Smoothing a image while retaining the edges

In my previous post here it is mentioned that using ImageResize before ImageGraphics will increase image quality of the final vector image. So now I have another "blurry" image here, which is, a "colored" version of it.

For this, the simple trick does not work anymore. Using ImageResize ends up yielding a equally blurry image. So what can I use to get a smooth but sharp, version of this image? Using GaussianFilter will destroy the edges, which is not desired.

• Median filtering is a technique that can be effective at smoothing while preserving edges. I don't know if you think it is an improvement, but you can try MedianFilter[img, 1] – mikado Oct 6 '18 at 16:33