FFT based convolution

Abstract

The Fourier transform of the convolution of two images is equal to the product of their Fourier transform. With this definition, it is possible to create a convolution filter based on the Fast Fourier Transform (FFT). The interesting complexity characteristics of this transform gives a very efficient convolution filter for large kernel images. This paper provides such a filter, as well as a detailed description of the implementation choices and a performance comparison with the "simple" itk::ConvolutionImageFilter.