An Analysis on Inverted Mirrored Moiré and Ribbon of Band Moiré

  • Hui-Ying Liu
  • Dao-Shun WangEmail author
  • Xiang-Hui Zhao
  • Shun-Dong Li
  • Ching-Nung Yang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 895)


Band moiré pattern is produced by the superposition of the base layer with the revealing layer that has a different periodic frequency. Band moiré can effectively describe the geometric transformation of moiré, so that we can design more elements and specific moiré in band moiré image, which can be used to engage and decipher the secret image. Hersch et al. put forward a mathematical model to describe the geometric transformation of moiré pattern, and based on this, a method for constructing band moiré pattern was proposed. Furthermore, the inverted mirrored moiré effect is also described for the case that the period of the revealing layer is less than the period of the base layer. However, the principle and limitations of inverted mirrored moiré effect have not been given. In this paper, we introduce the principle of the inverted mirrored moiré effect and specify the conditions of producing inverted mirrored moiré, That is, when the period of the revealing layer is less than the period of the basic layer and more than half of the period of the base layer, the inverted mirrored moiré will be shown. We also noticed the phenomenon of the repeated local moiré pattern with the analysis of the moiré generation. We give the restriction of producing ribbon moiré, when the period of the revealing layer is equal to the period of the base layer, the ribbon moiré will show. The limitations of inverted mirror image or ribbon were analyzed and the results were verified by experiments.


Ribbon moiré Inverted mirrored moiré Moiré pattern 



This work was supported in part by the National Natural Science Foundation of China under Grant U1536102, and Grant U1536116, in part by China Mobile Research Fund Project (MCM20170407), and State Administration of Press, Publication, Radio, Film and Television (SAPPRFT) Key Laboratory of Digital Content Anti-Counterfeiting and Security Forensics.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Hui-Ying Liu
    • 1
  • Dao-Shun Wang
    • 1
    Email author
  • Xiang-Hui Zhao
    • 2
  • Shun-Dong Li
    • 3
  • Ching-Nung Yang
    • 4
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingChina
  2. 2.China Information Technology Security Evaluation CenterBeijingChina
  3. 3.School of Computer ScienceShaanxi Normal UniversityXi’anChina
  4. 4.Department of Computer Science and Information EngineeringNational Dong Hwa UniversityHualienTaiwan

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