# Data Hiding in Symmetric Circular String Art

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- This work is the first work addressing data hiding in string art images for copyright protection and secure communication.
- In order to minimize embedding distortion, a data hiding framework by odd–even modulation on node histogram is proposed, which gives sufficient freedom in choosing a string segment pair to modify.
- Four data embedding algorithms are designed in the proposed framework, in an effort to minimize the embedding distortion at low computational complexity.

**Notation:**Unless otherwise stated, scalars are denoted as lower-case letters, such as a variable n. Vectors and matrices are represented as low-case and upper-case boldface letters, respectively, such as a vector $\mathbf{b}$ and a matrix $\mathbf{A}$. Functions that operate on an entire image are represented as calligraphic form, such as operators $\mathcal{D}(\mathbf{A})$ and $\mathcal{R}(\mathbf{A})$. Set is represented in upper case San-serif font, such as a set $\mathsf{J}$.

## 2. The Digital String Art

**Regularly Spaced Nails.**For this type, the nails are regularly spaced on a wooden plate. The most popular arrangement of the nail positions is to put the nails on a circle. This will be the focus of our work. Other regular arrangements of nails are also possible, for example, by placing nails on a two-dimensional grid.**Irregularly Spaced Nails.**To better render the original image, the feature of the original image should be used to guide the placement of the nails. For example, in regions with more texture or structure, more nails should be placed.

#### 2.1. Data Structure for Digital String Art Images

- Node: A node of a string art image corresponds to one of the nails fastened at the edge of the circular plate. Each node is specified by its index number $n\in \left\{1,2,\dots ,N\right\}$.
- Segment: A line segment is determined by two nodes. For example, for a line segment starting at node m and ending at node n, it is denoted as $\u301am,n\u301b$.
- Joint: A joint is a common node shared by two adjacent line segments. For example, for two line segments $\u301am,n\u301b$ and $\u301an,\ell \u301b$, the node n is a joint between them. For example, the node 2 is a joint for line segments $\u301a0,2\u301b$ and $\u301a2,3\u301b$.
- Segment pair: Two line segments connected by a joint. For example, a segment pair formed by lines $\u301am,n\u301b$ and $\u301an,\ell \u301b$ is denoted as $\u301am,n,\ell \u301b$.

## 3. Data Hiding by Odd–Even Modulation

#### 3.1. Node Histogram

#### 3.2. Data Embedding

#### 3.3. Random Deletion

#### 3.4. Random Selection

#### 3.5. Minimal Distance Selection

#### 3.6. Simplified Minimum Distance Selection

- Calculating the distances ${L}_{m,n}$ and ${L}_{n,\ell}$.
- Searching the space of feasible solutions.

