1.1. Background and motivations

Breast cancer has developed as a notable global health issue, standing as one of the primary contributors to global mortality rates. According to the Global Cancer Observatory (GLOBOCON) in 2020, female breast cancer had an estimated incidence rate of 11.7%, resulting in 2.3 million new cases worldwide [1]. With a mortality rate of approximately 13.6%, this cancer type accounts for 1 in 6 deaths related to cancer, underscoring the crucial need for timely detection and treatment to enhance survival rates. Besides, the World Health Organization (WHO) emphasizes breast cancer’s global impact, with 2.3 million new cases and 685,000 deaths in 2020. Efforts to enhance diagnostic capabilities are crucial especially in the regions with high breast cancer rates. Advancements in breast cancer detection, including professional visual examinations to detect palpable lumps indicating cancerous tissue, are vital for accurate assessment and treatment planning (WHO, 2020) [2,3].

Various imaging techniques such as mammography, sonography, Magnetic Resonance Imaging (MRI), Single Photon Emission Computed Tomography (SPECT), Positron Emission Tomography (PET), optical, and microwave imaging are commonly utilized for breast cancer diagnosis. Despite being the standard method, mammography has limitations like radiation exposure, patient discomfort, and difficulty in imaging dense tissues [4]. Consequently, current research aims to enhance detection rates using existing methods and explore new diagnostic options. Additionally, to aid radiologists in improving mammography screening accuracy, Computer-Aided Diagnostic (CAD) software has been developed and used clinically. However, disappointing data indicates that CAD methods applying mammograms did not enhance diagnostic accuracy significantly [5]. Therefore, there is an urgent need for alternative detection methods in breast cancer diagnosis.

Recent advancements in infrared camera technology have generated clinical interest in thermal imaging, known as thermography, involves measuring the heat emitted by different parts of the human body. A patient’s thermogram provides a visual representation of heat distribution throughout the body. Tumors exhibit higher temperatures than surrounding normal tissue due to their elevated metabolic rate and increased vascular angiogenesis. Infrared imaging, a non-invasive method, is utilized as a diagnostic tool for various diseases such as cancer, diabetes, and hypertension [6]. Consequently, breast cancer tissue appears as a distinct focal point in infrared images. Modern infrared cameras are precisely calibrated, and there exist well-established standards for thermography. Breast thermography offers several advantages, including non-invasiveness, absence of radiation, quickness, painlessness, and cost-effectiveness [7–10]. Moreover, thermography is suitable for women of all ages, including pregnant women and those with dense breast tissue [11]. Fig 1 illustrates the process of acquiring breast thermographic images.

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Fig. 1. The procedure of acquiring breast thermograms [12].

https://doi.org/10.1371/journal.pone.0322934.g001

1.2. Literature review

Most of the research performed on breast cancer diagnosis using thermograms relies on the publicly accessible Database for Mastology Research with Infrared Image (DMR-IR) database [13]. Consequently, this paper will provide an overview of studies that have utilized this dataset. Considering the typical CAD system design for breast cancer detection involves preprocessing, segmentation, feature extraction, selection, and classification, a review of existing studies in these areas can be conducted [14,15].

An extended hidden Markov models, Bayesian networks, and random forest are employed in [16] to optimize breast segmentation techniques. However, their proposed method is limited to initial stages in automated or semi-automated systems and their algorithm requires enhancement for real-time applications. An automatic segmentation approach for extracting the ROI from breast thermograms was presented in [17]. The method relied on statistical and texture features extracted from normal and abnormal breasts. Besides, the dataset used in the study was limited and resulted in the mistakenly removal of some lower breast regions. An enhanced segmentation method was proposed in [18] via combining Neutrosophic sets with an optimized fast Fuzzy c-mean algorithm. Subsequently, different kernel functions of SVM were applied to discriminate between normal and abnormal breast tissue. The reported accuracy, recall, and precision rates were 92.06%, 96.55%, and 87.50%, respectively.

