Geometric Relation Distribution for Place Recognition

In this letter, we illustrate geometric relation distribution (GRD), a novel signature for place recognition and loop closure with landmark maps. GRD encodes geometric pairwise relations between landmark points into a continuous probability density function. The pairwise angles are represented by von Mises distribution whereas two alternative distributions, Erlang or biased Rayleigh, are proposed for distances. The GRD function is represented through its expansion into Fourier series and Laguerre polynomial basis. Such orthogonal basis representation enables efficient computation of the translation and rotation invariant metric used to compare signatures and find potential loop closure candidates. The effectiveness of the proposed method is assessed through experiments with standard datasets.