Embedding of binary image in the Gray planes

For watermarking of the digital grayscale image its Gray planes have been used. With the help of the introduced representation over Gray planes the LSB embedding method and detection have been discussed. It found that data, a binary image, hidden in the Gray planes is more robust to JPEG lossy compression than in the bit planes.

💡 Research Summary

The paper investigates the use of Gray planes of an 8‑bit grayscale image as carriers for binary watermark data and compares their robustness against JPEG lossy compression with the traditional bit‑plane approach. The authors first recall the definition of Gray code: each Gray plane G V is obtained by XOR‑ing the binary bit V with the next more significant bit V + 1. Consequently, modifying a Gray plane affects all lower‑order bit planes simultaneously, a property that can be exploited for more distributed embedding.

Two embedding schemes are described. In the bit‑plane method, the watermark M (a binary image) is XOR‑added to a selected bit plane B V: B V ← B V ⊕ M. In the Gray‑plane method, the same operation is performed on a Gray plane: G V ← G V ⊕ M. The resulting stego image S can be expressed as a weighted sum of bit planes, where the chosen plane and all less‑significant planes now contain the watermark.

Detection is divided into non‑blind (original cover C is available) and blind (C is not available) scenarios. Non‑blind detection simply XOR‑s the corresponding planes of C and S (formulas D1 and D2) to retrieve M. Blind detection relies on the fact that embedding a Gray plane changes two adjacent Gray planes; by extracting both the modified plane V and its neighbor V + 1 (or a designated plane K = V + 1) from the stego image, M can be reconstructed (formula D6). The authors note that blind detection cannot be reduced to the bit‑plane case, and therefore generally yields lower fidelity.

The experimental section evaluates the four possible extraction routes after JPEG compression: M_b (bit‑plane, non‑blind), M_gb (Gray‑plane, non‑blind), M_g (Gray‑plane, non‑blind using Gray plane), and M_gc (Gray‑plane, blind). JPEG quality factors q = 70, 80, 90 are used, and 200 grayscale test images (including complex textures from the “Caprichos” collection) are processed. Three distortion metrics are computed: Euclidean distance, Peak Signal‑to‑Noise Ratio (PSNR), and relative entropy (Kullback‑Leibler divergence).

Results show that embedding in the fourth Gray plane (G₄) consistently outperforms embedding in the fourth bit plane (B₄). For q > 50, PSNR of the Gray‑plane extracted watermark stays between 15 dB and 30 dB, indicating satisfactory visual quality, whereas the bit‑plane counterpart degrades more rapidly. Non‑blind detection always yields better scores than blind detection, confirming the advantage of having the original cover for error correction. Moreover, the degradation is monotonic with respect to the significance of the plane: lower‑order planes suffer more from JPEG quantization, but even the fourth plane remains visually indistinguishable from the original image after embedding.

The authors conclude that Gray‑plane LSB embedding provides a more robust alternative to traditional bit‑plane LSB embedding when the stego image is expected to undergo JPEG compression. The inherent coupling of multiple bit planes within a Gray plane distributes the watermark information, reducing the impact of quantization noise. Both blind and non‑blind extraction methods are feasible, though non‑blind extraction delivers higher fidelity. This work suggests that Gray‑plane based watermarking can be advantageous for practical applications where JPEG is the dominant storage format.