This study employed PIV to analyze the land surface displacement of a landslide. The analysis procedure was as follows: using an UAS to capture orthoimages of the study area; identifying appropriate ground control points within the area; use high-precision satellite positioning devices to obtain the three-dimensional coordinates of the ground control points; and inputting the high-resolution coordinate data when producing the orthomosaics to enhance the overall precision of the orthomosaics. Through this procedure, multiperiod orthomosaics were obtained and analyzed using PIV to calculate the land surface displacement at various periods. The subsequent paragraphs detail on the tasks involved at each stage of the procedure.

For producing orthomosaics, the authors ensured that the entire large-scale landslide potential area was covered in the images. Four ground control points were selected outside the main sliding area, where coordinate and elevation data were collected using high-precision satellite positioning devices (Fig. 7). The unmanned aerial vehicle was installed with a 24-million-pixel camera for capturing images and flew at 150 m. An image captured had an 85% overlap with the ones above and below it and a 70% overlap with the one to the left and right of it. The captured images were subject to matching, mosaicking, aerial triangulation, and point cloud densification in Pix4D mapper pro to produce orthomosaics and digital surface model data (Fig. 8). Following the aforementioned steps, the authors could maintain a precision of  ≥ 10 cm in the average ground sampling distance and ground control points.

Fig. 7
figure 7

Locations of ground control points and the coordinates and precision of TWD97

Fig. 8
figure 8

Orthomosaic and the corresponding sparse digital surface model (DSM)

The obtained multiperiod orthomosaics were used to analyze the land surface displacement in the landslide area on PIVview2C (version 3.6; PIVTEC). Figure 9 presents the mechanics of the software. First, an image is fixed and compared with another one to obtain the relative displacement. Comparison and correlation calculations were performed on similar pixels to detect the peak correlation coefficient. The coefficient indicates the vector field in which the two images’ particle features can be mutually superimposed and are completely matching, and the correlation offset is identical to the displacement. These steps were taken to identify the mean displacement of particles and thus understand the overall particle movement in the environment (PIVTEC GMBH 2015).

Fig. 9
figure 9

Procedure of PIV’s analysis

After images of two periods are imported to the software program, several critical parameter settings are required before the horizontal displacement analysis can be started. First, the first image was divided into a mesh of test patches with the same size; the amount of two-dimensional displacement of each test patch mesh was obtained after its analysis was complete. For calculating the amount of displacement between the test patches in two images, the size of search patch was set in another image; the search zone was determined to be the area of the maximum test patch movement in relation to the two directions in a two-dimensional space. A larger patch encompasses a greater number of image features and hence provides more precise results. However, a fixed-size image provides few measurement points for displacement calculation, making window size and step size of the search patch two critical parameter settings that require testing.

Search patches with identical coordinates in two images were subject to cross-correlation to determine the level of correlation between the two images. The cross-correlation analysis were performed using the following equation:

$$C(s){ = }int {int {W^{^{prime}} left( x right)I^{^{prime}} (x)W^{^{primeprime}} (x + s)I^{^{primeprime}} left( {x + s} right){text{d}}x} } ,$$

(1)

where (C{text{(s)}}) is the level of correlation; (I^{^{prime}}) and (I^{^{primeprime}}) are the window size of search patches; (W^{^{prime}}) and (W^{^{primeprime}}) are the image files of the first and second images, respectively; and s is the amount of displacement between the two images. Using search patches of varying sizes could directly undermine the precision of analysis results. The relationship between error and search window size is expressed as follows:

$$rho_{pixel} = 0.6/L + 150000/L^{8} ,$$

(2)

where L is the search window size and (rho_{{{text{pixel}}}}) is the standard error.

According to the literature, the larger the search patch, the more precise is the analysis results but the fewer are the obtained measurement points. Moreover, the analysis precision decreases if the amount of image displacement is not an integer multiple of the number of image pixels. In addition to window size and distance of movement, the image feature points are a primary factor affecting the analysis results. Image features are variable across times and seasons, such as vegetation; for buildings and construction structures, their features may change with the lighting and shadow conditions at the time of shooting. In situations where the study area is large and a low correlation is observed in the image analysis, valley or shadow areas can be excluded in the subsequent analyses because the surface features of valleys are highly variable, and shadowed features cannot be identified. Subjecting images to grayscale processing and equating the grayscale distribution before PIV analysis can effectively increase the matching correlation coefficient of non-shadowed areas. These are all the crucial factors affecting the result of PIV analysis (White et al. 2003; Tseng et al. 2009).

In comparing the differences between orthomosaics of different periods, the orthomosaics were cropped to the same photographic coverage and adjusted to the same level of resolution, with the effect of color minimized, to facilitate the analysis and comparison of land surface displacement under identical standards. Seven orthomosaics from the period of February 23 to March 26, 2021, were selected, cropped to the same photographic coverage, adjusted to the same level of resolution (10 cm/pixel), and processed using grayscale equation before further analyses were conducted (Fig. 10). According to the PIV user’s manual (2010), the interrogation window size is the rectangular size with which the PIV images are sampled to perform the local cross-correlation analysis. Frequently the interrogation window is also referred to as interrogation spot. The window dimensions can be freely set. Because the study area size is only 3335 × 2359 pixels (333.5 × 235.9 m), the search window size is set 256 pixels (25.6 m) which is less than the study area (Fig. 11). Step size defines the increment with which the images are sampled. These values define the mesh size of the final data size. Typical values are around 50% of the window size which satisfies the sampling criterion. Greater sample overlap (e.g., smaller step sizes) produces oversampled data, but does not necessarily yield additional information. Consequently, the step size is set 128 pixels (12.8 m), 64 pixels (6.4 m), and 32 pixels (3.2 m) to calibrate the best step size. The detailed results are shown in Fig. 12, when the step size is set large pixels (128 pixels) could not provide the representative slide movement with highly precision in the study area. When the step size is set as small pixels (32 pixels), only few feature points can be found. If the step size is greater than or close to the local horizontal displacement in the study area, some error results such as the error direction of sliding would occur. Through testing, the PIV search window size and step size for two-dimensional displacement of land surface analysis were determined to be 256 and 64 pixels, respectively.

Fig. 10
figure 10

Grayscale images of different periods

Fig. 11
figure 11

PIV evaluation setup in the study area

Fig. 12
figure 12

The testing of the PIV’s window size and step size

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