I am new to this forum, (and to this field) but there are great materials here, thanks for your effort. (and excuse me for my naive understanding …)
I came from the MRI neuro imaging community where where realignment between to image is a primary task. Every one is working with the Euler representation, and I thinks for the purpose (coregistration) it is just find. ( it is a mess because of different convention used by different software, but manageable)
I am also working on simulation of MRI acquisition during subject motion within the scanner, and I add to solve then a “new” problem :
How to compute an average affine ?
(Just for the context, I need this average, to remove it from the input motion time course, so that the simulated volume would be at the same spatial position as the motion free volume)
If I have only translation then the solution is simple : it is a simple vector arithmetic mean
but for rotation things get more complicate,
I saw a few mathematical paper on this topic, and then I realised the importance of dual quaternion and finally I come to look at PGA
So my question is to know if PGA will have a “smarter” answer to this question … ?