# Image Analysis Applications for Building Inter-Story Drift Monitoring
## 1 Introduction
Some structural experiments have been performed to measure the uniaxial displacements of structures by analyzing images taken by a single camera [43]. Three-dimensional displacements and accelerometers can be estimated by analyzing images taken by two or more cameras by using stereo triangulation techniques [44]. Strain fields of a plane structural surface can be estimated by tracking a dense mesh of feature points painted on regions of interest [45]. Strain fields of curved surfaces can be calculated by further employing image un-distortion and rectification techniques [42]. Concrete crack development can be observed and measured by using a displacement-to-crack mapping formula [46]. Structural damage can be further quantified by calculating certain damage indices using information obtained from image analysis [47]. Image analysis has potential for use in post-earthquake building safety evaluations by analyzing two or more surveillance cameras using stereo triangulation techniques [44; 48]. Some image analysis programs are freely [49] or commercially available in the market, and some of them are specifically designed for structural experiments. This study proposes a building deformation monitoring method that integrates a small single-board computer, computer vision technique, and a single-camera multiple degree-of-freedom algorithm. Based on the existing computer-vision techniques, the proposed method measures multiple degrees of freedom of the story displacements with consideration of the camera movement. Rather than using a conventional stereo triangulation method, which requires two or more cameras and a sophisticated calibration procedure, this method uses only one camera and is designed to monitor the inter-story drifts and torsional responses between the ceiling and the floor of a story in a building, aiming to simplify the installation and maintenance procedures and to maximize the monitored structural response. The system is capable of analyzing inter-story responses both online and offline. The offline analysis can analyze previous inter-story responses using recorded videos with a sampling rate of the highest imaging frame rate of the camera hardware. The online analysis can instantly monitor the current inter-story responses using a sampling rate that the computer speed can achieve. At the time of this article being written, the hardware cost of the device prototype, including a single-board Raspberry Pi 3B (manufactured by Raspberry Pi Foundation, UK) equipped with a small camera lens, is less than one-hundred US dollars. The proposed method and the device prototype can achieve an offline sampling rate of 30 Hz and an online sampling rate of 3 Hz, with an inter-story drift accuracy of 0.0175% (i.e., the ratio of relative displacement of 0.07 mm to a story height of 400 mm) and 0.075% (i.e., the ratio of 0.3 mm to 400 mm) from static and dynamic experiments, respectively. Since the proposed algorithm does not limit the computational speed and accuracy, the sampling rates and measurement accuracy will continue to increase as digital imaging technology keeps improving.