procrustes for incomplete point sets

I need to find a linear transformation (exaclty as funcion procrustes does) for overlapping, but incomplete point sets.

That means, not all points of X are present in Y, and vice versa, not all points of Y are present in X.

What is the best way to do that?

[Karel]

Perhaps some kind of RANSAC could be applied? A randomly selected subsamples of identical size from both sets should be selected and the tranformation calculcated for them? How large the subsamples should be? Any experience?

Answer 1

[Pratyush]

Hi Karel

To align incomplete point sets in MATLAB when using the "procrustes" function yo can do the following:

• Determine which points in set X correspond to points in set Y based on some criteria or identifiers.
• Form two new subsets containing only the corresponding points from the original sets X and Y.
• Use the "procrustes" function on these subsets to calculate the optimal linear transformation.
• Apply the obtained transformation to the full set X to align it with set Y.

Note that establishing correspondences between points is a crucial step and may require manual intervention or advanced feature matching techniques depending on the data.