammography dataset, consists of 339 images where incorrect Regions of Interest (ROIs) have been eliminated to improve the quality of the data. The study employs a dataset of 2,620 mammograms, each with its corresponding mask. This dataset provides information on factors such as BI-RADS, mass contour, calcification type, breast tissue density, abnormality severity, screening type, impacted breast, and patient age. [61, 62].

4.2 Experimental setup

The evaluation involved assessing the efficacy of the segmentation algorithm by measuring key metrics including accuracy (ACC), Dice Score, mean Intersection-over-Union (mIoU), and 95% Hausdorff Distance (HD95). These metrics help measure the algorithm’s performance by evaluating its accuracy, the level of agreement with the ground truth, and the overall quality of segmentation. The datasets utilized in this investigation are condensed in Table 2.

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Table 2. Overview of mammography datasets and acquisition details.

https://doi.org/10.1371/journal.pone.0309421.t002

We utilize the same preprocessing method as the winner of the BraTS 2013 Challenge for data augmentation. First, we resize the image to 256 × 256 and then normalize each modality’s images individually by subtracting the mean and dividing by the standard deviation. Afterwards, we crop the generated images at coordinates [5, 5] to remove any data points that deviate significantly from the average, and then we rescale the images to have a range of values from 0 to 1. Elastic deformation was employed to precisely replicate authentic medical imaging scenarios, thereby enhancing the quality of large-scale images.

The datasets used to evaluate the M3D-NCA and comparator models include INbreast, DBT, and CBIS-DDSM. Each trial consistently employs a 70% training and 30% test split, utilizing an Nvidia RTX 3090 graphics card and an Intel Core i5-13400 processor. The study employed the UNet, Segmentation Models Pytorch, and nnUNet libraries using the default configurations in PyTorch. The utilized optimization algorithm is Adam. The learning rate is 0.000015625, and the total number of epochs is 3000. The early stopping technique is implemented when the model’s performance does not show any improvement after 20 epochs. In addition, the model is saved once 10 epochs have been completed.

4.3 Results

The study aimed to evaluate the efficacy of a breast cancer segmentation model across three different datasets. The INbreast, DBT, and CBIS-DDSM datasets were used for training and testing. The optimal threshold for the model was determined through a process of randomly selecting participants from the training data.

The proposed solution underwent evaluation in comparison to cutting-edge methods including UNet, Swin-UNet, UTNet, SegFormer, ResUnet, and TransUnet. The training epochs were standardized to 300 for all methods to guarantee equitable comparisons, and three consecutive photographs were utilized as inputs. The Tables 3–5 display the comparison results between the proposed model and the most advanced methods on the INbreast, DBT, and CBIS-DDSM datasets.

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Table 3. Approaches comparison on the INbreast dataset.

https://doi.org/10.1371/journal.pone.0309421.t003

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Table 4. Approaches comparison on the DBT dataset.

https://doi.org/10.1371/journal.pone.0309421.t004

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Table 5. Approaches comparison on CBIS DDSM dataset.

https://doi.org/10.1371/journal.pone.0309421.t005

The performance metrics of the proposed model, with and without the SGS module, demonstrated substantial enhancements in segmentation accuracy, Dice Score, mean Intersection-over-Union (mIoU), and 95% Hausdorff Distance (HD95) across all datasets. The integration of SGS was demonstrated by combining it with selected benchmark models, namely U-Net and TransUnet, highlighting its impact because combining SGS with all six state-of-the-art methods would be ideal, given the extensive nature of these experiments. The outcomes of these supplementary experiments are presented in Tables 3–5 demonstrating enhancements in performance when SGS is integrated with these benchmark models.

The variance values in the performance metrics were derived using cross-validation, a technique that involves dividing the data into multiple folds and training and evaluating the model on each fold. The standard deviation reflects the degree of consistency in performance. This cross-validation procedure entailed dividing each dataset into five folds, training on four, and testing on one. The mean of the performance metrics on all folds is reported, with its standard deviation capturing the variability in this metric.

