A New Fairness Evaluation Metric of Biometric Systems Based on the Theil Inequality

accepté pour publication International audience Face recognition is increasingly deployed across a wide range of applications, from security systems to personal devices. However, these systems often exhibit significant performance disparities linked to demographic factors such as age, gender, or ethnicity. These biases raise serious technological, ethical, and societal concerns. The proposed paper first introduces a novel evaluation protocol that systematically injects controlled algorithmic biases into extracted biometric features. This setup enables a consistent and repeatable framework for comparing existing fairness metrics through correlation analysis, while ensuring that the same demographic groups are considered across evaluations. Our results show that most widely used fairness metrics, primarily due to their mathematical formulation tend to emphasize overall performance disparities between demographic groups (e.g., Asian, African, Black), thereby capturing inter-group differences. However, this often comes at the cost of neglecting intra-group variability, i.e., performance inconsistencies among individuals within the same demographic group. To address this limitation, we propose a novel fairness metric, TM-DP, grounded in Theil's inequality index. This metric is specifically designed to account for both inter-group and intra-group performance disparities, offering a more nuanced and comprehensive assessment of fairness applicable to all biometric modalities. We validate TM-DP using three publicly available face biometric datasets, evaluated with three different feature extractors and across four decision thresholds. Experimental results confirm the shortcomings of existing fairness metrics and demonstrate the effectiveness and robustness of TM-DP.