Besides, the application of various machine learning techniques, including SVM, KNN, Random Forest (RF), and Decision Tree (DT), for classifying breast images and detecting cancer investigated in [19]. Scale-Invariant Feature Transform (SIFT) and Speeded Up Robust Features (SURF) feature extraction methods were employed to characterize the image data. A comparative analysis of these machine learning models was conducted to evaluate their performance in cancer detection. Accurate segmentation of suspicious regions in thermal breast images which is crucial for breast cancer detection is considered in [20]. This study proposes a novel active contour model for this task that combines initial region localization, a refined energy function, and an optimized stopping criterion to improve segmentation accuracy and speed. Evaluation on standard datasets demonstrates superior performance compared to existing approaches. Furthermore, the segmented regions are effectively used to differentiate between normal and abnormal breasts, highlighting the importance of focusing on these areas for cancer diagnosis. A novel region-based level-set method was developed for the automated segmentation of suspicious regions in breast thermograms in [21]. Subsequently, a three-layer feed-forward neural network was trained on higher-order statistical and GLCM-based texture features extracted from these segmented regions. Using a randomly selected subset of 50 thermograms with confirmed hot spots from the DMR-IR database, the model achieved an 89.4% accuracy in differentiating between malignant and benign breast tissue.

Additionally, several CAD systems have been proposed for breast cancer detection using thermal images, with a primary focus on feature selection techniques. A CAD system is presented in [22] employing Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) for feature selection and SVM for classification, achieving accuracies of 94.29% and 97.14%, respectively, on the DMR-IR dataset. [23] introduced a CAD system utilizing PSO and Genetic Algorithms (GA) for feature selection and SVM for classification, reporting accuracies of 86.16% and 87.08% on a dataset of 336 thermal images after feature reduction. The CAD system proposed in [24] combining Extreme Learning Machines (ELM) and Optimized Directed Mutual Information (ODMI) for feature selection with various classifiers. Their system achieved a best accuracy of 98.49% on a dataset of 968 images while reducing the feature vector size by approximately 57%. [25] presented a CAD system employing Random Subspace Feature Selection (RSFS) and combinations of mRMR and GA with RSFS for feature selection and k-NN and SVM for classification. Their system achieved accuracies ranging from 77.41% to 87.83% on a dataset of 121 thermal images. A novel greedy search optimization method for feature selection within a Machine Learning (ML) framework introduced in [26]. They compared this approach to sequential backward, sequential forward, and exhaustive methods, finding that sequential backward selection was most effective for small datasets due to reduced redundancy and computational time with the accuracy of 88.57%.

Moreover, to classify images and extract relevant features, [27] integrated SVM with GA. The SVM was optimized through a 30-iteration process involving 140 participants in each iteration. Additionally, a GA with 100 iterations was employed to enhance SVM performance. The proposed method demonstrated high classification accuracy and an Area Under the Curve (AUC) of 97.91% when evaluated on the DMR-IR dataset. In addition, [28] proposed a novel image analysis and machine learning approach for breast cancer detection. Background noise was eliminated using the top-hat transform, followed by curve coefficient extraction through curve transform wrapping. Texture features derived from these coefficients were combined with geometric, statistical, and strength features to enhance classification accuracy. A comparative analysis of various machine learning methods revealed SVM as the superior classifier. Moreover, CNNs with Bayesian networks were used in [29] to improve breast cancer detection. Bayesian networks were introduced due to the black-box nature of Artificial Neural Networks (ANNs), which lack interpretability. This method was crucial for maintaining consistent probabilities and achieving full interpretability within the Bayesian network framework, as it is a probabilistic knowledge representation method. The CNNs and Bayesian networks were trained, evaluated, and integrated into a system, resulting in an improved diagnostic expert system. A model accuracy of up to 95% was achieved.

