Pair-Relative Partial Equivariance for Rotation-Robust Keypoint Descriptor Matching

Abstract

Learned keypoint descriptors trained on upright imagery often fail under large in-plane rotation. Steerers address this by applying a single exact SO(2) representation to the descriptor space, but this global group constraint can be too rigid for keypoint descriptors, whose angular responses need not follow a single group representation. We propose pair-relative partial equivariance, which measures equivariance under the empirical distribution of relative rotations in image pairs, and PaSteer, a relaxed descriptor-steering framework that allows the steering map to leave the exact representation manifold while retaining the lightweight, backbone-free design of steering. PaSteer instantiates this relaxation with two variants: an identity-preserving residual steerer (PaSteer-soft) and a free-form Fourier steerer (PaSteer-free). We show that the per-angle optimal linear steerer for a fixed non-equivariant descriptor generally does not obey the group composition law, explaining why exact representations can be suboptimal in the frozen-descriptor regime. On Roto-360, MegaDepth-1500, AIMS, and IMC-PT, PaSteer consistently improves rotation-robust matching over an exact steerer on frozen DeDoDe descriptors, especially under large relative rotations, with minimal upright degradation.