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We propose a fast and robust 2D-affine global motion estimation algorithm based on phase-correlation in the Fourier-Mellin domain and robust least square model fitting of sparse motion vector field and its application for digital image stabilization. Rotation-scale-translation (RST) approximation of affine parameters is obtained at the coarsest level of the image pyramid, thus ensuring convergence for a much larger range of motions. Despite working at the coarsest resolution level, using subpixel-accurate phase correlation provides sufficiently accurate coarse estimates for the subsequent refinement stage of the algorithm. The refinement stage consists of RANSAC based robust least-square model fitting for sparse motion vector field, estimated using block-based subpixel-accurate phase correlation at randomly selected high activity regions in finest level of image pyramid. Resulting algorithm is very robust to outliers such as foreground objects and flat regions. We investigate the robustness of the proposed method for digital image stabilization application. Experimental results show that the proposed algorithm is capable of estimating larger range of motions as compared to another phase correlation method and optical flow algorithm.