In addition, deep learning methods are being explored to analyze breast thermograms, aiming to improve early detection accuracy and potentially complement traditional diagnostic methods. A multi-input classification model was proposed by [30] to categorize breast thermal images. This model incorporated multiple perspectives of thermal images and patient-specific clinical data. By employing Convolutional Neural Networks (CNN), the model processed front, left (L90), and right (R90) view images simultaneously. The integration of diverse image angles with clinical information enhanced classification accuracy, as demonstrated by a 97% accuracy rate on the DMR-IR dataset. The study further highlighted the significant contribution of side view images in improving classification performance and the potential of clinical data for patient identification. In addition, [31] explored the optimization of CNN architectures using two biomimetic algorithms. Their primary objective was to determine the optimal structure for the fully connected layer to improve classification accuracy. The study revealed that GA surpassed PSO in refining model performance. Both optimization techniques outperformed traditional methods and exhibited adaptability to different network configurations. Besides, [32] introduces a novel breast segmentation approach that integrates curvature function (k) and gradient vector flow. Subsequently, a CNN was developed to classify the segmented breast images. The primary objective of this research was to evaluate the performance of CNN against traditional classification methods. To this end, each breast image was meticulously characterized by its shape, color, texture, and laterality (left or right). The resulting dataset was employed to train the CNN model and conduct comparative analyses with three established classifiers: random forest, multilayer perceptron, and Bayesian network. Experimental results demonstrate that the CNN model outperforms these conventional methods in breast image classification. Moreover, [33] employed PyTorch to preprocess and resize breast thermal images to a standardized 640x640 pixel format, excluding low-quality images. A CNN-based approach was adopted to detect breast cancer across five image views. Independent CNN models were developed and trained for each view, with their outputs subsequently combined to train a final neural network. This ensemble incorporated convolutional layers featuring 32, 64, and 128 channels, along with stride-2 and 2x2 pooling operations to reduce image dimensions to a probabilistic 1x2 matrix. Integrating clinical data into the CNN further enhanced performance, resulting in an improved accuracy of 93.80%. A pre-trained TransUNet network was first used to extract ROI areas from the DMR-IR dataset in [34]. The processed images were then inputted into four models, including EfficientNetB7 and VGG16, for classification. Accuracy rates of 98.39%, 97.26%, 77.53%, and 97.81% were achieved for EfficientNet-B7, ResNet-50, Visual Geometry Group (VGG)-16, and DenseNet-201, respectively. Additionally, [35] compared the performance of Inception V3, Inception V4, and a modified Inception V4 (MV4) model for classifying breast thermal images. Based on 467 experiments, all three models demonstrated classification capabilities with varying strengths. While Inception V3 excelled in grayscale image accuracy, both Inception V4 and MV4 exhibited strong performance with color images. Notably, the accuracy of the MV4 model improved with extended training time.

1.3. Contributions

The study’s significant contributions and key points can be outlined as follows:

• Unlike previous literature that has given less attention to nonlinear analysis of breast thermal images, this study applies various essential complexity measures such as fractal dimension, Lyapunov exponent, entropy, and correlation dimension. These measures capture different aspects of the chaotic characteristics of cancerous tumors.
• Texture features based on GLCM are employed to extract information from the images and calculate the characteristics of breast thermograms. Parameters such as contrast, correlation, energy, homogeneity, and diameter reflect aspects such as coarseness, linear dependency, textural uniformity, and pixel distribution within the image. Additionally, this paper introduces a combination of nonlinear and texture features to provide a comprehensive analysis of thermal images.
• A metaheuristic multi-objective optimization approach, NSGA III, is utilized to simultaneously minimize the objective function and the number of selected features and the results are evaluated in comparison to other metaheuristic optimization techniques, including GA, PSO, and Differential Evolution (DE) algorithms.
• The study employs k-fold cross-validation to mitigate the sensitivity of classification accuracy to training and testing datasets. It also explores diverse machine learning methods for effectively detecting breast cancer from digital thermography images.

Fig 2 illustrates the overall diagram of the proposed algorithm designed for diagnosing breast cancer from digital thermograms. Detailed explanations of each component are provided in the subsequent sections.

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Fig 2. Flowchart of the presented approach.

https://doi.org/10.1371/journal.pone.0322934.g002

1.4. Paper organization

The structure of the remainder of this work is outlined as follows. Section 2 describes the input dataset of DMR-IR breast thermograms. In Section 3, the various stages of the proposed CAD system are detailed, including pre-processing, feature extraction, feature selection, classification techniques, and the classification function. Experimental results and performance evaluation are presented in Section 4. Section 5 compares the proposed method with other related works, while Section 6 conclude the obtained results.

2.1. Ethics statement

This study utilized the DMR-IR database, a publicly available and anonymized dataset. As the data were previously collected and fully anonymized, this secondary analysis did not involve direct interaction with human subjects or access to identifiable personal information. Consequently, no additional ethical approval was required for this research.

3.1. Segmentation

Assessing the malignancy or benignity of an IR image requires segmenting its different sections to isolate and extract the Region of Interest (ROI) from the thermograms. Given the specific color representation of different temperatures in infrared images, each section of the image corresponds to a distinct color indicative of a particular temperature. Analyzing features within the hottest regions of the thermograms enables the detection of abnormalities [36].

