![Ninja'd :ninja](./images/smilies/ninjad4.png)
,i too agree that will be better use inkscape
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No she mean Layer menu/Transparency/alpha to selection that will work if there is alpha and transparency.
But i suppose she miss a step somewhere, between "alpha to selection" and "select none"
More the image you posted is a jpg it could not have transparency so i can't see how that could work ("alpha" indicate transparency if no transparency "alpha to selection" cannot work)
The best way to deal with a similar image would be convert to vector , vectors may be scaled at any size without quality loss ,but you would need a vector program (inkscape or illustrator )
With gimp you may try to
1 open the image go to Layers /transparency/add alpha channel
2 now get the color selector tool
3 chose white (click with the tool on a white spot in the image)
4 look well the selection you need all white selected
5 to really look the selection you should click that tiny rectangle at the lower left bottom of gimp image windows, that it is the Quickmask will show the selection as a red overlay on the image, it is more accurate because the "marching ant " display can't show partially selected pixels.
You may correct the quickmask with any painting tool, including eraser, and clicking again the quickmask toggle you correction will be applied to the selection
6 This is not strictly needed but will help to check for defects in your selection:
create a new layer below of a strong color (red, green), then on your image above do Edit/clear
You should now see clearly if are "white fringes" left or part of the black was eroded in case , correct
removing the white or filling the black
7 do again "alpha to selection" , "Selection to Path" and now you should have a clean path to enlarge and stroke as you wish