Rotational symmetry detection in 3D using reflectional symmetry candidates and quaternion-based rotation parameterization

Abstract

The property of symmetry in 3D objects is helpful in various applications such as object alignment, compression, symmetrical editing or reconstruction of incomplete objects. However, its robust and efficient detection is a challenging task. The two most commonly occurring types of symmetry are probably reflectional and rotational symmetry. While reflectional symmetry detection methods are quite plentiful, this does not seem to be the case with rotational symmetry detection. In this paper a use of approximate reflectional symmetries to derive plausible approximate rotational symmetries is proposed that can be integrated with multiple different approaches for reflectional symmetry detection. One such specific approach, based on maximizing a given symmetry measure, is chosen and combined with this idea. A modification of the maximization step for rotations is further proposed using a simple, yet efficient, quaternion-based parameterization of the rotation transformation which seems novel in the field of symmetry detection. The results confirm that this combination provides a robust and efficient solution for finding rotational symmetry in a 3D point set and can handle approximate symmetry, noisy input or even partial data.