Or a way to do it with an existing filter? So that you could take in video from a fisheye or dual fisheye camera (such as the Ricoh Theta) and directly output equirectangular, in real-time, to something like RTMP?
The Remap filter does just this:
This filter copies pixel by pixel a source frame to a target frame. It remaps the pixels to a new x,y destination based on two files ymap/xmap.
Basic command syntax is
ffmpeg -i fisheye_grid_input.jpg -i fisheye_grid_xmap.pgm -i fisheye_grid_ymap.pgm -filter_complex remap out.png
Also included at that link are the mapping files for
Ricoh Theta S camera: input files for resolution 1920x960(1080)