GP is an evolutionary computation technique that uses the principles of Darwinian evolution to automatically discover computer programs. In this population-based algorithm, each individual in the population (model or tree) represents a candidate solution to a problem [28]. GP utilizes selection, elitism, crossover, and mutation in evolution to renew populations. A flowchart of the GP algorithm is shown in Fig. 1. Many of these issues have been addressed incrementally, leading to more widespread application of GP in various domains.

Fig. 1.

Flowchart of the GP algorithm. The algorithm starts with an initial population, followed by fitness evaluation and selection. Genetic operators, including elitism, crossover, and mutation, are applied to generate new populations iteratively until a termination condition is met. GP, genetic programming.

Object detection is a computer technology related to computer vision and image processing that involves the detection of certain types of semantic objects (e.g., humans, buildings, or cars) in digital images and videos [29]. Most of the current state of-the-art object detectors are based on DL networks, which mainly use the backbone network for feature extraction of the input image or video, and the detection network for classification and localization. Mainstream object detectors are usually divided into two-stage detection (represented by Faster-RCNN [30]), one-stage detection (represented by YOLOv3 [31]), and a fast single-shot object detector (SSD) [32]. The one-stage detector has a high inference speed, while the two-stage detector has high object recognition accuracy. These object detectors have found a wide range of applications in medical imaging, including COVID-19 detection on X-ray images [33], lung nodule detection on computed tomographic (CT) images [34], and the detection of EC lesions on MRI images [18].

In this subsection, the proposed approach for classifying early EC patients was verified on three MRI datasets: axial diffusion-weighted imaging [DWI], axial T2WI, and sagittal T2WI images. The data and baseline classification methods used for comparison, experiments, and parameter settings are presented in this subsection.

3.2.1 Data Sources

The Institutional Review Board (IRB) of Fujian Maternity and Child Health Hospital (FMCHH) in China approved this retrospective study (No. 2025KY166). The requirement for informed consent was waived. A total of 207 patients clinically suspected of EC underwent 1.5T MRI before undergoing surgery in Fujian Maternal and Child Health Hospital from January 1, 2018, to December 31, 2020. Because this study was focused on MRI-based classification of early-stage EC, patients with stage II, III, and IV disease were excluded. The classification task was restricted to FIGO stage IA and IB, which are defined by the depth of myometrial invasion and can be assessed using preoperative MRI [37]. The additional inclusion criteria were as follows: (1) a clear MRI slice image of the uterus; (2) T2WI images had corresponding DWI images; and (3) the existence of a final pathological diagnosis result. The final number of enrolled EC patients meeting the criterion was 100, with an average age of 55.7 years. These comprised 43 patients with stage IA EC and 57 patients with stage IB EC. The experimental data consists of three modalities, as shown in Fig. 4. Detailed clinicopathological characteristics of the enrolled patients are summarized in Table 1.

Fig. 4.

The labelled ROI in MRI images. The figure shows representative ROI annotations for the three MRI modalities used in this study, including axial diffusion-weighted imaging (DWI), axial T2-weighted imaging (T2WI), and sagittal T2WI.

Table 1. Clinicopathological characteristics of stage IA and stage IB endometrial cancer patients.

Parameter		Stage IA (n = 43)	Stage IB (n = 57)	Total (n = 100)	p-value
Average age (years)		51.4 $\pm$ 8.9	58.9 $\pm$ 9.3	55.7 $\pm$ 9.8	0.001
Endometrioid type#					0.239
	Grade 1	27	28	55
	Grade 2	15	24	39
	Grade 3	1	5	6
Maximum diameter (cm)					0.001
	3	32	19	51
	$\ge$3	11	38	49
Myometrial invasion					0.001
	50%	43	3	46
	$\ge$50%	0	54	54
Mixed carcinoma*					0.245
	No	29	32	61
	Yes	14	25	39

^# Histological grading of endometrioid carcinoma. According to the solid range of tumors, the classification criteria are as follows: Grade 1: solid growth area accounts for $\le$5%; Grade 2: solid growth area accounts for 6%–50%; Grade 3: solid growth area accounts for $>$50%.

* Indicates the presence of other tumors, such as clear cell carcinoma, uterine fibroids, etc.

