* The well known method of Artistic Style Transfer can be used to generate new texture images (from an existing example) by skipping the content loss and only using the style loss.
  * The method however can have problems with large scale structures and quasi-periodic patterns.
  * They add a new loss based on the spectrum of the images (synthesized image and style image), which decreases these problems and handles especially periodic patterns well.

### How
  * Everything is handled in the same way as in the Artistic Style Transfer paper (without content loss).
  * On top of that they add their spectrum loss:
    * The loss is based on a squared distance, i.e. $1/2 d(I_s, I_t)^2$.
      * $I_s$ is the last synthesized image.
      * $I_t$ is the texture example.
    * $d(I_s, I_t)$ then does the following:
      * It assumes that $I_t$ is an example for a space of target images.
      * Within that set it finds the image $I_p$ which is most similar to $I_s$. That is done using a projection via Fourier Transformations. (See formula 5 in the paper.)
      * The returned distance is then $I_s - I_p$.

### Results
  * Equal quality for textures without quasi-periodic structures.
  * Significantly better quality for textures with quasi-periodic structures.


![Overview](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/Texture_Synthesis_Through_CNNs_and_Spectrum_Constraints__overview.png?raw=true "Overview")

*Overview over their method, i.e. generated textures using style and/or spectrum-based loss.*