I saw a picture like this on the lomosite. Everybody was asking how the guy did it, but he remained silent. It took me ten minutes in Photoshop to figure it out. You can do it in Gimp also. I will tell you how to do it.
First you need to take a pic with your Spinner 360. The pic needs to be quite level, the horizon on the left side should be on the same height as on the left side. When scanned, the sprockets have to be level too.
Open it in software and flip it vertically. Go to filter / distort / polar coordinates. execute the filter. Now you have a strange pic because the aspect ratio remains the same as the Spinner pic. Now you just have to adjust the ratio to 1:1.
I just opened a new empty square image and copy/pasted the pic into the square pic. Press Ctrl + T and you can adjust the aspect ratio.
This will be my only pic like this one because I like to stay analogue, this is to much digital enhancement for me.