Most of the time, the performance variation benchmarks will be prominent because of dataset variability, differences in the difficulty of samples within test/training folds, and how random the training process actually is. In that way, this study provides an all-round assessment of model performance based on both mean and standard deviation values, which, in turn, draw attention to consistency and resilience concerning data divisions. To visually represent the stability of each approach, Fig 4 depicts a radar graph comprised of the HD95 and MIOU values for all models. The results of flops and parameters in a horizontal graph for each model are displayed in Fig 5.

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Fig 4. Comparison of MIOU and HD95 of the proposed model with state of art methods.

https://doi.org/10.1371/journal.pone.0309421.g004

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Fig 5. Comparison of Parameters and Flops of the proposed model with state of art methods.

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4.3.2 Efficiency metrics.

By including these metrics, our proposed model, M3D-NCA+SGS, sounds perfect with respect to efficiency and performance, as shown in the Table 6.

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Table 6. Efficiency metrics for different models.

https://doi.org/10.1371/journal.pone.0309421.t006

While being very competitive in all aspects of the performance indicators with respect to speed of processing and inference times, it did maintain a lower level of memory use compared to some other models that are state-of-the-art.

4.4. Experimental comparison of loss functions

To validate the effectiveness of our combined loss function, we conducted experiments comparing it with other common loss functions, such as Focal Loss and IoU Loss. The performance metrics for these experiments are summarized in Table 7.

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Table 7. Comparison of different loss functions.

https://doi.org/10.1371/journal.pone.0309421.t007

The results in Table 7 indicate that our combined DiceLoss and BCE function outperforms other loss functions, providing a balanced approach that enhances both region-based and pixel-wise accuracy. The balanced approach of using both region-based and pixel-wise accuracy metrics provides better overall performance, especially in handling class imbalances and ensuring precise boundary delineation.

4.5. Ablation study

In this study, we have used three different datasets separately: CBIS-DDSM Dataset. First, we have trained and tested the results of this study using the Med-NCA framework on all three datasets. Later on, we have used the M3D-NCA framework on the same datasets with the same input sizes. Finally, for further evaluation, we have trained and tested our proposed model M3D-NCA+SGS on the same datasets with the same input sizes.

We excluded some convolutional layers in the proposed model and adopted the SGS method. The results for the three models are well documented in Tables 3–5, which clearly indicate that the proposed model outperformed both Med-NCA and M3D-NCA efficiently to the utmost. This basically tells us that the efficiency of the model increased at a higher percentage when the SGS method was used compared to excluding some convolutional layers.

It is worth mentioning that the computational time of the proposed model is at the same level of importance as M3D-NCA and far outweighs that of Med-NCA. The characteristic mentioned above underlines the efficiency and computational benefit coming from the proposed methodology. Plotting and quantitatively evaluating the data are important for completeness in this study. Further, discussion concerning the strengths and weaknesses of the proposed methodology adds to the overall understanding of the results obtained.

The efficacy of the methodology is illustrated in this study using three distinct datasets: INbreast, DBT, and the CBIS-DDSM dataset. After the Med-NCA framework, the M3D-NCA framework and the proposed M3D-NCA+SGS model were utilized in the initial implementation, as shown in Tables 3–5. By its SGS implementation, the latter model surpasses both Med-NCA and M3D-NCA. The computational efficacy of the model is equivalent to that of M3D-NCA, although it exceeds that of Med-NCA. The results demonstrate the effectiveness and computational benefits of the methodology.

The ablation study also considered the inclusion and exclusion of the SGS module. The performance metrics for the proposed model with and without SGS are presented in Tables 3–5, demonstrating the significant impact of SGS on improving segmentation accuracy, Dice Score, mean Intersection-over-Union (mIoU), and 95% Hausdorff Distance (HD95).

The result of segmentation using the proposed model with M3D-NCA and state-of-the-art methodologies are depicted in Figs 6 and 7. The effectiveness of state-of-the-art segmentation methods is illustrated in Fig 6, albeit with certain limitations in the outcomes. In contrast, Fig 7 demonstrates that the proposed method outperforms all state-of-the-art segmentation methods and M3D-NCA across all datasets utilized in the research.

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Fig 6. Segmentation results of state of art methods.

https://doi.org/10.1371/journal.pone.0309421.g006

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Fig 7. Segmentation result of proposed model, M3D-NCA and Med-NCAs.

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