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Uniqueness of rigid point-cloud registration

A necessary and sufficient condition for uniquely registering a system of point clouds (whose positions are known in different coordinate systems) in a global coordinate system [1] has been obtained. This was done by relating the registration problem to the rigidity of bar-and-joint frameworks. In particular,  a particularly simple connectivity-based test for point clouds in two dimensions. Was obtained. Testing uniqueness however remains open in three and higher dimensions.

References:

A. V. Singh and K. N. Chaudhury, “On uniquely registrable networks,” IEEE Transactions on Network Science and Engineering, 2019.

Website: http://www.ee.iisc.ac.in/faculty/kunal/