I see a couple of options depending on what you are after.
The lazy, easiest one would be to use the texture to control the transparency of your object. This would keep the poly count low, but you would not be dealing with real geometry.
Other option is to trace the shape on a program like the one you mention, or inkscape, illustrator or similar, and convert it into vector information, save it as SVG.(probably you can download the svg file directly on the same website you got that pattern from...) Import that into blender and use Knife Project or some form of boolean (you'd need to extrude the curves and convert to mesh to do that). Note that you'd have to rework your topology, as anytime you use booleans or knife project you'll end up with very ugly n-gons.