The *matching problem* is to find the correspondences
between two subsets of frames that are in the same configuration in the
two ``images'', up to a global rigid transformation. We have already developed
methods to solve the dual problem of *registration *of frames (i.e.
computing the transformation) [Reference
and demo]
so we only present here the *matching* algorithm we have developed
on frames.

The algorithm we have developed is a generalization of the geometric hashing technique that uses binary invariants of frames, which is the rigid transformation from one frame to the other, expressed in one of the two reference frame.

However, if we can compute the uncertainty on this transformation from the uncertainty on frames, indexing an uncertain rigid transformation in a hash table is a difficult problem. To bypass this problem, we have use the translation part of the transformation and the angles between the vectors of the thrihedra.

This way, the invariant space has bounds but is not ``circular'' as with the rotation vector. We can thus index with (approximate) error zones as usual.