User-friendly and practical ways to define a mapping between vector spaces

[uellue]

Defining reference points with coordinates in two vector spaces is probably a good way to define a mapping between the two vector spaces. Using a least squares optimization allows to over-determine the mapping and verify the mapping quality.

This works well for software as well, which would use correlation to find matching points.

Open question: How to handle undefined directions, for example defining reference points in 2D where each vector space is, in fact, 3D? The result is an equation, which could be difficult to use in subsequent processing steps.

How to handle "certainty information" in the data, i.e. the information how reliable a specific point is?