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Intensity-based methods work well for multimodal image registration owing to their effectiveness and simplicity, but the computation for geometric transforms is a heavy load. To accelerate the transformation, in this paper, we present two shear-resize matrix factorizations for general 3D linear transformation, to factorize a transform matrix into three shears and a fixed resize, or four shears and a customizable resize. Shears can be implemented very fast by memory shift and a resize can be done by axis-aligned resampling. The factorizations can be applied to both rigid-body and affine transformations. The experiments on MRI and CT volumes show that our method is 10 times faster than the naive transformation. The method is quite promising for hardware and parallel implementation, and is also valid for monomodal image registration.