arXiv:2605.26702cs.CVcs.AI2026-05被引 1

提出三维旋转不变的全景水印方法,解决任意3D旋转下的水印可靠性问题。

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

论文配图:Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling
图 1 · 摘自论文原文
  • 基于SO(3)表示理论构建三阶旋转不变量,保留相位信息。
  • 在连续旋转下水印提取准确率接近100%,视觉保真度高。
  • 适合需要强鲁棒性全景图像水印的场景,如虚拟现实、卫星影像。

全景图像的可靠水印技术面临任意三维旋转的根本挑战。由于全景图定义在球面上,其自然地在SO(3)作用下变换,导致传统平面表示和基于增强的鲁棒性策略无效且缺乏理论保证。为此,我们将全景图视为球面信号,利用SO(3)表示理论推导出可证明的旋转不变描述符。虽然球谐系数在旋转下等变,但自然的不变构造通常仅限于零阶统计量,会消除方向信息并严重限制嵌入容量。本文通过张量积耦合更高阶SO(3)不可约表示,并投影到平凡表示,提出一种原则性的三阶不变构造。该方法生成保留相位信息且严格旋转不变的球面双谱。利用此性质,将水印嵌入高阶球谐系数,并从不变双谱标量中恢复,实现任意3D旋转下的可靠提取。我们提供了SO(3)不变性的理论证明,并实验验证其对连续旋转具有近乎完美的鲁棒性,同时保持高视觉保真度。

原文摘要 · Abstract (English)

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.

水印球面表示SO(3)旋转不变

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