Estimation of geometric transformation matrices using grid-shaped pilot signals

TL;DR

This paper introduces a watermarking technique that embeds a grid-shaped pilot signal into images, enabling accurate estimation of geometric transformations like cropping, scaling, and rotation for robust watermark synchronization.

Contribution

The proposed method uniquely uses a grid-shaped pilot signal and Radon transform analysis to estimate geometric transformations, including cropping, which is challenging for existing techniques.

Findings

Accurately estimates transformation matrices under various attacks.

Robust against cropping, scaling, rotation, and shearing.

Low error in transformation estimation demonstrated through simulations.

Abstract

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.