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Interferometric imaging radar altimeter (InIRA) integrating synthetic aperture radar (SAR) and synthetic aperture radar interferometry (InSAR) is a new type of radar altimeter. InIRA will be widely adopted in marine scientific research and surface water topography measurements. Owing to the geometric distortion of InIRA images, there are difficulties in feature point extraction and matching, making InIRA registration challenging. Here, an improved SAR‐scale invariant feature transform (SIFT, SAR‐SIFT) algorithm is proposed to address these difficulties. First, a modified Harris non‐linear scale space is constructed using the Harris function and non‐linear scale space, and extracted the feature points according to the SAR‐SIFT algorithm. Second, the orbital parameters of InIRA are used to calculate the geographic coordinates of each feature point by Hermit interpolation. Subsequently, a geographic‐coordinate‐based method is proposed to match the feature points. The results show that the proposed algorithm gained more correct matches and improved the registration accuracy by 13% and 16.7% compared with the SIFT and SAR‐SIFT algorithms, respectively, and was 18% more time efficient than the SAR‐SIFT algorithm. The experiments demonstrate that the proposed algorithm outperforms the SAR‐SIFT algorithm for InIRA image registration in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]