Application of rank metric codes in digital image watermarking

Abstract In this paper, we propose a new digital image watermarking algorithm where the resistance against attacks is studied using error correcting codes. Using the well known Lattice QIM in the spatial domain, we propose to use a different kind of error correcting codes called rank metric codes. These codes are already well used in cryptography and communications for network coding but not used yet in the context of watermarking. In this article, we show how this metric permits to correct errors with a specific structure and is adapted to specific image attacks when combined with a watermarking technique. In particular, we describe a rank metric code family called Gabidulin codes analogous to the well known Reed–Solomon codes. If one considers a rank code over a finite field extension, then any codeword has a matrix representation. One can decode the original message if the matrix rank of the detected codeword is small enough. We propose a study to validate the concept of rank metric in watermarking applications. First, we introduce a theoretically invariant method to luminance additive constant change. After combining the Lattice QIM method and rank metric codes, we add a multi-detection strategy on the damaged images with controlled luminance distortions. Then, using a block-based watermarking approach, we show how the proposed association can also be robust to an image distortion we called content erasure or copy-paste. The proposed approach completes other watermarking strategies against attacks with random errors such as JPEG compression.