Artistic style transfer with FFT
Fourier-based approach
The idea is that high frequencies in images preserve the import content in order to recognize structures and the hope is that style can be preserved in the low frequencies. We move both content and style image to the Fourier domain and apply a high pass filter on the contant image and a low pass filter on the style image, we then add them together in the Fourier domain and apply the inverse Fourier to get the style transfered image.
This is an illustration of the different steps in the style transfer method. For both the content and style image, we apply the Fourier transform, then we do a filtering, then we sum the two images together and apply inverse Fourier transform to get it back to the spatial domain.
This example shows a style transfer that meets our assumption about style is low frequent and we see that the style transfered image has the style of the style image and the content (the castle structures) of the content image.
In this example we can see that the low frequent objects are kept with the same spatial position in the style transfered image. This is a limitation of the method and shows why a different method is needed for a general style transfer method.