This paper presents a novel framework for drone-based displacement measurement of infrastructures, achieving sub-millimeter accuracy. The approach leverages phase information from drone camera footage and a group of strategic reference markers on bridge girders. Inspired by human auditory equilibrium, the method integrates phase-based sampling moiré technique with four degrees-of-freedom geometric modeling to accurately measure structural displacements. The proposed scheme demonstrates high precision, with accuracy reaching 1/100th of a pixel. Real-world validations confirm the reliability and efficiency of the technique, making it a practical tool for bridge displacement measurement. The methodology holds promise for future autonomous infrastructure inspection systems, offering flexibility, cost efficiency, and autonomous processing. The research addresses the challenges of aging and deficient infrastructure, which pose significant safety and economic risks, by providing a non-destructive and cost-effective solution for assessing structural integrity.This paper presents a novel framework for drone-based displacement measurement of infrastructures, achieving sub-millimeter accuracy. The approach leverages phase information from drone camera footage and a group of strategic reference markers on bridge girders. Inspired by human auditory equilibrium, the method integrates phase-based sampling moiré technique with four degrees-of-freedom geometric modeling to accurately measure structural displacements. The proposed scheme demonstrates high precision, with accuracy reaching 1/100th of a pixel. Real-world validations confirm the reliability and efficiency of the technique, making it a practical tool for bridge displacement measurement. The methodology holds promise for future autonomous infrastructure inspection systems, offering flexibility, cost efficiency, and autonomous processing. The research addresses the challenges of aging and deficient infrastructure, which pose significant safety and economic risks, by providing a non-destructive and cost-effective solution for assessing structural integrity.