An Improved Bidirectional Shift-Based Reversible Data Hiding Scheme Using Double-Way Prediction Strategy

Table 1

Notations of the proposed method (all variables marked with a star are used in embedding process 2).

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PEH: prediction-error histogram

PE: prediction error

S: secret information in binary bits with elements s₁, s₂, s_i, …, , …, s_j, …, , …, s_L, where L is the length of S

TH, : [−TH, TH], [] are the ranges of peak bins

PK, : the quantity of peak bin values

PK_l, : double the number of peak bins

I, I (i, j): an 8 bit grayscale cover image with a size of H × W (H is the height and W is the width), I (i, j) is a pixel of I in row number i and column number j

I₁, I₁ (i, j): the first-stage stego image and one of its pixels

, : the final stego image and one of its pixels

P (i, j), : prediction value of I (i, j), I₁ (i, j)

P_e (i, j), (i, j): prediction error of pixel I (i, j)

P_el (i, j), (i, j): prediction value of pixels I_1r (i, j) and I₁ (i, j) after left shifting

P_er (i, j), (i, j): prediction value of pixels (i, j) and after right shifting

h (p_e): the frequency of the prediction-error value p_e in the histogram, where

I_1r (i, j): the stego image after right shifting of PEH in embedding process 1

: the stego image after left shifting of PEH in embedding process 2

, : the quantity of units to move during expanding and shifting in right shift and left shift in embedding process 1

, : the quantity of units to move during expanding and shifting in left shift and right shift in embedding process 2

n, : the number of zero bins between the current positive bin value and the peak bins

m, : the number of zero bins between the current negative bin value and the peak bins

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