Information Hiding Based on Statistical Features of Self-Organizing Patterns
Abstract
:1. Introduction
2. Preliminaries
2.1. Beddington-DeAngelis-Type Predator-Prey Model with Self- and Cross-Diffusion
2.2. The Numerical Model and Types of Self-Organizing Patterns
2.3. A Secure Communication System Based on Self-Organizing Patterns
2.4. The Wada Index for the Evaluation of the Image Complexity
- s—the size of the border of a square observation window measured in the number of pixels; .
- m—the number of different colors in the observation window; .
- , —the number of the k-th color pixels in the observation window.
- , —the discrete probability of the k-th color in the observation window.
- The indicator function is equal to 1 if the number of colors in the observation window is greater or equal than 2:
- The indicator function is equal to 1 if the number of colors in the observation window is greater or equal than 3:
- The Shannon entropy of different colors in the observation window:
2.5. Other Statistical Indicators for the Evaluation of the Image Complexity
3. Results and Discussion
3.1. Optimal Information Hiding in Stripe-Type Patterns
- The Wada index should drop down from the initial value and should get stabilized before growing back again.
- The mean of the brightness of the pattern should remain around the average between black and white before dropping down significantly below the average.
- The p-value of the Kolmogorov-Smirnov criterion should grow above what indicates that the distribution becomes Gaussian.
3.2. Optimal Information Hiding in Patterns of Spots
3.3. Optimal Information Hiding in Unstable Patterns
3.4. The Robustness of the Proposed Scheme
3.5. More Examples of Different Carrier Patterns and Hidden Images
4. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Saunoriene, L.; Jablonskaite, K.; Ragulskiene, J.; Ragulskis, M. Information Hiding Based on Statistical Features of Self-Organizing Patterns. Entropy 2022, 24, 684. https://doi.org/10.3390/e24050684
Saunoriene L, Jablonskaite K, Ragulskiene J, Ragulskis M. Information Hiding Based on Statistical Features of Self-Organizing Patterns. Entropy. 2022; 24(5):684. https://doi.org/10.3390/e24050684
Chicago/Turabian StyleSaunoriene, Loreta, Kamilija Jablonskaite, Jurate Ragulskiene, and Minvydas Ragulskis. 2022. "Information Hiding Based on Statistical Features of Self-Organizing Patterns" Entropy 24, no. 5: 684. https://doi.org/10.3390/e24050684
APA StyleSaunoriene, L., Jablonskaite, K., Ragulskiene, J., & Ragulskis, M. (2022). Information Hiding Based on Statistical Features of Self-Organizing Patterns. Entropy, 24(5), 684. https://doi.org/10.3390/e24050684