Abstract: This paper proposes a rigid point set matching
algorithm in arbitrary dimensions based on the idea of symmetric
covariant function. A group of functions of the points in the set are
formulated using rigid invariants. Each of these functions computes a
pair of correspondence from the given point set. Then the computed
correspondences are used to recover the unknown rigid transform
parameters. Each computed point can be geometrically interpreted as
the weighted mean center of the point set. The algorithm is compact,
fast, and dimension free without any optimization process. It either
computes the desired transform for noiseless data in linear time, or
fails quickly in exceptional cases. Experimental results for synthetic
data and 2D/3D real data are provided, which demonstrate potential
applications of the algorithm to a wide range of problems.