用网格导频信号精准估算图像几何变换，支持裁剪后水印同步。
Estimation of geometric transformation matrices using grid-shaped pilot signals
- 嵌入带方向编码的网格导频信号，通过畸变分析反推变换矩阵。
- 在缩放、旋转、剪切和裁剪下，变换估计误差极低。
- 适合需要鲁棒同步的数字水印场景，尤其抗裁剪能力强。
数字水印技术对防止图像被盗用至关重要。由于盗版图像常经缩放、裁剪等几何操作，准确同步——即检测水印嵌入位置——对正确提取极为关键，尤其是裁剪会改变图像原点，使同步困难。然而现有方法大多对裁剪不鲁棒。为此，我们提出一种利用导频信号估计载体图像几何变换的方法，实现裁剪后的同步。在图像中嵌入具有明显水平与垂直特征的网格状导频信号；当图像发生变换时，网格随之畸变，通过分析该畸变可估计变换矩阵。对畸变图像应用Radon变换，可估计网格角度与间隔；因水平与垂直线编码不同，可确定网格方向，降低歧义。通过各向异性缩放、旋转、剪切和裁剪的仿真验证，结果表明该方法在单一或复合攻击下均能以低误差准确估计变换矩阵。
原文摘要 · Abstract (English)
Digital watermarking techniques are essential to prevent unauthorized use of images. Since pirated images are often geometrically distorted by operations such as scaling and cropping, accurate synchronization - detecting the embedding position of the watermark - is critical for proper extraction. In particular, cropping changes the origin of the image, making synchronization difficult. However, few existing methods are robust against cropping. To address this issue, we propose a watermarking method that estimates geometric transformations applied to a stego image using a pilot signal, allowing synchronization even after cropping. A grid-shaped pilot signal with distinct horizontal and vertical values is embedded in the image. When the image is transformed, the grid is also distorted. By analyzing this distortion, the transformation matrix can be estimated. Applying the Radon transform to the distorted image allows estimation of the grid angles and intervals. In addition, since the horizontal and vertical grid lines are encoded differently, the grid orientation can be determined, which reduces ambiguity. To validate our method, we performed simulations with anisotropic scaling, rotation, shearing, and cropping. The results show that the proposed method accurately estimates transformation matrices with low error under both single and composite attacks.
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