Convolving Image with Kernel with Fourier

1. What is the fastest way to take the convolution of an image?
2. What is convolution in Fourier transform?
3. What does this kernel do in a convolution?

What is the fastest way to take the convolution of an image?

FFT is the fastest technique known for convolving signals, and FFTW is the fastest free library available for computing the FFT.

What is convolution in Fourier transform?

The convolution theorem (together with related theorems) is one of the most important results of Fourier theory which is that the convolution of two functions in real space is the same as the product of their respective Fourier transforms in Fourier space, i.e. f ( r ) ⊗ ⊗ g ( r ) ⇔ F ( k ) G ( k ) .

What does this kernel do in a convolution?

The 2D convolution is a fairly simple operation at heart: you start with a kernel, which is simply a small matrix of weights. This kernel “slides” over the 2D input data, performing an elementwise multiplication with the part of the input it is currently on, and then summing up the results into a single output pixel.