As described in [19], the conventional PEE can be conducted in an equivalent way by modifying 2D-PEH. The corresponding 2D modification mapping for conventional PEE with T = 1 is shown in the left figure of Fig. 2. Here, similar to Fig. 1, the dots represent prediction-error pairs, the red and green arrows show the expansion and shift directions, respectively. Moreover, the adaptive PEE embedding introduced in (4) can also be conducted based on 2D-PEH modification. The corresponding mapping for (4) with (a, b) = (−3, 2) is shown in the right figure of Fig. 2. In particular, the four points (0,0), (0,1), (1,0) and (1,1) remain unchanged in this mapping. For clarity, only the first quadrant of these modification mappings are plotted in Fig 2. One can compare Fig. 1 with Fig. 2 for a better understanding, they are exactly the same for data embedding.