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Owing to its effectiveness and simplicity, intensity-based method works well for registration of images. However, it needs a large amount of computation for geometric transformation. In this paper, we present two shear-resize matrix factorizations to accelerate the transformation. A transform matrix can be factorized into two shears and a fixed non-uniform resize, or three shears and a customizable resize. A customizable resize can be uniform in all dimensions or scaling just in one dimension. Shears can be implemented very fast by memory-shift, and a resize can be done by simple axis-aligned interpolation. The factorizations can be applied to both rigid-body and affine transformations. Their efficiency is performed by experiments on some standard test images and fingerprint images. The methods are quite promising for hardware implementation, and can also be extended to 3D or higher dimensional fast geometric transformation.