# A Phase Correlation Anti-Noise Displacement Estimation Method Based on PSD Phase Screening
## 3 Experiment and Analysis
### Simulation Experiment
#### 3.1.2 Results and Discussion  
The six sets of images used in the simulation experiment were converted to the frequency domain using the two-dimensional discrete Fourier transform, then windowing was performed to prevent the spectrum from leaking, and, finally, two sets of images were converted to the frequency domain. Interferometric processing of the image can obtain the cross-power spectrum matrix. The phase of the cross-power spectrum matrix of the six sets of data are shown in Figure 9, where (a) and (d) are iron textures, (b) and (e) are cement textures, and (c) and (f) are soil textures. It can be seen from the spectrogram that the area with clear fringes in the spectrogram is very small due to severe noise interference, which makes displacement estimation a great challenge. At the same time, when the texture information of the image is not rich enough, such as the experimental data shown  
Figure 8: Simulation data, where (**a,d**) are iron texture, (**b,e**) are cement texture, and (**c,f**) are soil texture. Figure 7: The workflow of gain simulation experiment data. in Figure 8d, the frequency domain component brought by the texture information is even smaller than the frequency domain component caused by the noise, resulting in a smaller clear stripe area in the spectrogram. This further increases the difficulty of displacement estimation. Therefore, it is necessary to automatically filter out the regions with clear stripes in the spectrogram, which can improve the accuracy of the displacement estimation and the anti-interference ability of the displacement estimation against noise. The five kinds of phase correlation methods mentioned above are used to estimate the displacement of the analog data. The absolute accuracy of the displacement results obtained by these five methods is shown in Figure 10 and Table 2. From the results, it can be seen that the proposed method is still able to estimate the displacement with high accuracy, even in the case of severe noise. At the same time, another interesting phenomenon can be seen from the experimental results: the absolute accuracy is about several to a dozen pixels, when using the SVD-based method or the RANSAC-based method alone. However, when combining SVD with RANSAC, the absolute accuracy of the displacement estimation is improved directly to the subpixel level. Of course, this is explainable: (1) When using the RANSAC algorithm for straight-line fitting, there is an important premise that the correct data accounts for the majority of all data; however, in the simulated data used in this paper, due to severe noise interference, the regions with clear stripes in the cross-power spectrum matrix also contain a certain percentage of noise. This leads to a small percentage of the correct data contained in the phase being used for straight-line fitting, which, in turn, makes the RANSAC-based method unable to obtain accurate displacement results. (2) When the SVD is used to process the cross-power spectrum matrix, there is also an important premise that the main component of the matrix is the correct information (stripes); however, due to the serious interference of noise, the main component of the cross-power spectrum matrix is not the correct information. This leads to the fact that SVD cannot fully recover the clear stripes in the whole region, which, in turn, makes the SVD-based method unable to obtain accurate displacement results. (3) When RANSAC is combined with SVD, the noise part is first removed from the clear-stripes region with the SVD strategy, so that the stripes are all correct information in the clear region; then RANSAC is used to fit the straight line, the correct straight line can be obtained, and the correct displacement result can be obtained; this is true even for the experimental data (c), where the noise is not particularly serious in comparison, as the data can acquire a better result than our method.