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In this letter, we propose a novel method based on bilateral filter (BF) scale-invariant feature transform (SIFT) (BFSIFT) to find feature matches for synthetic aperture radar (SAR) image registration. First, the anisotropic scale space of the image is constructed using BFs. The constructing process is noniterative and fast. Compared with the Gaussian scale space used in SIFT, more accurately located matches can be found in the anisotropic one. Then, keypoints are detected and described in the coarser scales using SIFT. At last, dual-matching strategy and random sample consensus are used to establish matches. The probability of correct matching is significantly increased by skipping the finest scale and by the dual-matching strategy. Experiments on various slant range images demonstrate the applicability of BFSIFT to find feature matches for SAR image registration.