A Functional Energy Minimization Framework for the Detection of Crash Stones on Road Surfaces in Intelligent Transportation Systems

Accurate detection of road surface anomalies remains a fundamental challenge in ensuring vehicular safety, particularly within the domain of intelligent transportation systems and autonomous driving technologies.Among such anomalies, crash stones-defined as irregular, protruding, and often unstructured fragments on the road-pose considerable risks due to their heterogeneous morphologies and unpredictable spatial distributions.In this study, a novel mathematical model is proposed, formulated through a functional energy minimization framework tailored specifically for the detection and segmentation of crash stones.The model incorporates three principal components: geometric edge energy to emphasize structural discontinuities, local variance descriptors to capture micro-textural heterogeneity, and fuzzy texture irregularity measures designed to quantify non-uniform surface patterns.These components are integrated into a unified total energy functional, which, when minimized, facilitates the precise localization of obstacle regions under diverse illumination, weather, and pavement conditions.Final detection is achieved through adaptive thresholding informed by fuzzy logic-based classification, enabling robust performance in scenarios with high noise or low contrast.Unlike deep learning-based methods, the proposed approach is fully interpretable, non-reliant on extensive annotated datasets, and computationally efficient, making it well-suited for real-time applications in resource-constrained environments.Experimental validations demonstrate high detection accuracy across varied real-world datasets, substantiating the model's generalizability and resilience.The framework contributes a mathematically rigorous, scalable, and explainable solution to the enduring problem of small obstacle detection, with direct implications for the enhancement of road safety in next-generation transportation systems.