Safety space index (SSI): A two-dimensional metric for quantifying drivers' perceived risk

With the advancement of autonomous driving, there is increasing demand for systems that mimic human decision-making in complex traffic environments. Modeling such behavior requires understanding drivers' cognitive mechanisms during dynamic interactions. Subjective risk quantification is a key link between perception and decision-making, impacting the system's ability to generate human-aligned responses. However, existing risk quantification methods predominantly emphasize objective risk assessment or are limited to one-dimensional subjective risk quantification, lacking effective metrics that can comprehensively characterize generalized subjective risk perception in two-dimensional scenarios. To address this gap, this study proposes a novel two-dimensional risk perception metric, the Safety Space Index (SSI), which integrates psychological safe space theory and risk field modeling to quantify drivers' subjective risk levels. Experimental results show SSI improves correlation with car-following behavior by 32.2%, and achieves a reaction time calibration of 0.92 s. Moreover, SSI effectively distinguishes differences in perceived risk among drivers facing the same conflict scenarios, reflecting strong alignment with human cognitive processes. Extended analyses further reveal that SSI captures the risk homeostasis characteristic of driving behavior, exhibiting centrally clustered target levels that follow a normal distribution in typical scenarios. Additionally, SSI demonstrates robust cross-scenario generalization, maintaining an average target level of 0.50, thereby affirming its adaptability and scalability. As a powerful tool for characterizing drivers' subjective risk perception in two-dimensional dynamic environments, SSI offers critical theoretical support for human-like behavior modeling, autonomous decision-making strategies, and validation frameworks in intelligent driving systems.