Fig. 1. Hyper-chaotic attractor of the Chen 4D system. (a) Projection in x-y-z; (b) projection in x-y; (c) projection in x-z; (d) projection in y-z

Fig. 2. Diagram of FZP focus and imaging. (a) FZP focus; (b) FZP imaging

Fig. 3. Flow chart of watermark embedding and extraction procedure. (a) Embedding procedure; (b) extraction procedure

Fig. 4. Optoelectronic setup of the optical watermarking

Fig. 5. Results of watermark encryption experiment. (a) Original host image; (b) watermark image; (c) hyper-chaotic random phase mask R(x,y); (d) encrypted watermarking image; (e) watermarked image; (f) reconstruction result

Fig. 6. Key security test for watermarking algorithm. (a) Decrypted MSE curves for Δα and Δβ; (b) decrypted MSEcurves for Δx0, Δy0, Δz0 and Δw0; (c) decrypted MSE curve for Δf; (d) decrypted MSE curve for Δλ

Fig. 7. Encryption experiment results for different host images. (a)-(d) Host grayscale images of pepper, baboon, pavilion, and sculpture; (e)-(h) watermarked images of pepper, baboon, pavilion, and sculpture; (i)-(l) original watermarked grayscale images extracted from Fig.7 (e)-(h)

Fig. 8. Effect of the implant weighting factor γ on the quality of the recovered watermark images. (a) RPSN for different weighting factor γ; (b) NCC for different weighting factor γ

Fig. 9. Watermark images extracted after noise attack. (a)-(d) Salt and pepper noise when p is 0.01, 0.02, 0.04, and 0.06; (e)-(h) Gaussian noise when k is 0.2, 0.4, 0.6, and 0.8

Fig. 10. Watermark images extracted under different occlusion areas. (a)-(c) Occlusion attack is 10%, 25%, and 50%; (d)-(f) corresponding reconstruction under the watermark image

Fig. 11. Results of compression attack experiment. (a) Q=20; (b) Q=40; (c) Q=60; (d) Q=80

Fig. 12. Effect of the axial error of the mask on the decryption. (a) Watermark extracted after the mask is horizontally shifted to the left by 1 pixel; (b) watermark extracted by shifting the mask vertically upward by 1 pixel; (c) watermark extracted after axial correction

Fig. 13. Autocorrelation of the images. (a) Pepper image; (b) man image; (c) encrypted watermark image; (d) watermarked image

Fig. 14. Results of chosen-plaintext attack. (a) House pseudo watermark; (b) starfish pseudo watermark; (c) ship pseudo watermark; (d) host image; (e)-(f) watermarks extracted from Fig. 5(e)