# An InSAR Interference Fringe-Matching Algorithm Based on Mountain Branch Points
## 3 Results
### Position Error Experiment and Attitude Error Experiment  
To verify the effectiveness of the proposed method, the proposed algorithm is compared with other image matching algorithms under the above two error conditions, and a position error experiment and attitude error experiment are carried out. Since no matching algorithms have been reported for interference fringe data, comparisons with the classic algorithms SIFT and SURF are presented in this paper. The parameters for the proposed algorithm are set as follows: the scale of the Gaussian function is set to 2, \(T_{ridge}\) is set to 0.7 and \(T_{valley}\) is set to \(-0.7\). The threshold value for eliminating the mountain branch points that are detected by mistake due to the interference phase mutation is set to 3, the grid size around the branch point is selected as 4\(\ast\)4 in the generation description sub-stage, and the radius around the branch point is calculated according to Equation (9). Point pairs less than 0.6 under the Euclidean distance are identified as homonymous points, the RANSAC algorithm is set with an error threshold less than 1, and the number of iterations is 2000. To objectively compare the strengths and weaknesses of different algorithms, the evaluation metrics used in this paper are inliers, precision, recall, and the overall evaluation metric (Fl-Score). Precision is defined as the number of inliers filtered by RANSAC divided by the number of correspondences output by the algorithm, and it evaluates the effect of the designed descriptor. Recall is defined as the number of correspondences actually correct among all the feature pairs calculated by the algorithm. Recall evaluates the value of the algorithm in finding keypoints. F1-Score evaluates the overall performance of the algorithm, and the three are defined as follows:  
\[ \begin{cases}Precision=\frac{\textit{Inliers}}{\textit{Matrices}}\\ Recall=\frac{\textit{Inliers}}{\textit{Correspondence}}\\ Precision=2\ast\frac{\textit{PrecisionRecall}}{\textit{Precision+Recall}}\end{cases}  \tag{10}\]  
Figure 16: Reference interference fringe. (**a**) Reference interference fringe without errors. (**b**) Example of reference interference fringe with position errors. (**c**) Example of a reference interference fringe with attitude errors. First, the position error experiment is shown. Figure 17a-c show the matching results of the three algorithms without any error, and the matching results were eliminated by the RANSCA algorithm. From Figure 17a, we can see that the SIFT algorithm does not obtain the correct matching point, which means that it is completely mismatched; Figure 17b shows the matching results of the SURF algorithm. The algorithm obtains fewer correct matching points and there are wrong matching items; Figure 17c shows the matching results of the proposed algorithm, which obtains the most correct matching points. Figure 17d-f shows the matching results of the 3 algorithms under the conditions of simulated interference fringe azimuthal error \(-500\) m and range error \(-500\) m. It can be seen from Figure 17d and Figure 17e that the matching results of the algorithms participating in the comparison are still poor under error conditions, while from Figure 17f it can be seen that the algorithm can still achieve stable and correct results under error conditions. To quantitatively describe algorithm performance, the above algorithm is run under the dataset of 41 simulated interference fringes with a positional error of plus or minus 500 m and an error interval of 25 m. Inliers, precision, recall, and F1-Score are quantified, and the results are shown in Figure 18. The mean values of the quantitative evaluation metrics are shown in Table 3.  
Figure 17: Comparison of interference fringe-matching algorithm results in the position error experiment. (**a–c**) Without error. (**d–f**) With error. (**a,d**) SIFT. (**b,e**) SURF. (**c,f**) Proposed algorithm.