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

• URL: http://arxiv.org/abs/2605.26702v1
• Date: Tue, 26 May 2026 08:43:40 GMT
• Title: Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling
• Abstract summary: Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations.<n>We formulate panoramas as spherical signals and leverage $SO(3)$ representation theory to derive provably rotation-invariant descriptors.
• Score: 28.45286547806906
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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