I'm surprised this isn't even mentioned in the article. I guess there are issues with boundary effects, but those can be overcome in a variety of ways.
Also, if your convolution kernel is short enough, you can beat an FFT. So, in 2D with an NxN image, an FFT filter will have a complexity of about (N^2 + N^2 Log N). If your kernel is KxK, then direct convolution will be (N^2 K^2), so you have to compare Log N with K^2. But keep in mind 1.) these are asymptotic complexities the coefficients matter 2.) K may or may not depend on N 3.) FFTs are may have larger memory requirements, although you may be able to get away with in-place FFTs, and you don't have to explicitly compute the FFT of the gaussian - you can work that out analytically (you should get another gaussian...).
Also, as someone pointed out, the gaussian is separable, so then the complexity of the direct convolution is (K N^2).
Anyway, what are FFT libraries like for iOS? I suppose with Apples policies, you can't compile FFTW for your App?
Last I played with FFT convolution it didn't end up being a win for any sane filter size, even compared to brute-force convolution with arbitrary non-separable kernels. Admittedly I was using off-the-shelf tools in Nuke, but I would imagine both their FFT and Convolve nodes are reasonably optimized.
Also, if your convolution kernel is short enough, you can beat an FFT. So, in 2D with an NxN image, an FFT filter will have a complexity of about (N^2 + N^2 Log N). If your kernel is KxK, then direct convolution will be (N^2 K^2), so you have to compare Log N with K^2. But keep in mind 1.) these are asymptotic complexities the coefficients matter 2.) K may or may not depend on N 3.) FFTs are may have larger memory requirements, although you may be able to get away with in-place FFTs, and you don't have to explicitly compute the FFT of the gaussian - you can work that out analytically (you should get another gaussian...).
Also, as someone pointed out, the gaussian is separable, so then the complexity of the direct convolution is (K N^2).
Anyway, what are FFT libraries like for iOS? I suppose with Apples policies, you can't compile FFTW for your App?