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arXiv · 2605.26702

Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling

Pengzhen Chen·Yanwei Liu·Xiaoyan Gu·Antonios Argyriou·Wu Liu·Weiping Wang
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Abstract

Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations. As panoramas are defined on the sphere, they naturally transform under the action of $SO(3)$, rendering conventional planar representations and augmentation-based robustness strategies inadequate and devoid of theoretical guarantees. To address this, we formulate panoramas as spherical signals and leverage $SO(3)$ representation theory to derive provably rotation-invariant descriptors. While spherical harmonic coefficients transform equivariantly under rotations, the natural invariant constructions are typically limited to zeroth-order statistics which eliminate directional information and severely constrain embedding capacity. In this work, we introduce a principled third-order invariant construction by coupling higher-order $SO(3)$ irreducible representations via tensor products and projecting onto the trivial representation. This yields a spherical invariant bispectrum that preserves phase information while remaining strictly rotation-invariant. Leveraging this property, we embed watermarks into higher-order spherical harmonic coefficients and recover them from invariant bispectral scalars, enabling reliable extraction under arbitrary 3D rotations. We provide a theoretical proof of $SO(3)$ invariance for it and demonstrate experimentally its near-perfect robustness to continuous rotations while maintaining high visual fidelity.

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Pengzhen Chen, Yanwei Liu, Xiaoyan Gu, Antonios Argyriou, Wu Liu, Weiping Wang. 2026-06-11. Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling. https://arxiv.org/abs/2605.26702

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