I have created an image (1200x1200) with white background (I had had some problems if I used transparent backgrounds.). I have pasted the source image in the center. Then I selected with "Fuzzy select tool" the white outside. And applied Map > Resynthesize:
In "Options" tab, I have marked the three options in "Output".
In "Tweaks" tab:
Neighbourhood size: 100
Search thoroughness: 500
Sensitivity to outliers: 0.12
In Resynthesizer v1 in "Options" tab I have had to select the source image as "Texture source". In Resynthesize v0.16 that is not necessary.
Edit:
In the method I had used before, I realized that it was not necessary to paste the source image on the white image. My mistake is because I had tried creating a transparent image, and does not work on transparent backgrounds.
So, just open the source image and then create a new image with white background. Apply Resynthesizer on this new image choosing the source image as "texture source". In this way you will not notice that the center does not match the rest.
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Edit 2:
I compiled Resynthesizer v2.0 and this is the result:

So you can compare V0.16 v1.0.1 and v2.0. I did not notice a big difference.
I think it is possible to better match the source image in the center with the rest, if the filter is applied on the center this time, choosing as source texture the new image we got. It's a matter of doing more tests.