<p>Is it possible to convert an image image to STL file format? </p>

<p><img src="https://i.stack.imgur.com/Y6SYj.png" alt="png image"></p>

<p>E.g. I don't need the coloring, I need the lines.</p>

PNGs are 2-dimensional picture data files. STL however is a 3-dimensinal surface data files. The two are not inherently transformable into one another, as there simply is no 3rd dimension encoded in the PNG.
However, there are ways to generate a 3rd dimension from a color picture:
Lithophanes
take color information and use that as a degree of deviation from a base plane.
Using 3D design software that supports importing image data, one can trace the areas in 2D and
extrude
them to different heights or
emboss
the patterns into a block, even with different depths for each color.