Table 3 Components of a key-based watermarking model

Key generation, K e y(·)

Image data, i

Generation key, g

Message, m

Embedding key, e

Other image data, (j:j≠i)

Detection key, d

Extraction key, x

Watermark encoding

Generation, G(·)

Generation key, g

Watermark, w

Image data, i

Message, m

Other image data, (j:j≠i)

Embedding, E(·)

Embedding-key, e

Watermarked image-data, ī

Image-data, i

Watermark, w

Watermark decoding

Detection, D(·)

Detection-key, d

$\left\{\begin{array}{l}\text{Estimated image data,}ĩ\\ \text{Estimated watermark,}\tilde{w}\end{array}\right.$

Watermarked image data, ī

Image data, i

or, failure, ⊥

Watermark, w

Extraction, X(·)

Extraction key, x

$\left\{\begin{array}{l}\text{Estimated message,}\tilde{m}\\ \text{Estimated other image data,}\tilde{j}\end{array}\right.$

Watermarked image data, $\bar{w}$

Image data, i

or, failure, ⊥

Estimated watermark, $\tilde{w}$