Sex estimation from foot morphometric measurements using machine learning methods

Authors

Abstract

Aim The identification of human remains resulting from mass disasters, explosive-induced demolitions, or attacks constitutes one of the most critical areas of forensic medicine. The aim of this study is to enable high-accuracy sex prediction using foot morphometric measurements using both classical statistical analyses and machine learning algorithms.
Materials and Methods A total of 1000 individuals, 500 females and 500 males, aged 18-36, were included in the study. Parameters such as foot length, foot metatarsal width, foot calcaneal width, medial and lateral malleolus distance to the ground, unweighted navicular height, and ASIS-heel distance. The Mann-Whitney U test was used to assess differences between genders, and prediction models were developed using logistic regression and various machine learning algorithms.
Results Foot length/height, ASIS-heel distance/height, and foot length/ASIS-heel distance ratios were the strongest predictors of gender differentiation. Machine learning models achieved very high accuracy. Random Forest and SVM achieved near-perfect classification performance, while the Logistic Regression model achieved 99% accuracy in predicting gender. Decision Tree model achieved 98.4% accuracy. Feature importance analysis determined that foot length/ height, ASIS-heel distance/height, and foot length/ASIS-heel distance ratios were the most critical parameters for gender prediction.
Discussion Foot morphometric measurements provide high accuracy for sex estimation when used with both traditional statistical methods and machine learning algorithms. The results demonstrate that biometric sex estimation based on foot morphology can be used as a practical and effective method in fields such as forensic science and sports science.

Keywords

Introduction

The identification of human remains resulting from mass disasters, explosive-induced demolitions, or attacks constitutes one of the most critical areas of forensic medicine. Particularly in cases where bodily integrity has been severely compromised, reliable sex determination not only accelerates the identification process but also provides direction for investigations by narrowing down the match areas. The resistance of bone tissue to environmental influences allows for the preservation and analysis of morphological characteristics, such as the structure of an individual’s foot. Although foot skeletal morphometric structures are influenced by genetic variation and environmental factors among individuals, they provide valuable biological clues in identification processes due to their distinct structural differences between the sexes. In this context, sex prediction models developed based on measurements such as foot length, width, and height are used as scientifically valid, noninvasive classification tools in forensic anthropology and medicine [4]. It is known that foot dimensions, foot index, and footprint ratios are frequently used for gender discrimination in different populations [5, 6, 7, 8].
Radiological evaluation processes often focus on identifying distinct disease-specific anomalies. While this facilitates rapid and systematic image analysis, it can also lead to the oversight of structural details that are not directly pathological but have potential clinical significance. The limited resolution capacity of human perception can lead to the oversight of some diagnostic clues, particularly in medical images containing complex anatomical structures. The use of artificial intelligence technologies supports diagnostic processes and offers a new perspective in medicine by facilitating the analysis of complex data patterns [9]. Machine learning is a type of artificial intelligence (AI) that uses algorithms to make data-based predictions or decisions. It encompasses various techniques, including supervised (classification and regression), unsupervised (clustering), and reinforcement learning. Its primary goal is to create models that can generalize by learning patterns in data. Models such as Random Forest, SVM (Support Vector Machine), Logistic Regression, KNN (K-Nearest Neighbors), and Decision Tree are available. The preferred algorithms vary depending on the characteristics of the data to be analyzed. Recent studies have shown that these technologies can produce highly accurate results in many clinical applications, such as skin lesion classification, wound analysis, cardiovascular risk prediction, and trauma pattern identification [9, 10]. However, most existing approaches focus on modeling the interpretation styles of human experts and utilize the discovery potential of artificial intelligence to a limited extent. However, machine learning, thanks to its ability to analyze subtle variations in structural data with high accuracy, can also yield robust results in classifications based on biometric features. It offers innovative applications in identification processes, particularly in anatomical regions with inter-individual variation, such as foot morphology [11]. In this study, we aimed to achieve high accuracy in sex estimation using data obtained from foot morphometric measurements using machine learning. We also aimed to identify the most effective foot parameters for sex discrimination and to contribute to the potential applications of these findings in forensic anthropology, orthopedics, and biometric authentication.

