**5. Conclusions**

In this paper, we have presented a modality-free multimodal remote sensing image registration method named SRIFT, which has the advantage of scale, radiation, and rotation invariance, making it suitable for use with di fferent multimodal remote sensing images. The building of a robust NDS space, the definition of a new concept called LOSPC, and the development of a new RIC system are the three main contributions of the proposed SRIFT method. The NDS space is constructed to resist the scale distortion of image pairs with a large di fference in gradient distribution. LOSPC is computed in the NDS space of the images, in which the same kind of ground object will present similar structural distributions, and thus the features of these images are mapped into the same space. The idea of the RIC system is that the points in the neighborhood are statistically calculated through a continually changing local coordinate system, which is more suitable for the feature matching task than a global coordinate system, and realizes rotation invariance, without the need for the estimated orientation to be assigned. In the experimental analysis, two simulated datasets and nine sets of real data were used to qualitatively and quantitatively compare the registration performance of SIFT, ASIFT, SAR-SIFT, PSO-SIFT, DLSS, HOPC, PCSD, RIFT, and the proposed SRIFT method. The registration performance of the SRIFT algorithm on the multimodal images with NRD was superior to that of the other state-of-the-art image registration methods. Our future study will focus on research into a correction model and error elimination for multimodal image registration.

**Author Contributions:** S.C. established the motivation, designed the method, developed the code, performed the experiments, and wrote the manuscript; M.X. and Y.Z. provided funding; A.M. and Y.Z. reviewed and improved the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the National Key Research and Development Program of China under gran<sup>t</sup> nos. 2018YFB0504801 and 2017YFB0504202, and in part by the Fundamental Research Funds for the Central Universities under grand no. 2042020kf0014, and in part by the National Natural Science Foundation of China under gran<sup>t</sup> nos. 41622107 and 41801267.

**Acknowledgments:** The authors would like to thank Yuanxin Ye for sharing the code of the HOPC method and some of the experimental data, and Wenping Ma for sharing the code of the PSO-SIFT method.

**Conflicts of Interest:** The authors declare no conflicts of interest.
