# Full-Field Mode Shape Identification Based on Subpixel Edge Detection and Tracking
## 1 Introduction  
Large-scale (long-span or high-rise) engineering structures are prone to vibrate under external loadings such as wind, earthquake, traffic, etc. These vibrations can cause damage (e.g., fatigue and cracking) to the structural components, which can lead to the destruction of the structure, resulting in huge economic losses [1, 2]. The monitoring of structural vibration and modal properties can provide crucial information both for the evaluation of structural safety and for maintenance purposes in civil engineering [3, 4]. Therefore, the accurate determination of vibration displacements and modal parameters is of great importance to the structural condition assessment during its service life. Traditionally, the vibration response of structures has mainly been measured through contact sensors (e.g., accelerometers or linear variable differential transducer (LVDT) [5]. However, these contact-type sensors need to be installed at specific locations on structures, which is often difficult or even impossible in some cases. Recently, the non-contact sensing system based on computer vision (CV) has been developed and applied to vibration measurement [6, 7, 8]. The CV-based photogrammetry techniques for structural vibration measurement mainly include the template-matching method [9], digital image correlation(DIC) [10], and the optical flow method [11]. [PERSON] et al. [12] adopted the template-matching algorithm with upsampled cross-correlation to determine the structural displacement by tracking the artificial target on the structure and verified its feasibility on a steel frame in the laboratory [13]. The DIC method uses dense speckle patterns as artificial targets on the structure surface and calculates the grayscale variations to acquire the vibration response [14]. The above methods require manually adding high-contrast patterns on the test object as optical targets for CV processing. To address this limitation, many researchers utilize the internal features of the test object to perform the optical measurement. The optical flow method is one such method that works by calculating the brightness variation of pixels in image sequences [15]. [PERSON] et al. [16] used this method [17] to measure the displacement of the region of interest (ROI) on cables without the set of any targets, and the reverse synthesis algorithm was used to further reduce the computation time [18]. Although the full-field optical flow method stated above can compute the Eulerian velocity field of the whole image, the computational time is too long for online monitoring. Hence, [PERSON] et al. [19] adopted the phase-based optical flow algorithm to measure the displacement of a few specific pixels in the image. [PERSON] et al. [20] employed deep learning to automatically select pixels for target tracking to obtain the vibration displacement time history of the structure, which was verified in laboratory experiments. Most research on CV-based vibration measurement is limited to the determination of the displacement or frequencies of vibrating structures. The mode shapes of structures are also critical indicators for structural health monitoring and damage detection. Recently, a few researchers have developed CV-based methods for the identification of structural mode shapes. [PERSON] et al. [21] used the template-matching method to synchronously measure the dynamic displacements of the structure at various locations to identify mode shapes of a simply supported rectangular steel girder. [PERSON] et al. [22] combined the Harris corner detection algorithm with the Kanade-Lucas-Tomasi tracking algorithm to obtain the displacement time history of the structure and extract the discrete mode shapes of the structure using the eigensystem realization algorithm. The above methods only obtain discrete mode shapes of structures, while the heterogeneity of the integral mechanical properties of structures needs the acquisition of the high-resolution full-filed mode shapes of structures to identify and localize the damage [23].