Angular Radon spectrum for rotation estimation

Abstract

This paper presents a robust method for rotation estimation of planar point sets using the Angular Radon Spectrum (ARS). Given a Gaussian Mixture Model (GMM) representing the point distribution, the ARS is a continuous function derived from the Radon Transform of such distribution. The ARS characterizes the orientation of a point distribution by measuring its alignment w.r.t. a pencil of parallel lines. By exploting its translation and angular-shift invariance, the rotation angle between two point sets can be estimated through the correlation of the corresponding spectra. Beside its definition, the novel contributions of this paper include the efficient computation of the ARS and of the correlation function through their Fourier expansion, and a new algorithm for assessing the rotation between two point sets. Moreover, experiments with standard benchmark datasets assess the performance of the proposed algorithm and other state-of-the-art methods in presence of noisy and incomplete data.