Fastest Gaussian blur implementation

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You should use the fact that a Gaussian kernel is separable, i. e. you can express a 2D convolution as a combination of two 1D convolutions.

If the filter is large, it may also make sense to use the fact that convolution in the spatial domain is equivalent to multiplication in the frequency (Fourier) domain. This means that you can take the Fourier transform of the image and the filter, multiply the (complex) results, and then take the inverse Fourier transform. The complexity of the FFT (Fast Fourier Transform) is O(n log n), while the complexity of a convolution is O(n^2). Also, if you need to blur many images with the same filter, you would only need to take the FFT of the filter once.

If you decide to go with using an FFT, the FFTW library is a good choice.

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