#### 3.7. Data Extraction

## 4. Experimental Evaluation

#### 4.1. Performance Metric

#### 4.2. Parameter Setup and Optimization

#### 4.3. Distortion Testing and Comparison

#### 4.4. Machine Time

#### 4.5. Security

#### 4.6. Qualitative Comparison with Other Copyright Protection Approaches

**Visible watermarking:**Visible watermarking overlays a small-sized image (watermark) on the image to be protected, for notifying users of copyright issues [39,40]. This overlay brings high distortion to the original image. Furthermore, its security is low since the very existence of the watermark is known to everyone. This approach has higher flexibility than a registration-based approach since the owner is free to change his/her watermark.**Registration-based approach:**This approach is widely used in digital rights management (DRM) of multimedia signals shared over networks, such as Internet, DVD and CCTV (Closed Circuit Television) [41,42,43]. A salient feature of this approach is that the quality of the media signal is not affected. Furthermore, it has high security and is supported by display devices from various vendors. However, this approach is not flexible since the owner of the content needs to register his/her media to a centralized organization.**Data hiding approach:**Compared with visible watermarking, data hiding brings low distortion to the multimedia signal. Furthermore, it has higher security than visible watermarking since the watermark is hidden and encrypted. Compared with the registration-based approach, the data hiding approach has higher flexibility because the copyright message is embedded in the media signal itself. No centralized organization is needed to extract the copyright message.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Stoppel, S.; Bruckner, S. LinesLab: A Flexible Low-Cost Approach for the Generation of Physical Monochrome Art. Comput. Graph. Forum
**2019**, 38, 110–124. [Google Scholar] [CrossRef] - Blanken, R. String Art Magic: Secrets to Crafting Geometric Art with String and Nail; Spring House Press: Berlin/Heidelberg, Germany, 2018. [Google Scholar]
- Vrellis, P. A New Way to Knit. Available online: http://artof01.com/vrellis/works/knit.html (accessed on 12 July 2020).
- Birsak, M.; Rist, F.; Wonka, P.; Musialski, P. String Art: Towards Computational Fabrication of String Images. Comput. Graph. Forum
**2018**, 37, 263–274. [Google Scholar] [CrossRef] [Green Version] - Ostanin, I. “String art” approach to the design and manufacturing of optimal composite materials and structures. Compos. Struct.
**2020**, 246, 112396. [Google Scholar] [CrossRef] [Green Version] - Jovanović, M.; Vučić, M.; Tepavčević, B.; Raković, M.; Tasevski, J. Robotic Knitting in String Art as a Tool for Creative Design Processes. Advances in Service and Industrial Robotics. RAAD 2019. In Advances in Intelligent Systems and Computing; Berns, K.G.D., Ed.; Springer: Cham, Switzerland, 2019; Volume 980. [Google Scholar]
- Barni, J.; Bartolini, F. Watermarking Systems Engineering: Enabling Digital Assets Security and Other Applications; Marcel Dekker Inc.: New York, NY, USA, 2004. [Google Scholar]
- Bender, W.; Gruhl, D.; Morimoto, N.; Lu, A. Techniques for data hiding. IBM Syst. J.
**1996**, 35, 313–336. [Google Scholar] [CrossRef] - Cox, I.; Miller, M.; Bloom, J.; Fridrich, J.; Kalker, T. Digital Watermarking and Steganography, 2nd ed.; Morgan Kaufmann Publishers Inc.: San Francisco, CA, USA, 2007. [Google Scholar]
- Pan, J.S.; Li, W.; Yang, C.S.; Yan, L.J. Image steganography based on subsampling and compressive sensing. Multimed. Tools Appl.
**2015**, 74, 9191–9205. [Google Scholar] [CrossRef] - Cox, I.J.; Kilian, J.; Leighton, T.; Shamoon, T. Secure spread spectrum watermarking for images, audio and video. In Proceedings of the 3rd IEEE International Conference on Image Processing, Lausanne, Switzerland, 19 September 1996; Volume 3, pp. 243–246. [Google Scholar]
- Wu, H.; Cheung, Y.; Wang, Y. Data Hiding on 3D Meshes Based on Dither Modulation. In Proceedings of the 2006 World Automation Congress, Budapest, Hungary, 24–26 July 2006; pp. 1–6. [Google Scholar]
- Jiang, R.; Zhou, H.; Zhang, W.; Yu, N. Reversible Data Hiding in Encrypted Three-Dimensional Mesh Models. IEEE Trans. Multimed.
**2018**, 20, 55–67. [Google Scholar] [CrossRef] - Hao, L.; Yan, B.; Pan, J.; Chen, N.; Yang, H.; Acquah, M.A. Adaptive Unified Data Embedding and Scrambling for Three-Dimensional Mesh Models. IEEE Access
**2019**, 7, 162366–162386. [Google Scholar] [CrossRef] - Luo, H.; Lu, Z.; Pan, J. A Reversible Data Hiding Scheme for 3D Point Cloud Model. In Proceedings of the 2006 IEEE International Symposium on Signal Processing and Information Technology, Vancouver, BC, Canada, 27–30 August 2006; pp. 863–867. [Google Scholar]
- Celik, M.U.; Sharma, G.; Tekalp, A.M.; Saber, E. Reversible data hiding. Proc. Int. Conf. Image Process.