The flowchart for ROI detection is shown in Fig. 5. The confidence was set to 0.75 to display more accurate results, where confidence refers to the ratio of the intersection to the union between the detection result and the ground truth. In the test set, the model with pre-training weights from the VOC dataset achieved an average precision (AP) of 95.81% with all three kinds of MRI images. The model with pre-training weights from the Common Objects in Context (COCO) dataset achieved an AP of 87.46% on the same set of MRI images. However, the detection model without pre-training had an AP of only 77.19%. The precision-recall (PR) curves for the three models of ROI detection are shown in Fig. 6. The horizontal axis of each subplot represents the recall, while the vertical axis represents precision. The PR curves indicate the detection model with pre-training performed exceptionally well and could accurately localize the ROI (i.e., the uterine region). This model was used in the first step of Fig. 2 to process all MRI images and obtain the corresponding ROI images.

Fig. 5.

Flowchart for ROI detection on MRI images. The SSD-based detection model localizes the uterine region on MRI images, followed by cropping and resizing to obtain the ROI images.

Fig. 6.

PR curve for ROI detection on MRI images. (a) Detection model trained without pre-training; (b) detection model pre-trained on the Common Objects in Context (COCO) dataset; and (c) detection model pre-trained on the Visual Object Classes (VOC) dataset.

The results of the GP-based methods and of the baseline methods for stage IA and IB EC classification on the three types of MRI images are shown in Table 4. The best classification results for each dataset are highlighted in bold. In addition, the accuracy of the classification of the boxed ROI images was tested against that of the raw images. The Wilcoxon Rank Sum Test was utilized to analyze the experimental results and assess the impact of incorporating object detection on the classification accuracy. The resulting significant data was used to identify potential differences between the two groups of data (raw MRI images and ROI images). The Wilcoxon Rank Sum Test was conducted across three distinct methodologies, including ML-based methods, DL-based methods, and GP-based methods.

The first four rows of Table 4 show the classification results based on the ML classification algorithm. The classification accuracies were higher on ROI images than on raw MRI images. A significant difference was observed between the raw MRI images and ROI images on Axial T2WI and Sagittal T2WI images. The highest classification accuracy was 0.77 on ROI images of Axial DWI and Axial T2WI images using LR. These results indicate that cropped ROI images help to classify stage IA and IB EC better than raw MRI images. The raw images and ROI images on Axial DWI showed no significant difference, mainly because the DWI images highlight tumor lesions.

Rows 6 to 11 of Table 4 show the classification results based on the DL classification algorithm. No significant improvement in classification accuracy based on ROI images was observed compared to raw MRI images. Moreover, no significant differences were observed between raw MRI images and ROI images on Axial DWI and Axial T2WI images at the 0.05 significance level (all p-values $>$ 0.05). The highest classification accuracy was 0.85 on ROI images of axial DWI using ViT. Furthermore, most of the classifications based on raw images resulted in relatively low accuracies, generally ranging from 0.40 to 0.70. These results show that cropped ROI images do not significantly improve the classification performance of DL-based methods. In addition, the DL model is difficult to train well using only a small number of training instances, leading to low classification accuracy.

Rows 11 to 14 of Table 4 show the classification results based on the GP classification algorithms. The classification accuracies were significantly higher on the ROI images than on the raw MRI images. A significant difference was found between the raw MRI images and the ROI images (p 0.05). The highest classification accuracy observed was 0.92 on ROI images from axial DWI using FELGP. Furthermore, the classification accuracies on raw and ROI images from axial T2WI images were 0.63 and 0.87, respectively. For ROI images of sagittal T2WI images, the classification accuracy reached 0.83, which was the best result of all classification algorithms. These results demonstrate that cropped ROI images can help GP methods extract and reconstruct features from MRI images, significantly improving their classification accuracy.

Columns 1, 3, and 5 of Table 4 show the classification results from the raw MRI images, while columns 2, 4, and 6 show the classification results from ROI images. None of the classification methods achieved a good result from the raw images, with accuracies of between 0.40 and 0.60. In contrast, the classification accuracies were higher with the ROI images. The FELGP-based classification method performed better on the ROI images than the ML- and DL-based classification algorithms. These results indicate that cropped ROI images improve the classification accuracy of all employed algorithms for the classification of stage IA and IB EC. In summary, GP-based algorithms are more effective than ML-based and DL-based classification algorithms.

Since the diagnosis of stage IA and IB EC is a dichotomous problem, a classifier should not be judged solely on its classification accuracy. To better illustrate that cropped ROI images help GP with feature extraction and construction, the receiver operating characteristic curves (ROC curves) and the area under the curve (AUC) of the four GP-based methods were compared to those of the raw MRI images and the ROI images (Fig. 7). The horizontal axis of each subplot represents the false positive rate (FPR), while the vertical axis represents the true positive rate (TPR). As shown in Fig. 7, the classification performance of the four GP-based classification methods on ROI images was significantly better than that of the raw MRI images. FlexGP and FELGP showed the best classification performances on ROI images of axial DWI images, with AUCs of 0.92 and 0.96, respectively. IDGP also demonstrated good classification performance on sagittal T2WI images, with an AUC of 0.92. In summary, the use of ROI images can help GP extract and construct valuable image features, thereby improving the accuracy and reliability of the classifier. Additionally, the classifier’s reliability is often more important in the diagnosis of medical images.

