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Remap warps an entire image. It therefore requires an image the size of the maps to warp.
undistortPoints is indeed the method you want. It doesn't have NEON support, but adding parallel for looks very easy. If you want to do it quickly and have OpenMP, just add #pragma omp parallel for above the final loop in the function. If you want to do it right, you can take a look at any of the other parallel functions to see how they do it, like remap.
It doesn't look that hard to add vectorization instructions either. The math and data structures involved are much less complicated than in remap.
