1. A Neural Network Approach for Visual Cryptography Tai-Wen Yue and Suchen Chiang IEEE 2000

2. What is Visual Cryptography? Target image Share image2 Share image1

3. The Procedure Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) The original taget image Halftone Plain Shadow Image

4. Image Halftoning Error Aggregated Scan-Line Algorithm e0E0 e0e1E1 e0e1e2E2

5. The Q ’ tron(Quantum) NN for (2, 2) Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 )

6. Q ’ tron---Q-State Neuron External stimulus Active value Internal stimulus

7. Q ’ tron---Q-State Neuron Q ’ tron ’ s Input Internal Stimulus External Stimulus Noise

8. Q ’ tron---Q-State Neuron State Updating Rule:

9. The Q ’ tron(Quantum) NN Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) halftoning restoration +

10. Image Halftoning Energy Function: Sum of graylevel in a 3×3 area for graytone image Sum of halftone in a 3×3 area for halftone image  Minimizing the error square corresponds to halftoning -

11. Image Restoration Energy Function: - (i,j) i j r=3

12. s1s1 s2s2 0 0 1 1 0 1 0 1 h 0 1 1 1 E2E2 0 0.25 0 0 1 1 0 1 0 1 1 0 0 0 2.25 1 1 1 s1s1 s2s2 h E2E2 FeasibleInfeasible LowHigh Cost Function

13. Stacking Rule Satisfaction Energy Function: _ Minimizing this term tends to satisfy the stacking rules

14. Share Image Assignment For simplicity, shares are plain images S1 S2 Mean Gray level K 1 K2K2 Result

15. Build Plain Shadow Images Energy Function: [g low,g high ] : K 1 =K 2 ≦ g low <g high ≦ min(2K,255) 例如 : [135,235] ; K1=K2=118 - -

16. Total Energy Halftoning Restoration Share Images Cost Function

17. Conclusions Share images size = target image size. Code book is free.

18. Future Works Design language to specify an access scheme. Extend to color images