Geomorph is able to export its maps (*.gmp) to several graphics formats - including the PNG. It doen't seem any other program is capable of this, as the GMP format from Geomorph is not well supported in other programs.
Convert Geomorph tile map file to Portable Network Graphic.
We found one software available in the database for this conversion.
Linux/Unix software - convert gmp to png on Linux
A height field generator and editor for Linux
Convert from gmp file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.