Here is my take on image based GI with shadow catching in P 11 and Superfly

I think this exact way hasnt been described yet and it seems the most straight forward and useful way to me

1. add a background sphere that is slightly larger than the GROUND object, put your HDRI on it, ambient channel only, switch visibility for raytracing and shadows off this sphere is for preview only

2. add an IBL light, put your HDRI on it, this light is for preview only and will not be rendered in Superfly later delete all other lights (unless you really need some)

3. put your image on the Background part of the GROUND Object, ambient channel only, increase ambient amount factor to taste ( I seem to use 3 most of the time), shader as follows:

TextureCoordinate Camera --> Vector transform Camera to World --> Environment Texture Vector --> Ambient Color

Set other channels to 0/black

4. put your image on the Ground part of the ground Object, as follows:

TextureCoordinate Camerea --> Vector transform Camerea to World --> Environment Texture Vector --> Diffuse Color

TextureCoordinate Camerea --> Vector transform Camerea to World --> Environment Texture Vector --> Ambient Color

Now use the 2D Wave shader to fade out the Ambient amount on the Ground towards the center of the object so it does not emit on that part, but is only illuminated passively for most parts (use upos: 1.5, vpos 0.5, frequency 1, phase offset -0.25 for instance for a large black center area)

**5.: **now switch GROUND prop on for rendering, off for preview.

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this works for me better than all other solutions, and you can modify it easyly for uneven terrain or ojects in the background image which catch shadows via dummy objects