Axis-level Symmetry Detection with Group-Equivariant Representation

Abstract

Symmetry is a fundamental concept that has been extensively studied, yet detecting it in complex scenes remains a significant challenge in computer vision. Recent heatmap-based approaches can localize potential regions of symmetry axes but often lack precision in identifying individual axes. In this work, we propose a novel framework for axis-level detection of the two most common symmetry types--reflection and rotation--by representing them as explicit geometric primitives, i.e., lines and points. Our method employs a dual-branch architecture that is equivariant to the dihedral group, with each branch specialized to exploit the structure of dihedral group-equivariant features for its respective symmetry type. For reflection symmetry, we introduce \orientational anchors, aligned with group components, to enable orientation-specific detection, and a reflectional matching that measures similarity between patterns and their mirrored counterparts across candidate axes. For rotational symmetry, we propose a rotational matching that compares patterns at fixed angular intervals to identify rotational centers. Extensive experiments demonstrate that our method achieves state-of-the-art performance, outperforming existing approaches.