Materials and Methods

Measurements
This study evaluated the unilateral foot morphometric measurements of 1000 adults (500 women, 500 men) aged 18–36. Individuals with congenital or acquired foot or lower extremity anomalies, a history of trauma or orthopedic surgery, rheumatic (rheumatoid arthritis, osteoarthritis, gout) or neurological (peripheral neuropathy, cerebral palsy, poliomyelitis) diseases that could affect standing and walking functions were excluded from the study. Age, gender, height, and weight of all individuals were recorded.
All measurements were performed barefoot using a standardized method based on fixed anatomical reference points. A Valkyrie 150 x 0.01 mm Digital Stainless Steel Electronic Precision Caliper was used for measurements. Foot length and width, calcaneal width, ASIS (Anterior superior iliac spine)-heel distance, medial and lateral malleolus to floor distance, and navicular height were measured. The hallux valgus angle was determined using a Loyka 5522-200 Digital Goniometer. The obtained measurements were compared to height and ASIS- heel distance to determine parameters such as foot length/ height, metatarsal width/height, calcaneal width/height, ASIS- heel distance/height, and foot length/ASIS-heel distance. This allowed for standardized comparisons, taking into account individual height differences.
Machine Learning Applications
The study was conducted in the Google Colab environment using the Python programming language. Libraries such as Pandas were used for data reading and processing, Numpy for numerical operations, matplotlib.pyplot for graphical drawings, and Scikit-learn (sklearn) for evaluation metrics. The dataset in the study was trained and tested separately using machine learning models commonly used in the literature: Random Forest, SVM, Logistic Regression, KNN, and Decision Tree. 80% of the dataset was used for model training and 20% for testing. Performance analysis of each model was conducted using a five-fold cross-validation technique. This ensured that all data in the dataset was used for both training and testing.
Statistical Analysis
SPSS was used for statistical analyses. Because the assumption of normal distribution was not met, the Mann-Whitney U test was used to assess differences in measurements between male and female groups. Multivariate logistic regression analysis was performed to assess the effect of independent variables on gender; regression coefficients, significance levels (p-values), and confidence intervals were calculated for each variable. The overall performance of the model was assessed using the area under the ROC curve (AUC). In all statistical analyses, p < 0.05 was considered significant.
Ethical Approval
This study was approved by the Ethics Committee of Tokat Gaziosmanpaşa University, Faculty of Medicine (Date: 2025- 03-04, No: 25-MOBAEK-088).

Results

Morphometric Measurements
50% of the individuals in the study were female, and 50% were male. The mean age was 24.92 ± 4.38 years in males and 24.02 ± 3.08 years in females. The mean height was 173.31 ± 10.58 cm in males and 163.57 ± 10.59 cm in females. Basic descriptive statistics of the key foot morphometric measurements are summarized in Table 1.
In this study, there were statistically significant differences between male and female individuals in many foot morphometric parameters. The Mann-Whitney U test results indicated that male individuals had generally higher mean values (p < 0.001), as shown in Table 2.
Machine Learning Analyses
The dataset in the study was trained and tested separately using machine learning models commonly used in the literature: Random Forest, SVM, Logistic Regression, KNN, and Decision Tree. Confusion matrices containing the number of correct and incorrect predictions obtained for each model are presented in Supplementary Figure S1. Accordingly, the Random Forest model yielded the highest number of correct predictions, and this model produced only one incorrect prediction in the entire dataset.
The values obtained for Accuracy, Precision, Recall, and F1 Score, which are other metrics expressing model performance, are given in Table 3. The most successful model was determined to be Random Forest.
The ROC curve is one of the important tools for visualizing the classification performance of a model. The ROC curves of the models used in the study are given in Supplementary Figure S2.