For this purpose, the grayscale breast thermographic images from the DMR-IR dataset were first thresholded using Otsu’s method. This method was employed for image thresholding in this study due to its simplicity, computational efficiency, and automated threshold selection based on histogram analysis. Widely used in image processing, Otsu’s method calculates an intensity threshold to divide pixels into two distinct classes: foreground and background by minimizing intra-class variance or maximizing inter-class variance. This approach is particularly effective for segmenting thermograms with distinct temperature differences between regions of interest and the background. As a non-parametric technique, Otsu’s method requires no prior assumptions about data distribution, making it suitable for diverse thermographic datasets. Compared to alternative techniques like manual, adaptive, iterative, k-means clustering, and entropy-based methods, Otsu’s method offers superior stability in segmentation results, eliminates the need for manual parameter adjustment, and benefits from widespread validation and adoption in medical image processing. Its algorithmic equivalence to globally optimizing a k-means clustering algorithm applied to the image intensity histogram further highlights its robustness for precise delineation of object boundaries [37].

Subsequently, the Hue, Saturation, Intensity (HIS) color space was employed for pseudo-coloring the grayscale images. Pseudo-coloring is a technique that transforms grayscale thermal images into colorized visuals by mapping intensity values to a predefined color spectrum. This process assigns distinct colors to temperature ranges, with hotter areas often appearing in red and yellow and cooler areas in blue and turquoise, visually highlighting regions of abnormal heat distribution. By enhancing the visibility of subtle intensity differences, pseudo-coloring improves input quality for automated feature extraction algorithms and supports healthcare professionals in identifying potential malignancies. Additionally, the human eye’s heightened sensitivity to color differences makes pseudo-coloring effective for emphasizing specific image attributes, aiding in clinical interpretation without advanced tools. The HSI color space is often used for this purpose, with hue, saturation, and intensity selected as coordinate axes. More details about this algorithm are provided in [38,39].

Finally, the Fuzzy C-Means (FCM) clustering algorithm was utilized to separate the various clusters within the image and extract its ROI. This algorithm was chosen in the current study due to its ability to handle ambiguity and overlapping clusters, crucial for analyzing breast thermograms [40]. Unlike strict clustering methods like k-means, FCM assigns membership values to pixels, reflecting gradual transitions in temperature. This flexibility is essential for capturing subtle intensity variations in thermograms, aiding in tumor detection and segmentation [41]. Various similarity measures such as distance, connectivity, and intensity are used to identify groups in different datasets and applications. In this research, feature values are leveraged to classify images into four groups: white matter, grey matter, Cerebrospinal Fluid (CSF), and abnormal tumor regions. While membership functions from FCM do not directly reveal real data distributions or facilitate fuzzy pattern recognition, they are constructed using available data. To achieve this, an appropriate clustering algorithm is essential for grouping data based on similarity or dissimilarity measures like distance. The C-means clustering algorithm, a simple unsupervised learning method suitable when the number of clusters is known, is employed in this work. The FCM method for image segmentation involves specific steps outlined in [42].

Step 1: Assign a number ( ) to denote the clusters.

Step 2: Arbitrarily select vectors from the learning data as the initial centers of clusters.

Step 3: Employ the Euclidean distance measure to assign each vector (where the dimension of input vectors is denoted by ) to the cluster with the closest center :

(1)

Step 4: Recalculate the estimated cluster centers . Let be the vectors assigned to cluster i, and m be a fuzziness exponent. The new cluster center c_im\m is obtained as:

(2)

where the number of vectors in the i_th cluster is denoted by N_i.

Step 5: If all of the cluster centers do not change in Step 4, terminate the algorithm; otherwise, return to Step 3.

3.2. Feature extraction

As mentioned previously, this study concentrates on two categories of extracted indices: complexity measures or nonlinear indices, and texture features.

3.2.2. Chaotic indices.

Chaotic time series offer valuable tools for developing procedures to assess nonlinear systems. In the case of biomedical image processing, leveraging nonlinear analysis and chaotic indices can effectively characterize complex patterns within the data [44]. This study utilizes techniques such as FD, LE, KSE, and CD to offer robust tools for analyzing complex and dynamic phenomena evident in biomedical images. These methods contribute to enhancing diagnostic approaches within the field.

Fractal dimension: The concept of FD relates to a geometric representation across multiple dimensions, where the inherent structure of the original image remains consistent irrespective of scale. This quality of self-similarity seen in fractal images suggests that every subsection tolerates resemblance to the original image. The “partial dimensions” concept can be effectively described using the FD, with the Box-Counting Method (BCM) being a popular approach for FD estimation in the literature. The BCM involves dividing the image into square boxes of similar sizes and counting the number of boxes that cover parts of the image. By repeating this process with smaller boxes, the numbers of containing boxes are counted at each step. The FD of the pattern is then determined by plotting the logarithm of the counted box numbers against the logarithm of the magnification index for each partitioning step and calculating the slope of the best-fitting line. This slope represents the FD (D) value, providing insight into the complexity and structure of the strange attractor [40].

