Enhanced edge-based steganography using image segmentation and random LSB substitution for secure data hiding

Require: Cover image C, Message image M

Ensure: Stego image S

• 1: Step 1: Preprocessing and Image Segmentation

• 2: Load C and M

• 3: if C and M are color images then

• 4: Convert them to grayscale using [32]: G(i,j)=0.2989R(i,j)+0.5870G(i,j)+0.1140B(i,j) G(i,j) = 0.2989R(i,j) + 0.5870G(i,j) + 0.1140B(i,j)

• 5: end if

• 6: Apply threshold T for binarization: B(i,j)=1,if G(i,j)>T0,otherwise B(i,j) = \left\{{\matrix{{1,} \hfill & {{\rm{if}}\,G(i,j) > T} \hfill \cr {0,} \hfill & {{\rm{otherwise}}} \hfill \cr}} \right.

• 7: Use Otsu's method to calculate T: T=argmaxTσB2(T) T = \arg {\max_T}\sigma_B^2(T) where σB2(T) \sigma_B^2(T) is the between-class variance.

• 8: Perform segmentation on B_C(x, y) and B_M (x, y).

• 9: Step 2: Edge Detection

• 10: Apply Canny edge detection on B_C(x, y) [33]: |∇I|=∂I∂X2+∂I∂Y2 |\nabla I| = \sqrt {{{\left({{{\partial I} \over {\partial X}}} \right)}^2} + {{\left({{{\partial I} \over {\partial Y}}} \right)}^2}}

• 11: Retain edge pixels whose lengths match edges in B_M (i, j).

• 12: Step 3: Randomization and LSB Substitution

• 13: Randomly select edge pixels using a pseudo-random number generator RNG with secret key K [34]: Q(j)=RNG(EC(i,j),K) Q(j) = RNG({E_C}(i,j),K)

• 14: Perform LSB substitution: Q′(i,j)=Q(i,j)−(Q(i,j)mod2)+b,if embedding bit b=1Q(i,j)−(Q(i,j)mod2),if b=0 Q'(i,j) = \left\{{\matrix{{Q(i,j) - (Q(i,j)\bmod 2) + b,} \hfill & {{\rm{if}}\,{\rm{embedding}}\,{\rm{bit}}\,b = 1} \hfill \cr {Q(i,j) - (Q(i,j)\bmod 2),} \hfill & {{\rm{if}}\,b = 0} \hfill \cr}} \right.

• 15: Step 4: Stego Image Generation

• 16: Combine modified edge pixels with non-edge regions to form S(i, j).

• 17: Step 5: Post-Processing and Quality Metrics

• 18: Compute PSNR [35]: PSNR=10⋅log10MAX2MSE {\rm{PSNR}} = 10 \cdot {\log_{10}}\left({{{MA{X^2}} \over {MSE}}} \right) where MSE=1MN∑i=1M∑j=1N(C(i,j)−S(i,j))2 MSE = {1 \over {MN}}\sum\limits_{i = 1}^M {\sum\limits_{j = 1}^N {{{(C(i,j) - S(i,j))}^2}}}

• 19: Accept S only if PSNR > 40.

• 20: Step 6: Embedding Time

• 21: Measure embedding time T_e [26]: Te=Tpre+Tembed {T_e} = {T_{pre}} + {T_{embed}}

• 22: Optimize T_e by refining edge detection and randomization steps.