Question

I am looking for the following type of algorithm:

There are n matched pairs of points in 2D. How can I identify outlying pairs of points according to Affine / Helmert transformation and omit them from the transformation key? We do not know the exact number of such outlying pairs.

I cannot use Trimmed Least Squares method because there is a basic assumption that a k percentage of pairs is correct. But we do not have any information about the sample and do not know the k… In such a sample of all pairs could be correct or vice versa.

Which types of algorithms are suitable for this problem?

Answer 1

Use RANSAC:

Repeat the following steps a fixed number of times:

• Randomly select as much pairs as are necessary to compute the transformation parameters.
• Compute the parameters.
• Compute the subset of pairs that have small projection error (the ‘consensus set’).
• If the consensus set is large enough, compute a projection for it (e.g. with Least Squares).
• Computer the consensus set’s projection error
• Remember the model if it is the best you found so far.

You have to experiment to find good values for

• “a fixed number of times”
• “small projection error”
• “consensus set is large enough”.