Convert your image to scalable vector graphics (either through free online, or inkscape itself), then watch this (The inset command in Inkscape): Inkscape Inset, Outset,...

Like in the example, you will need to take it slow, and not select the whole picture at once, but work each element separately for better effect, although selecting all and insetting 3 times gave the left tree a nice thin line, and the branches looked quite good.

If you are not satisfied with the conversion, use GIMP or another program to depekle (remove the jpeg artifacts) before converting. Also, convert to, say, 8 grayscale colors before you do that, it will save you time. Remember: For a good quality, you need to spend time. Heh... graphics answer on a Perl forum... sorry for that.