It is unlikely you can directly convert just any random PNG pictures to STL format for 3D printing. But some programs may be able to process "png slices" and recreate a 3D model from that that can then be used for the purposes of 3D printing. Sometimes shades of gray are used to define the "plasticity" of the 3D model, but that works only for a very specific kind of PNG images.
Convert Portable Network Graphic to Stereolithography CAD file.
We found 3 software records in the database related to .png to .stl file format conversion.
Microsoft Windows software - convert png to stl on Windows
A 3D CAD translation softwate
Convert from png file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned png to stl. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
A 3D general-purpose modeling program
Apple macOS / Mac OS X software - convert png to stl on OS X
3D modeling application for Mac