On affine registration of planar point sets using complex numbers

We propose a novel algorithm for affine registration of 2D point sets. The main idea is to treat the 2D points as complex numbers and from each point set, a polynomial with complex coefficients can be computed whose roots are the points in the given point set. The two-step algorithm first reduces the affine registration problem to a rigid registration problem, and the unknown rotation is then computed using the coefficients of these polynomials. The algorithm is entirely algebraic with clear underlying geometric motivation. The implementation is straightforward and it takes less than a second to compute the affine transformation for point sets containing hundreds of points. We validate the algorithm on a variety of synthetic 2D point sets as well as point sets extracted from real-world images.

Research highlights
► The main idea is to treat the 2D points as complex numbers and from each point set, a polynomial with complex coefficients can be computed whose roots are the points in the given point set.
► The two-step algorithm rst reduces the affine registration problem to a rigid registration problem, and the un- known rotation is then computed using the coefficients of these polynomials.
► The algorithm is entirely algebraic with clear underlying geometric motivation.
► The implementation is straightforward and it takes less than a second to compute the affine transformation for point sets containing hundreds of points.