Fig. 7.

ROC Curves for the four GP-based methods. These compare the classification performance of COGP, IDGP, FlexGP, and FELGP using raw MRI images and the corresponding ROI images. The horizontal axis represents the false positive rate (FPR), and the vertical axis represents the true positive rate (TPR). Abbreviations: GP, genetic programming; ROI, region of interest.

As shown in Table 5, executing the process of evolutionary learning (step 2) is time-consuming. The experiments based on DL methods were conducted on another computer equipped with a high-performance Graphics Processing Unit (GPU). This allows faster model training compared to other methods that run on a Central Processing Unit (CPU), with a computation time on small datasets of 2 minutes. At present, strongly typed GP cannot be implemented on GPU and is not comparable with DL methods in terms of running time. Therefore, only the computation time for the GP-based method was assessed on the raw MRI and ROI images.

Table 5 shows the evolutionary learning time (in hours) and the execution times (in seconds) of the GP-based methods. A significant difference was observed between different GP methods for the same modality (p 0.05). Moreover, the time for evolutionary learning on ROI images using the IDGP, FlexGP, and FELGP methods was considerably shorter compared to the evolutionary learning time on the raw MRI images, by an order of magnitude (102 to 101 and 101 to 10-1). The longest learning time on ROI images was approximately 31 hours with FELGP. It is worth noting that all evolutionary processes in this study were executed on a single Intel 11th generation i5 processor, without using the DEAP multi-program option [42]. The learning time could potentially be reduced using faster hardware, or through the implementation of parallel computing methods.

Fig. 8 shows the best individual evolved by FELGP on the ROI image from axial DWI. Accuracies of 98.57% and 92.00% were achieved on the training and test sets, respectively. The relatively small gap between training and testing performance indicates that this representative FELGP model generalized well to unseen data, suggesting limited overfitting in this example despite being trained on a small dataset. This tree/program structure illustrates how valuable features are extracted from ROI images, and how effective classification of stage IA and IB EC is achieved. The GP method uses different features and functions to train the GP programs shown in Fig. 8. To illustrate the interpretability of the GP, the SVM classifier branch at the bottom of Fig. 8 is further visualized in Fig. 9. This shows how the GP extracts features, with two example images from stage IA and stage IB as inputs. As shown in Fig. 9, the image undergoes initial processing using various filtering and pooling functions to enhance the informative image characteristics. Edge filters (LoG1, LoG2, LaP, SobelX) are employed for extracting edges and textures, while blur/smoothing filters (Gau, Gabor) reduce image noise. The weight operator (W-sub) is mainly used to weight the image in order to highlight crucial information. Subsequently, the processed images undergo a feature extraction function (HOG, SIFT, uLBP) to obtain specific image features such as gradient direction, unique key points, and local texture patterns. These features are combined through the feature concatenation function to create high-level features suitable for classification. The high-level feature vectors and some image information are then fed into the classification algorithms, such as SVM and extreme random forests (ERF), as new features for training. Lastly, the final classification result output is obtained using an ensemble of the three classifiers. Overall, this structure allows different numbers and types of features to be extracted from the image, and the corresponding filtering and pooling operations to be performed under each branch to construct the high-level features. The ensemble learning approach enhances the robustness of this classification algorithm and improves its performance.

Fig. 8.

Example solution found by FELGP on axial DWI ROI images. This shows the best individual evolved by FELGP on the ROI image from axial DWI. The tree/program structure illustrates how image features are extracted using edge filters, blur/smoothing filters, and weight operators for the classification of stage IA and IB EC. Abbreviations: FELGP, feature-ensemble-learning genetic programming; DWI, diffusion-weighted imaging; ROI, region of interest; EC, endometrial cancer.

Fig. 9.

Features produced by the example program from different classes. The figure shows example images from stage IA and IB EC processed by the GP program. Image features were extracted using HOG, SIFT, and uLBP, concatenated to form high-level features, and classified using SVM and ERF with ensemble learning. Abbreviations: GP, genetic programming; HOG, Histogram of Oriented Gradients; SIFT, Scale-Invariant Feature Transform; uLBP, uniform Local Binary Patterns; SVM, Support Vector Machine; ERF, Extreme Random Forest. * denotes multiplication by a coefficient in the GP-derived expression.