(3)

where

(4)

Lyapunov exponent: LE serves as a metric for quantifying how rapidly two trajectories diverge when they originate from nearly identical initial conditions within a state space. This sensitivity to initial conditions is a fundamental characteristic of chaotic systems. By calculating the LE, one can gauge the degree of chaos present within the system. In this study, we utilize the same methodology for computing LE as outlined in [46]. This approach involves reconstructing a pseudo Phase Space (PS) through a Time-Delay Embedding (TDE) technique applied to the breast thermal image time series. Subsequently, the Lyapunov exponents are determined using the Jacobian method. In this study, the largest Lyapunov exponent (LLE) is regarded as an index.

K-S entropy: Entropy, defined as the logarithm of the number of microstates of a dynamic system [47], reflects the system’s level of irregularity. KS entropy is a modified version of Approximate Entropy (ApEn) and serves as a measure of complexity in dynamic systems. A low ApEn value typically indicates high predictability and low complexity within a time series. KS entropy, in contrast, demonstrates a high degree of independence from the length of historical data and maintains a consistent value compared to ApEn. Additionally, the algorithm for calculating KS entropy is simpler than that for ApEn, resulting in reduced computation time. The equation representing KS entropy for a symbol of length is expressed as Equation (5).

(5)

represents the probability of similarity between two sequences within m points (based on distance), while denotes the probability of similarity within points. When is constrained to a specific value, the entropy value of the estimated sample can be expressed using Equation (6).

(6)

In this equation, m refers to the length of the sequence being examined, and represents the tolerance level used to determine the similarity between sequences [46].

Correlation dimension: One method for assessing the chaotic nature of a signal is by calculating the correlation dimension. Several methods exist for computing the correlation dimension, such as Grossberger’s method, Thickens’ method, Chord’s method, and Ellner’s method. In Grossberger’s method, the first step involves determining the distance between each pair of points within the phase space. The correlation sum for each radius can be calculated as the sum, over all points on the attractor, of the count of points within radius , normalized by the total number of points in the attractor as (7).

(7)

In Equation (7), the norm denotes the Euclidean distance between points, where represents the neighborhood radius, is the total number of points, and is the Heaviside function. The term preceding the summation represents the reciprocal of the total number of possible vector pairs that could be formed. Therefore, we can interpret the correlation sum as the probability that a randomly selected vector pair will be closer than . After calculating the correlation sum with different values, the correlation dimension is determined by the slope of a log-log plot of the correlation sum against the radius [48].

3.3. Feature selection with meta-heuristic algorithms

Metaheuristic techniques are considered highly effective for solving optimization problems, particularly in feature selection tasks. They excel at efficiently navigating complex scenarios to find optimal solutions.

Genetic algorithm GAs are versatile techniques that can effectively address various optimization problems, including those with constraints and without constraints. By employing iterative processes such as mutation, crossover, and selection, GAs generate optimal solutions from the initial population [49].

Particle swarm optimization This method mimics the behavior of social animals to achieve optimization goals. By continuously modifying particle positions and velocities, PSO strives to minimize optimization challenges and attain optimal solutions [50].

3.4. Cross-validation

To mitigate the over-fitting effect and enhance classifier reliability, the k-fold cross-validation method is utilized [55]. Using as an example, the dataset is divided into ten random combinations of training and test sets. Each subsample is of equal size, with nine used for training and one for testing in each iteration. This process is repeated ten times, ensuring all subsamples are utilized for both training and testing stages.

3.5. Classification

To assess the effectiveness of selected computational features in distinguishing breast thermograms, five different machine learning classifiers, namely KNN, SVM, LDA, Pat net, and Fit net, are utilized.

K-nearest neighbors The KNN algorithm is acknowledged as a simple yet effective classification method that works by categorizing an input feature vector according to its proximity to the k nearest training vectors, identified using a suitable distance metric. The vector is then assigned to the class with the highest popularity among its nearest neighbors. KNN classification is a traditional nonparametric supervised technique renowned for its favorable accuracy, especially when the optimal parameter k is chosen considerately [56].

