# 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
However, when the  
Figure 9: The cross-power spectrum corresponding to the simulated data, where (**a**,**d**) are iron textures, (**b**,**e**) are cement textures, and (**c**,**f**) are soil textures. noise is particularly serious, even if RANSAC is combined with SVD, the accuracy of the displacement results obtained is still inferior to our method. From the result, it can be seen that among the three texture scenes, the accuracy of the proposed method performed best, especially for the steel-texture scene; the other four phase correlation methods can only obtain the displacement results with integer pixel accuracy, while the method in this paper can obtain subpixel precision displacement results. This is also interpretable. The essence of the phase correlation method is to use the texture changes of the photographed surface to perform correlation analysis. Therefore, the texture of the photographed surface needs to be rich enough to ensure sufficient correlation and obtain accurate displacement results. However, under the condition of a pure iron texture, the texture of the photographed surface is composed of the rust on the photographed surface and the surface itself, causing its texture to be far less rich than the cement texture or the soil texture. The proportion of areas with clear streaks is very small; that is, gross errors account for a large proportion of all the observed data. In this case, even if the RANSAC method against gross errors is used, accurate displacement results cannot be obtained. However, the method in this paper first removes the completely invisible areas of the cross-power spectrum matrix, and then performs subsequent displacement estimation to avoid the interference of the unclear areas of the cross-power spectrum matrix, so that accurate displacement results can be obtained. In addition, it can also be seen that for the cement and soil scenes with rich-enough textures, the local up-sampling method and the SVD + RANSAC method can also obtain better displacement estimation accuracy, which indicates that in the case of sufficiently rich textures, the displacement estimation method using anti-gross error can also resist noise \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Methods** & **(a)** & **(b)** & **(c)** & **(d)** & **(e)** & **(f)** \\ \hline Local up-sampling & 0.436 & 0.383 & 0.27 & 91.273 & 0.4 & 1.425 \\ SVD & 7.502 & 10.973 & 6.914 & 4.372 & 2.81 & 11.626 \\ RANSAC & 14.809 & 16.514 & 11.051 & 7.912 & 6.974 & 3.867 \\ SVD + RANSAC & 0.745 & 0.156 & **0.072** & 6.064 & 0.415 & 1.704 \\ Ours (PSD + SVD) & **0.135** & **0.087** & 0.202 & **1.153** & **0.341** & **0.479** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of absolute accuracy of simulation experiments, where the unit is the pixel, and the bold font is the minimum error value among the five methods. Figure 10: Comparison of absolute accuracy of simulation experiments. interference better. However, the accuracy of the proposed method is higher. This shows that it is effective, for a weak texture and a severe noise scene, to screen out the regions with clear fringes in the cross-power spectrum matrix first and then perform subsequent processing.