Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling
A recent study presents a watermarking technique that remains unaffected by rotation for panoramic images. This method conceptualizes panoramas as spherical signals and employs SO(3) representation theory to create descriptors that are demonstrably rotation-invariant. Although spherical harmonic coefficients undergo equivariant transformations with rotations, current invariant methods are restricted to zeroth-order statistics, which discard directional data and limit embedding capacity. The innovative approach utilizes a third-order invariant construction by linking higher-order SO(3) irreducible representations through tensor products and projecting onto the trivial representation, thus facilitating resilient watermarking against any 3D rotations.
Key facts
- The paper is published on arXiv with ID 2605.26702.
- It addresses the challenge of reliable watermarking for panoramic imagery under arbitrary 3D rotations.
- Panoramas are defined on the sphere and transform under the action of SO(3).
- Conventional planar representations and augmentation-based strategies lack theoretical guarantees.
- Spherical harmonic coefficients transform equivariantly under rotations.
- Natural invariant constructions are typically limited to zeroth-order statistics.
- Zeroth-order statistics eliminate directional information and constrain embedding capacity.
- The method introduces a third-order invariant construction using tensor products of higher-order SO(3) irreducible representations.
Entities
Institutions
- arXiv