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.