**2002**, 2, II156–II160. [Google Scholar] - Cox, I.J.; Kilian, J.; Leighton, F.T.; Shamoon, T. Secure spread spectrum watermarking for multimedia. IEEE Trans. Image Process.
**1997**, 6, 1673–1687. [Google Scholar] [CrossRef] - Yan, B.; Guo, Y.J.; Wang, X.M. Performance Of Spread Spectrum Watermarking In Autoregressive Host Model Under Additive White Gaussian Noise Channel. J. Meas. Sci. Instrum.
**2010**, 1, 271–275. [Google Scholar] - Cheng, Q.; Sorensen, S. Spread Spectrum Signaling For Speech Watermarking. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Salt Lake City, UT, USA, 7–11 May 2001; Volume 3, pp. 1337–1340. [Google Scholar]
- Garcia, R.A. Digital Watermarking Of Audio Signals Using A Psychoacoustic Auditory Model And Spread Spectrum Theory. Master’s Thesis, Music Engineering Technology, University of Miami, Miami-Dade County, FL, USA, 1999. [Google Scholar]
- Chen, B.; Wornell, G.W. Quantization index modulation: A class of provably good methods for digital watermarking and information embedding. IEEE Trans. Inf. Theory
**2001**, 47, 1423–1443. [Google Scholar] [CrossRef] [Green Version] - Lu, Z.M.; Xing, W.; Xu, D.G.; Sun, S.H. Digital Image Watermarking Method Based On Vector Quantization With Labeled Codewords. IEICE Trans. In. Syst.
**2003**, E86-D, 2786–2789. [Google Scholar] - Lu, Z.M.; Xu, D.G.; Sun, S.H. Multipurpose Image Watermarking Algorithm Based on Multistage Vector Quantization. IEEE Trans. Image Process.
**2005**, 14, 822–831. [Google Scholar] [PubMed] - Moriya, T.; Takashima, Y.; Nakamura, T.; Iwakami, N. Digital Watermarking Schemes Based On Vector Quantization. In Proceedings of the IEEE Workshop on Speech Coding For Telecommunications, Pocono Manor, PA, USA, 7–10 September 1997; pp. 95–96. [Google Scholar]
- Shi, Y.; Li, X.; Zhang, X.; Wu, H.; Ma, B. Reversible data hiding: Advances in the past two decades. IEEE Access
**2016**, 4, 3210–3237. [Google Scholar] [CrossRef] - Weng, S.; Chen, Y.; Ou, B.; Chang, C.; Zhang, C. Improved K-Pass Pixel Value Ordering Based Data Hiding. IEEE Access
**2019**, 7, 34570–34582. [Google Scholar] [CrossRef] - Zhang, X. Reversible Data Hiding in Encrypted Image. IEEE Signal Process. Lett.
**2011**, 18, 255–258. [Google Scholar] [CrossRef] - Qian, Z.; Zhang, X. Reversible Data Hiding in Encrypted Images With Distributed Source Encoding. IEEE Trans. Circuits Syst. Video Technol.
**2016**, 26, 636–646. [Google Scholar] [CrossRef] - Yan, X.; Lu, Y.; Liu, L.; Song, X. Reversible Image Secret Sharing. IEEE Trans. Inf. Forensics Secur.
**2020**, 15, 3848–3858. [Google Scholar] - Zhang, W.; Wang, H.; Hou, D.; Yu, N. Reversible Data Hiding in Encrypted Images by Reversible Image Transformation. IEEE Trans. Multimed.
**2016**, 18, 1469–1479. [Google Scholar] [CrossRef] - Jain, A.K. Fundamentals of Digital Image Processing; Prentice-Hall, Inc.: Upper Saddle River, NJ, USA, 1989. [Google Scholar]
- Je, S.; Abileva, Y.; Bianchi, A.; Bazin, J.C. A computational approach for spider web-inspired fabrication of string art. Comput. Animat. Virtual Worlds
**2019**, 30, e1904. [Google Scholar] [CrossRef] - Lau, D.; Arce, G. Modern Digital Halftoning, 2nd ed.; Taylor & Francis: Boca Raton, FL, USA, 2001. [Google Scholar]
- Liu, Y.; Guo, J.; Lee, J. Inverse Halftoning Based on the Bayesian Theorem. IEEE Trans. Image Process.
**2011**, 20, 1077–1084. [Google Scholar] [PubMed] - Wang, Z.; Bovik, A.C.; Sheikh, H.R.; Simoncelli, E.P. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process.
**2004**, 13, 600–612. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Karras, T.; Laine, S.; Aittala, M.; Hellsten, J.; Lehtinen, J.; Aila, T. Analyzing and Improving the Image Quality of StyleGAN. arXiv
**2019**, arXiv:cs.CV/1912.04958. [Google Scholar] - String Art Generator. [EB/OL]. Available online: http://github.com/halfmonty/StringArtGenerator/ (accessed on 12 July 2020).
- Biomedical Image Data Set. [EB/OL]. Available online: http://decsai.ugr.es/cvg/dbimagenes/index.php/ (accessed on 12 July 2020).
- Huang, C.-H.; Wu, J.-L. Attacking visible watermarking schemes. IEEE Trans. Multimed.
**2004**, 6, 16–30. [Google Scholar] [CrossRef] - Hu, Y.; Kwong, S. Wavelet domain adaptive visible watermarking. Electron. Lett.
**2001**, 37, 1219–1220. [Google Scholar] [CrossRef] - Ma, Z. Digital rights management: Model, technology and application. China Commun.
**2017**, 14, 156–167. [Google Scholar] - Camp, L. Access denied [digital rights management]. IEEE Secur. Priv.
**2003**, 1, 82–85. [Google Scholar] [CrossRef] - Subramanya, S.R.; Yi, B.K. Digital rights management. IEEE Potentials
**2006**, 25, 31–34. [Google Scholar] [CrossRef]

