# An InSAR Interference Fringe-Matching Algorithm Based on Mountain Branch Points
## 4 Discussion  
Based on the information presented in Tables 3 and 4, it is clear that the traditional algorithm fails to achieve accurate matching, while the proposed algorithm has shown promising results. Our analysis suggests that there may be two reasons for this discrepancy. First, the traditional algorithm mainly describes the feature points through a gradient, which has no physical significance in the interference fringes. However, the proposed algorithm excavates the rich terrain features contained in the interference fringes to serve the matching task, so it can achieve good results. Second, the interference phase will inevitably feature phase winding, and phase winding will bring with it phase mutation. Although it is mentioned in Section 3.1 that we assume that there is no error in the POS data of the aircraft, there will still be some error in the actual flight process, which will lead to the difference between the winding of the reference interference fringe retrieved from the DEM data and the actual interference fringe; this can be seen from Figures 15 and 16. The traditional algorithm will detect a large number of key points in the phase mutation region, because the winding situation of the reference interference fringes is different from that of the measured interference fringes, which will cause the two to be unable to be matched correctly. Through the analysis results in Figure 9, this algorithm designs a threshold to eliminate the false detection caused by phase mutation, thus avoiding this situation. Figures 17 and 19 illustrate the matching results, revealing that the traditional algorithm is prone to detecting incorrect matching points in the phase mutation region. In contrast, the proposed algorithm does not encounter this issue and can identify matching points across different winding cycles. fringes are the same as those of the reference interference fringes. This paper first obtains line features with a pixel width of 1 by performing threshold segmentation and skeletonization on the eigenvalue map of the interference fringes. Then, it detects the branch points of the mountain using a branch point template. This image processing operation cannot guarantee that the detected branch points in the real data and reference data correspond exactly in position, introducing errors, which can be defined as \(E_{t}\). This algorithm introduces mountain line thresholds and phase mutation thresholds, which are hard thresholds that cannot fully and accurately detect mountain line features, and can also introduce errors, which are defined as \(E_{t}\). The DEM data resolution required to generate the reference interference fringes cannot be guaranteed to be consistent with the real interference fringes, which can also introduce errors, defined as \(E_{s}\), the error introduced by different interference fringe scales. \(E_{i}+E_{t}+E_{s}\) is the source of all errors in this algorithm, and it is the theoretical basis for optimizing the algorithm in the future. In this study, the traditional image matching idea of directly detecting feature points is discarded, and we innovatively propose using mountain range branch points as feature points for interference fringe matching, making full use of terrain features for the matching task. It can be seen from the experiments that the proposed algorithm has good results for matching interference fringe data, which opens up new ideas for subsequent research. This line of thought also applies to other data with topographical information, such as DEMs. It is worth noting that, since the reference interference fringe data are interpolated from the scale of the measured data, the algorithm does not take into account the effect of scale on the algorithm, but this needs to be taken into account if it is used for other tasks. The algorithm mentioned in the paper is based on the operation of the image domain and uses a more traditional principle.