Finding Mirror Symmetry via Registration and Optimal Symmetric Pairwise Assignment of Curves: Algorithm and Results

We demonstrate that the problem of fitting a plane of mirror symmetry to data in any Euclidian space can be reduced to the problem of registering two datasets, and that the exactness of the solution depends entirely on the registration accuracy. This new Mirror Symmetry via Registration (MSR) framework involves (1) data reflection with respect to an arbitrary plane, (2) registration of original and reflected datasets, and (3) calculation of the eigenvector of eigenvalue -1 for the transformation matrix representing the reflection and registration mappings. To support MSR, we also introduce a novel 2D registration method based on random sample consensus of an ensemble of normalized cross-correlation matches. We further demonstrate the generality of MSR by testing it on a database of 3D shapes with an iterative closest point registration back-end.