A hierarchical method is proposed for synthetic aperture radar (SAR) and optical image coregistration. We use local invariant salient points extracted by the binary robust invariant scalable keypoints (BRISK) algorithm for SAR and optical image coregistration. However, the matched points are highly erroneous because of the speckle noise in SAR images and the different structures of SAR and optical images. Therefore, an adaptive and elliptical bilateral filter is used to remove the speckle noise. Additionally, a hierarchical approach is used for coregistration using the local and global geometrical relationship of BRISK features. For each salient point in the optical image, three closest matched points are found in the SAR image. The geometrical relationship of the matched points is determined in the local areas around the salient and matched points, and matched pairs with fewer geometrical matching scores are removed. At the final stage of the algorithm, the projective global model between optical and SAR images is obtained using a robust statistic and the remaining false matches are refined. Experimental results and the comparison of the results of the proposed algorithm with those of the existing approaches show that the proposed algorithm is more efficient.