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EquiPose: Exploiting Permutation Equivariance for Relative Camera Pose Estimation

CVPR 2025 · 3D vision › Human pose estimation · approach: Learned camera pose estimation · 3 citations (OpenAlex)

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Proposes EquiPose, a framework that makes any end-to-end relative pose network permutation-equivariant (P21 = P12^-1) by symmetrizing its two-order predictions via a geodesic rotation mean, improving baselines with or without fine-tuning.

Problem

End-to-end relative camera pose networks do not satisfy pose permutation equivariance: estimating pose from I1 to I2 and from I2 to I1 yields inconsistent results (the reverse should be the inverse).

Approach

Define a pose permutation equivariant (PPE) mapping and construct it from any baseline by averaging the two orderings: rotation is the geodesic mean of R12 and R21^T, translation is (t12 - R*12 t21)/2; a theorem proves the output is PPE, and only one extra forward pass of the decoder is needed by reusing shared encoder features.

Key results

• On ScanNet, GRelPose+EquiPose† reduces rotation error from 8.16 to 7.61 and translation error from 0.38 to 0.28 m.
• Inference-only EquiPose improves all five baselines on ScanNet across the eight metrics (e.g., GRelPose RE 8.16 to 7.97).
• EquiPose enforces dR and dt of zero exactly, while random permutation training leaves nonzero differences (e.g., GRelPose dR 3.2 to 0 vs 2.1 with RP).

Measured effects reported in the paper

Surprising findings

• Random permutation training improves average errors but cannot strictly enforce the PPE property, and EquiPose trained under random permutation still gains further.

Limitations

• Extra computation depends on baseline decoder/aggregation cost; heavy decoders incur high overhead.
• Requires two decoder passes at inference, doubling cost in the worst case.
• Evaluated only on indoor and outdoor pose datasets with specific baselines.

Experimental setup

Datasets: ScanNet 7-Scenes 12-Scenes Mapfree

Benchmarks: ScanNet 7-Scenes 12-Scenes Mapfree

Metrics: rotation AUC @3/5/10 deg translation AUC @0.1/0.2/0.5 m rotation error translation error pose error VCRE dR dt params FLOPs

Baselines: ExtremeRotation Reg6D EightVit MF6D GRelPose MFBin MFBinTS MFQuat MFQuatTS

Builds on: ExtremeRotation GRelPose MF6D EightVit Reg6D

Closest papers by meaning

• From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation (CVPR 2024 · similarity 0.87)
• 3D-Aware Hypothesis & Verification for Generalizable Relative Object Pose Estimation (ICLR 2024 · similarity 0.85)
• Relative Pose Estimation through Affine Corrections of Monocular Depth Priors (CVPR 2025 · similarity 0.85)
• UNOPose: Unseen Object Pose Estimation with an Unposed RGB-D Reference Image (CVPR 2025 · similarity 0.85)
• FAR: Flexible Accurate and Robust 6DoF Relative Camera Pose Estimation (CVPR 2024 · similarity 0.85)
• CARL: A Framework for Equivariant Image Registration (CVPR 2025 · similarity 0.85)