This study evaluated a GP-based classification framework for distinguishing FIGO stage IA and IB endometrial cancer based on the automatic detection of ROIs in MRI images. The results obtained with this approach demonstrated high classification performance for distinguishing FIGO stage IA from IB across multiple MRI sequences. Specifically, the FELGP-based model achieved an accuracy of 0.92 and an AUC of 0.96 on the test set, while the FlexGP-based model achieved an accuracy of 0.87 and an AUC of 0.92. These results demonstrate the effectiveness and robustness of GP-based feature construction for the staging of early EC. Comparative results presented in Table 4 and Fig. 7 show that FlexGP and FELGP consistently outperform COGP and IDGP, which may be attributed to the design of their function sets. First, FlexGP and FELGP incorporate an additional filtering and pooling layer, enabling the extraction of more informative texture and structural features from MRI images. Second, FELGP further introduces ensemble learning strategies through classification and combination layers, allowing the integration of multiple classifiers and resulting in improved robustness. Performance differences across MRI sequences were also observed. Axial DWI achieved higher classification accuracy than sagittal T2WI, which can be explained by intrinsic modality characteristics. Although this study did not explicitly quantify image contrast or analyze GP features at the contrast level, DWI is clinically known to provide higher lesion-to-background contrast and greater sensitivity to tumor cellularity. The superior classification performance achieved on DWI therefore suggests that the discriminative patterns captured by the GP framework are more effectively represented in this modality, providing indirect evidence that DWI is more suitable for GP-based feature construction in early-stage EC classification. In contrast, sagittal T2WI images often contain more anatomical variability and may suffer from partial volume effects, increasing the difficulty of accurately distinguishing between stage IA and IB. Despite these challenges, the GP-based framework showed consistently competitive performance across modalities. From a computational perspective, GP-based feature construction is computationally expensive during training. However, all evolutionary optimization procedures are performed offline. During online inference, only ROI detection, evaluation of evolved GP expressions, and a single classifier prediction are required. This design enables near real-time inference and allows the proposed automated classification framework to provide objective decision-support information in clinical workflows, particularly during the preoperative staging of early-stage EC. Compared with existing methods, such as manually engineered feature-based ML models or CNN-based classifiers that require large training datasets, the proposed GP-based approach offers clear advantages in terms of small-sample learning and interpretability. Once trained, the model can make predictions using only a limited number of images, making it suitable for many real-world medical imaging scenarios where annotated data are scarce.

Despite the promising results, several limitations should be acknowledged. First, this study was conducted on a relatively small dataset collected from a single institution, which may limit the generalizability of the findings. Nevertheless, the primary aim of this work was to investigate the feasibility of GP-based classification under limited data conditions, which are common in medical imaging applications. Future studies will focus on validating the proposed framework using larger, multi-center datasets to assess robustness across different MRI scanners and acquisition protocols. Second, ROI images were used for GP-based classification. While ROI cropping improves classification accuracy and reduces the computational burden, it may lead to partial loss of tumor volume and spatial contextual information. Exploring strategies that incorporate more global spatial context is another potential direction for future research. Third, although different MRI modalities were evaluated independently in this study, multimodal feature fusion was not explored. Combining complementary information from DWI and T2WI within a unified GP framework has the potential to further improve staging performance. However, direct multimodal fusion would substantially increase the feature dimensionality and GP search space, which may increase the risk of overfitting under the current setting of limited samples. Future work with larger datasets and more efficient GP search strategies should investigate multimodal GP-based feature fusion to further enhance robustness and classification accuracy. Fourth, the general-purpose GP function sets in this study were intentionally adopted to maintain broad applicability and reduce the risk of overfitting under a small-sample setting. Although several existing GP classification algorithms were evaluated, no GP method was specifically designed for MRI image analysis. The development of domain-specific GP architectures and the incorporation of medical imaging–oriented function sets may further improve performance and interpretability. Finally, the reference labels used in this study were derived from clinician-confirmed, postoperative pathological staging, which served as the gold standard. Although preoperative MRI staging is routinely performed in clinical practice, structured and standardized radiologist-assigned MRI staging results were not consistently available in this retrospective dataset. In some cases, MRI reports contained descriptive assessments without explicit stage assignment, while in others, formal staging conclusions were not reported. Consequently, paired preoperative–postoperative staging outcomes could not be extracted reliably, and discrepancies between preoperative MRI staging and final pathological staging could not be quantitatively analyzed. Future work will involve the collection of more complete and standardized preoperative MRI staging reports, together with postoperative pathology. This will allow a systematic head-to-head comparison, enabling further evaluation of the clinical utility of the proposed GP-based classification framework.