Support vector machine SVM is a robust tool used for classifying various image sets. It functions by separating data points into separate categories using a hyperplane, which maximizes the margin between the categories. The Radial Basis Function (RBF) kernel is frequently employed in SVM due to its flexibility. Equation (8) delineates the decision function linked with the RBF kernel:

(8)

In Eq. (8), is the Lagrange coefficient, , represents the separating plane and denotes the bias term and the number of support vectors is denoted by . Additionally, Eq. (9) as a Gaussian radial basis function is applied in SVM to handle nonlinear data and defines the decision function [57].

(9)

In which, is the variance of the selected hyper parameter and denotes the Euclidean distance between these two points.

Linear discriminant analysis: LDA is a probabilistic method that operates under the assumption that the probability of a sample belonging to a specific class follows a multivariate Gaussian distribution. LDA calculates this probability based on a formula known as the classification law. From a geometric perspective, this involves defining decision boundaries that partition the v-dimensional hyperspace into regions corresponding to different classes. Notably, the separating hypersurfaces in the multidimensional space are linear, hence it is known as LDA [58].

Pattern recognition network In the Pat net approach, inputs are categorized into target classes through the training of an artificial neural network. For pattern recognition networks in Pat net, the target data must consist of zero-valued vectors with only one element set to 1, representing the target class [55].

Fitting neural network In Fit net methodology, the training process adapts performance based on a specific input set and generates corresponding target outputs. Once the network structure, including desired hidden layers, is established, training is conducted using a designated training dataset. As the neural network learns from the data, it constructs a representation of the input-output relationship [55].

3.6. Performance evaluation

To assess the effectiveness of the proposed approach, various statistical metrics are employed, such as True Positive (TP), True Negative (TN), False Negative (FN), and False Positive (FP). These metrics play a crucial role in calculating important statistical functions. Sensitivity, specificity, and accuracy are fundamental statistical metrics defined as follows (see Equation 10) [59].

(10)

4.1. Evaluation of the proposed method

As previously mentioned, this study builds on the idea of combining texture analysis with non-linear methods to extract features from breast thermal images. To show how well this approach works, an experiment is performed. Different classifiers were employed, utilizing both texture-based and non-linear features independently for the classification of health status within the thermograms. Similar to the previous experiment, 10-fold cross-validation was applied to eliminate the over-fitting effect and enhance the reliability of the classifiers. The accuracy achieved for these classifications is presented in Table 7. Furthermore, a comparison between the evaluation metrics of the selected classifiers for various extracted feature types and the proposed method is illustrated in Fig 8.

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Table 7. Accuracy related to different feature domains on different classifications.

https://doi.org/10.1371/journal.pone.0322934.t007

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Fig. 8. The graph bar of the accuracy comparison for three types of feature sets applying 10-fold cross-validation method.

https://doi.org/10.1371/journal.pone.0322934.g008

Table 7 and Fig 8 showcase the effectiveness of the proposed method, which extracts features by combining texture analysis with non-linear methods, for cancer diagnosing trough breast thermograms. When using the Pat net classifier, which achieved the best results, accuracy reached approximately 85% for texture-based features and 84% for features derived from chaotic characteristics. These results recommend that using only one type of feature is not sufficient for high classification accuracy, highlighting the benefit of combining them. Similar trends are observed with other classifiers. Notably, the features chosen by the NSGA III algorithm include representatives from both texture and non-linear categories, further emphasizing the importance of utilizing them together.

4.2. Comparison with other studies

In order to evaluate the effectiveness of the proposed method in classifying benign and malignant tumors within breast thermal images, a comparison was conducted between its achieved results and those of other techniques employed in prior research utilizing the same dataset. Table 8 summarizes various studies that were performed on a range of datasets, with a particular focus on DMR-IR. These studies implemented diverse feature extraction methods, feature selection approaches and machine learning algorithms for breast cancer detection. The explored approaches encompassed Bayes network, Naïve Bayes, SVM, DT, Multilayer Perceptron (MLP), ELMs, KNN, ANN, RBF, and various deep neural network methods such as CNNs, multi-input CNNs, CNNs with Bayes optimization, transfer learning CNNs, and Mask R-CNN. As illustrated in Table 8, the proposed method by this paper outperforms these existing approaches in the diagnosis of breast cancer from thermal images.

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Table 8. A comparison between accuracies of the present method and the other published results used the same database (DMR-IR).

https://doi.org/10.1371/journal.pone.0322934.t008