## 1 Introduction  
The dynamic responses of structures with complex configurations, such as mechanical equipment, bridges, and buildings, are typically measured using a set of mounted transducers, such as accelerometers and strain gauges. The development of high-speed camera systems and image-processing techniques has promoted the use of vision-based measurement in the study of structural health monitoring [1; 2; 3], dynamics modal analysis [4; 5; 6], and nondestructive testing [7; 8; 9]. In contrast with traditional contact sensors, vision-based methods provide an intuitionistic demonstration of actual structural vibration and are more convenient for installation under conditions where contact sensors have difficult access. Without additional mass on the surface of the measurement target, vision-based measurement devices rarely affect the natural properties of flexible or lightweight objects. Moreover, vision-based devices often have a flexible composition and provide relatively high spatial resolution in an efficient and automated manner [10]. The emergence of high-speed imaging sensors allows the camera to work at a high sampling rate with considerable resolution in the film. Structural high-frequency motions can be recorded in a high-speed video file, and noises from frame interpolation are technically avoided in subsequent image processing. Valuable motion signals hidden in video frames can be extracted by combining image processing algorithms, such as optical flow [11; 12] and image correlation [13; 14] (including digital image correlation (DIC)). Therefore, motion estimation from a sequence of video has become a popular problem in the computer vision field. High-speed video cameras have potential applications and have been successfully used for experimental modal analysis [15; 16], sound information recovery [17; 18; 19], and fault diagnosis [20; 21]. Traditional image template matching algorithms calculate cross-correlation parameters between the selected template subimage and subimages in the following video frames and locate the best matching pixel coordinates [22; 23; 24]. However, the cross-correlation function may be valid when facing poor and repetitive textures. The deviations of structural idealized edge profiles can be employed to extract effective motion signals. This method is simplified from a deviation magnification (DM) algorithm [25] without the magnification and image reconstruction processes. In contrast to intensity- and phase-based optical flow [11; 26], which calculate the relative spatial and temporal derivative field by solving the aperture equation at each pixel between consecutive frames, the deviation extraction algorithm reveals geometric deviations from their idealized edge profiles (e.g., straight-line and curves) in a single image. With all deviations from a selected contour extracted, the global variations in these signals can be applied to analyze structural vibration characteristics. The variations in deviations are sensitive to structural low-frequency vibration, which has a relatively large amplitude. However, this method exhibits limitations when handling low-level motions on the idealized edge profile that reflect high-frequency components. In this regard, the Eulerian video magnification (EVM) algorithm [27; 28; 29] is introduced to preprocess subtle high-frequency vibrations in video before deviation extraction. Subtle motions and deviations in video are usually difficult to perceive with the human eye without any image processing. The core concept of motion magnification is to allow subtle variations in a specific frequency band to be observed intuitively by magnifying small intensity or phase variations in the video. Compared with intensity-based video magnification [27], the magnification of phase will not be restrained by the imitation of the pixel value and has better control of additional image noise. Therefore, phase-based video magnification can be used to enhance the low-level variations of the selected edge profile.