Sorry - I see that Ariel has asked about this as well - but are 'forward' and 'backward' the usual terms here?

As I understand it, you have a 'moving' image and a 'static' image.  The optimization finds the transformation from the grid of the 'static' image to the grid of the 'moving' image.  Then, the 'forward' transform is where you take a grid corresponding to the 'static' image, and resample the 'image' onto that grid using the calculated transform.  Is that right?

If so, then 'forward' seems an odd name for it - it could just as well be 'backward' couldn't it?  Could you use another term like static2moving or something?