Discussion

Today’s medicine requires solutions with high accuracy and efficiency in areas such as rapid diagnosis, personalized treatment, and healthcare services. Artificial intelligence algorithms, such as machine learning, stand out as tools that enable meaningful analysis from large and complex healthcare data. Machine learning, due to its ability to learn from and predict data over traditional statistical methods, is becoming increasingly widespread in the field of forensic science. These technologies minimize human error, strengthening the forensic validity of scientific evidence and enabling data-driven decision-making processes to proceed quickly and reliably. The human foot exhibits significant individual differences in length and width between males and females. These morphometric features stand out as important biometric indicators in sex determination and individual identification processes [12, 13]. When comparing foot length between men and women in the literature, it is reported that foot length is significantly longer in men. A study by Bindurani et al. evaluated both foot length and foot width, and found that both parameters were significantly greater in men [12, 14]. Similarly, in our study, foot length and foot width measurements were significantly larger in men.
In a study conducted by Bidmos and Asala (2004) on South African individuals, measurements obtained from 116 intact calcanei demonstrated significantly higher values in males compared to females. Furthermore, discriminant function analyses reported an accuracy of up to 86% in sex estimation. [15]. In our study, the significant difference observed in calcaneal width between sexes is consistent with findings in the literature and supports the consideration of this parameter as a reliable indicator in sex determination.
Zeybek et al. investigated the differences in malleolar and navicular bone height between sexes and reported significantly higher values in males compared to females [16]. Our results were also consistent with the literature. In our study, we specifically aimed to contribute novel approaches to sex estimation by normalizing parameters such as navicular height and ASIS–heel distance to stature. In this context, our study is not limited to linear foot measurements alone but holds particular originality by incorporating ratio-based analyses that can reveal inter-individual morphological differences with greater sensitivity.
Previous studies have frequently utilized basic measurements such as foot length, foot width, and calcaneal parameters in sex differentiation; however, parameters such as navicular height, malleolar height, or ASIS–heel distance have been less frequently assessed. In particular, variables generated by normalizing these measurements to stature or other parameters have not yet been incorporated into standard anthropometric assessments [17]. Based on the results of our study, we suggest that parameters such as Foot Metatarsal Width/Height, Calcaneus Width/Height, and ASIS–Heel Distance/Height could be integrated into anthropometric measurements and employed in sex estimation.
The prevalence of hallux valgus is approximately 2–3 times higher in females compared to males. The mean angle is also significantly greater in females than in males. In the study by Jiao et al. (2022), an analysis based on 3D foot scanning data reported mean HVA values of 9° (±6°) in males and 11° (±7°) in females, indicating that females exhibited greater hallux valgus angles than males [18, 19]. These findings are consistent with our data (male: 5.11°, female: 6.78°). Although HVA was found to differ significantly between sexes, given that the values remain below the pathological threshold of 15° and the male and female means are relatively close, its reliability as a standalone parameter for individual sex estimation may be considered debatable.
In our study, the evaluation of machine learning algorithm results demonstrated that the measured parameters could be utilized with near-perfect reliability in sex estimation. Based on the ROC curve analysis, although the hallux valgus angle may not serve as a reliable predictor on its own, it could be valuable when considered in conjunction with other parameters. This suggests that, particularly in forensic examinations where body integrity is compromised, accurate predictions may still be achieved solely through lower extremity parameters.
From a machine learning perspective, the most reliable parameters for sex estimation were height, foot length, metatarsal width, and ASIS–heel distance, while the weakest predictors were hallux valgus angle and lateral malleolus height. Furthermore, ratios such as Foot Length/ASIS– Heel Distance (the strongest), Navicular Height/ASIS–Heel Distance, and Lateral Malleolus/ASIS–Heel Distance emerged as powerful indicators for sex differentiation. Regarding the performance of machine learning models, Random Forest, SVM, and Logistic Regression achieved the highest accuracy rates, whereas the Decision Tree model showed relatively lower performance. Among them, Random Forest can be considered the most effective artificial intelligence tool for sex prediction using foot and lower extremity anthropometric parameters. With these parameters, sex estimation based on the Random Forest algorithm is expected to yield results approaching 100% accuracy. In particular, Random Forest and SVM achieved over 99% success in sex classification using these anthropometric data [20, 21, 22]. Bakan et al. stated that KNN and Random Forest models performed well in gender prediction from the sternum, although not in the best performance, in line with the literature [23]. Çiftçi et al. reported that the Random Forest algorithm was the most contributive method for age estimation based on X-ray images of the calcaneus [24].

Limitations

In this study, participants were healthy individuals aged 18–36, meaning the findings may not be generalizable to pediatric, elderly, or individuals with musculoskeletal deformities or systemic diseases affecting bone structure. The foot measurements were taken under controlled conditions; variations in posture, weight-bearing, or dynamic gait analysis were not incorporated, which may influence morphological characteristics.

Conclusion

In this study, the predictive value of foot morphometric measurements in sex determination was evaluated using both statistical analyses and machine learning methods. The findings revealed that certain dimensional and proportional parameters of the foot were significantly associated with sex. This suggests that foot morphology may serve as a reliable indicator for biological sex determination. Classification analyses performed with machine learning applications demonstrated that some algorithms, particularly when proportional measurements were utilized, achieved remarkably high classification accuracy. In this context, the integration of information provided by traditional statistical methods with artificial intelligence–based approaches allows for the development of more robust models in the fields of forensic anthropology and biometric identification. This study demonstrates that it is possible to achieve highly accurate sex estimation using basic anthropometric measurements combined with machine learning techniques.

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