Not sure if this should be moved to the math section...

Suppose I have a 3D object in some reference position/orientation R. It undergoes a, relatively small, rigid-body transform M to get in new position/orientation R'. Then R and R' will have different projected images I and I' relative to some camera C. I want to find the alignment transform to align I and I'. I know there are 2D algorithms for this to estimate the transform by identifying several feature pixels on the images, and then find a 2D affine transform.

Question is: does knowing M help? That is, does knowing the 3D transform help me get a more accurate image alignment algorithm or help me get it faster?

So far, I think it will help somewhat. Given the known feature pixels in image I from the reference position and their 3D points on the model, I can apply M, then project back to I' so that I know the feature pixels for R'. This saves me having to search for matching feature pixels. But is there room for more improvement?