# A Phase Correlation Anti-Noise Displacement Estimation Method Based on PSD Phase Screening
###### Abstract  
When using digital images to obtain the displacement of a structure, noise is always a factor that greatly affects the accuracy of the displacement results. To overcome this problem, a phase-correlation improvement method, based on phase filtering by phase standard deviation (PSD), is proposed. We use PSD to remove the severe noise interference area in the cross-power spectrum matrix, then the singular value decomposition (SVD) is used to convert the two-dimensional phase to one-dimensional to reduce the difficulty of phase unwrapping. Finally, straight-line fitting is used to obtain the high-precision displacement results. Experiments were carried out using both simulated data and real data. For the simulated data, the absolute accuracy of the proposed method is around 0.3 pixels, while, for the real data, the absolute accuracy of the proposed method is 0.018 mm. The experimental results show that the method can effectively resist noise interference and still obtain accurate displacement estimation results in the case of severe noise. displacement estimation; digital image correlation; phase correlation; noise +
Footnote †: journal: Applied  
Using the visual-based method to monitor the deformation of tracks and bridges, the general process is as follows: a camera is used to continuously capture images for the monitoring object, and then the frame and inter-frame displacement information (pixel unit) is obtained according to the image, then the corresponding scale of the image (the real size corresponding to each pixel) is calculated, and, finally, the physical displacement is calculated according to the real scale. There are two commonly used ways to obtain frame and frame displacement. (1) Pasting targets or speckle patterns on bridges and capturing the displacement sequences of rails and bridges by shooting and tracking the targets or speckle patterns [14]; this method needs to paste the targets or digital speckles on the monitoring objects, which may not be applicable in some situations. (2) Depending on the characteristics of bridges and rails, a digital image correlation is used to obtain the target displacement sequence [15; 16; 17]. In the high-frequency vibration monitoring of tracks and bridges, due to the high shooting frequency of the camera and the long shooting distance [18], the image quality is not ideal, which makes it difficult to directly track the target on the grayscale image. Therefore, the phase correlation method, which is more noise-resistant, is a better choice. Research into the phase correlation algorithm has a long history. The algorithm uses a Fourier transform to transfer digital image from a space domain to a frequency domain, and then correlation operations are performed on the two images in the frequency domain to obtain the displacement between the two images [19; 20]. In 1975, [PERSON] and [PERSON] [21] first proposed a digital image phase correlation algorithm and applied it to image registration. Compared with digital image grayscale correlation, it has a certain anti-noise performance and has a certain degree of anti-noise performance. It has advantages such as insensitivity [22], so it is widely used to calculate the displacement between images [23; 24; 25; 26]. The most primitive phase correlation method can only obtain pixel-level displacement. So, there were several scholars working to improve the performance of phase correlation, who proposed phase line fitting [27; 28; 29], phase plane fitting [30; 31; 32], tooth signal number estimation [33; 34], frequency estimation [35], local up-sampling [36], and other optimization methods [37; 38; 39] to enable the phase correlation method to obtain subpixel precision displacement. Although the phase correlation method has better anti-noise performance than the grayscale correlation method, the signal-to-noise ratio would be extremely low in images captured in some scenes, such as high-frequency shooting, insufficient ambient light, etc.