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A matching parameter estimation method with subpixel accuracy is derived by using the radial basis function (RBF) interpolation. This method reconstructs two analogue images from two given digital images by the RBF, and then minimises a non-linear cost function by the steepest-descent algorithm to estimate translation, rotation, scaling factor and intensity change between the two analogue images. The RBF provides accurate interpolation, resulting in accurate estimation. A Gaussian weighting function is introduced into the cost function to provide a local estimate within a region of interest (ROC). Then double integrals included in the cost function are analytically computed and the computational complexity is significantly reduced by exploiting the property that the Gaussian function decays rapidly. When the matching parameters are not constant over the whole image, or equivalently, the ROC is set to be small, the proposed method is better than the conventional phase correlation method in estimation accuracy.