**Figure 3.**Node histogram of the string art Mona Lisa. (

**a**) String art image Mona Lisa. (

**b**) The Node histogram of (

**a**).

**Figure 5.**Relationship between distance L and index distance D. (

**a**) Plotting ${L}_{0,n}$ and ${D}_{0,n}$ as a function of index n. (

**b**) Plotting of ${L}_{0,n}$ vs. ${D}_{0,n}$.

**Figure 6.**A Gaussian weighting mask for calculating weighted Human Peak Signal to Noise Ratio (HPSNR).

**Figure 7.**The four testing string art images that are used in parameter optimization. These images are generated using the algorithm in [32]. (

**a**) Mona Lisa, (

**b**) Lena, (

**c**) Fab, and (

**d**) Odry.

**Figure 8.**The weighted PSNR as a function of the weighting parameter $\alpha $ or $\widehat{\alpha}$. (

**a**) Weighted HPSNR vs. $\alpha $ for minimum distance selection algorithm. (

**b**) Weighted HPSNR vs. $\widehat{\alpha}$ for simplified minimum distance selection algorithm.

**Figure 9.**The rendered string art images of Mona Lisa before and after data hiding. (

**a**) Original string art image, (

**b**) random deletion (weighted HPSNR = 30.92 dB), (

**c**) random selection (weighted HPSNR = 31.56 dB), (

**d**) minimum distance selection (weighted HPSNR = 47.19 dB), and (

**e**) simplified minimum distance selection (weighted HPSNR = 47.15 dB).

**Figure 10.**Comparing distortion for four typical string arts. (

**a**) Weighted HPSNR, and (

**b**) weighted structure similarity measure (SSIM).

**Figure 11.**Data set for batch test. (

**a**) A set of faces generated by styleGAN [36]. (

**b**) The corresponding string art images ready for data embedding.

**Figure 12.**Batch test for distortion on a data set consisting of 20 string arts. (

**a**) Weighted HPSNR, and (

**b**) weighted SSIM.

**Figure 13.**Correlation coefficient $\rho $ between two distortion measures: weighted HPSNR and weighted SSIM. The overall correlation coefficient for all algorithms is 0.96.

**Figure 14.**Testing result for three biomedical images. The first column contains the original images. The second column contains the corresponding string art. The last column contains the string art after data embedding.

**Figure 15.**Plotting two empirical cumulative distribution functions (CDFs) $H(n)$ vs. $\widehat{H}(n)$.

${s}_{1}$ | ${d}_{1}$ |
---|---|

${s}_{2}$ | ${d}_{2}$ |

⋯ | ⋯ |

${s}_{L}$ | ${d}_{L}$ |

Parameter | Value | Setting Method | |
---|---|---|---|

Original string art | N: Number of nodes | 200 | Typical value as used in [32] |

L: Number of line segments | 3000 | Typical value as used in [32] | |

r: Radius of the plate | 180 mm | Typical value as used in [32] | |

Data hiding algorithm | $\alpha $: weighting parameter for minimum distance selection | 0.35 | Parameter optimization |

$\widehat{\alpha}$: weighting parameter for simplified minimum distance selection | 0.65 | Parameter optimization | |

$\sigma $: parameter of the Gaussian mask for HPSNR calculation | 1.2 | From [34]. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yan, Y.-S.; Cai, H.-L.; Yan, B.
Data Hiding in Symmetric Circular String Art . *Symmetry* **2020**, *12*, 1227.
https://doi.org/10.3390/sym12081227

**AMA Style**

Yan Y-S, Cai H-L, Yan B.
Data Hiding in Symmetric Circular String Art . *Symmetry*. 2020; 12(8):1227.
https://doi.org/10.3390/sym12081227

**Chicago/Turabian Style**

Yan, Yu-Song, Hui-Li Cai, and Bin Yan.
2020. "Data Hiding in Symmetric Circular String Art " *Symmetry* 12, no. 8: 1227.
https://doi.org/10.3390/sym12081227