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The minimization process of the Levenberg-Marquardt algorithm (LMA) used in estimating the global motion parameters tends to be very expensive computationally due to the involvement of all the pixels of an image frame. We propose to reduce the computational complexity of the LMA by using only a small portion of the image data in two stages. In the first stage, we seek to reduce the complexity of the initial guess of the transformation parameters, which is critical to the final convergence of the algorithm. The complexity of computing the initial guess can be lowered by using just a small subset of the pixels in the calculation of the translational components. The second stage of the LMA algorithm is to find the final motion parameters in an iterative fashion, based on the coarse estimate of the motion parameters obtained in the previous stage. The LMA in this stage again operates on a subset of the pixels to further reduce the overall computational complexity. Both analytical and simulation results showed that the proposed partial-data algorithm could achieve a speedup factor of over 25 for global motion estimation (GME) with an eight-parameter perspective motion model on several video sequences, without significant loss in the estimation accuracy compared with the conventional LMA on the full image data.