Abstract
With the expansion of applications, such as image processing, scientific computing, numerical simulation, biomedicine, social network and so on, enormous quantities of data need to be crunched in order to get the valuable parts and discard redundant ones. For those data represented as two-dimensional digital matrix, two alternative schemes by scanning the elements of the matrix in zigzag route have been proposed. Fixed-point mode and navigation mode used in the proposed schemes are introduced. Performance comparison between the two schemes and previous works are analyzed. The experimental results show that our proposed schemes perform well with large scales of matrices. Moreover, the design of parallel programming based on our proposed scheme has been given. Finally, we have discussed the efficiency of parallelization. The speedup we get is from 3.413 to 3.996, which is stably growth with the scales of matrices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Messaoudi, A., et al.: DCT-based color image compression algorithm using adaptive block scanning. SIViP 13(9), 1441–1449 (2019)
Zeng, P., Zhang, X.: Classified detection algorithm of zero-quantized DCT coefficient for H.264/AVC. J. Jiangxi Univ. Sci. Technol. 37(1), 87–94 (2016)
Dolati, N., Beheshti, S.A.A., Azagegan, H.: A selective encryption for H.264/AVC videos based on scrambling. Multimed. Tools Appl. 80, 2319–2338 (2021)
Hassan, E., George, L., Mohammed, F.: Color image compression based on DCT, differential pulse coding modulation, and adaptive shift coding. J. Theor. Appl. Inf. Technol. 96(11), 3160–3171 (2018)
Salman, N.H., Rafea, S.: The arithmetic coding and hybrid discrete wavelet and cosine transform approaches in image compression. J. Southwest Jiaotong Univ. 55(1), 1–9 (2020)
Yousif, R.I., Salman, N.H.: Image compression based on arithmetic coding algorithm. Iraqi J. Sci. 62(1), 329–334 (2021)
Xue, J., et al.: 3D DCT based image compression method for the medical endoscopic application. Sensors 21(5), 1817 (2021)
Li, S.S., Zhao, L., Yang, N.: Medical image encryption based on 2D zigzag confusion and dynamic diffusion. Secur. Commun. Netw. 7, 1–23 (2021)
Qayyum, A., et al.: Chaos-based confusion and diffusion of image pixels using dynamic substitution. IEEE Access 8, 140876–140895 (2020)
Ramasamy, P., et al.: An image encryption scheme based on block scrambling, modified zigzag transformation and key generation using enhanced logistic-tent map. Entropy 21(7), 1–17 (2019)
Wei, C.C., Boon, C.N., Ahmad, N.S., et al.: Modeling and simulation for transient thermal analyses using a voltage-in-current latency insertion method. J. Electron. Sci. Technol. 4, 383–395 (2022)
Partohaghighi, M., et al.: Numerical simulation of the fractional diffusion equation. Int. J. Mod. Phys. B 37(10), 2350097 (2022)
Win, A.N., Li, M.M.: Numerical method based on fiber bundle for solving Lyapunov matrix equation. Math. Comput. Simul. 193, 556–566 (2022)
Su, J., Zhai, A.P., Zhao, W.J., et al.: Hadamard single-pixel imaging using adaptive oblique zigzag sampling. Acta Photonica Sinica 50(3), 0311003 (2021)
Guo, Y., Wang, C.: Improved Zigzag traversal and Lorenz chaotic construction of hash. Opt. Precis. Eng. 29(2), 411–419 (2021)
Wen, H.P.: Cracking a color image encryption scheme based on Zigzag transformation and chaos. Comput. Appl. Softw. 36(10), 323–333 (2019)
CSDN, https://blog.csdn.net/Shenpibaipao/article/details/78877294. Last accessed 20 Mar 2023
Wang, X., Chen, X.: An image encryption algorithm based on dynamic row scrambling and Zigzag transformation. Chaos, Solitons and Fractals 147(C), 1–22 (2021)
Milosavljevic, N., Morozov, D., Skraba, P.: Zigzag Persistent Homology in Matrix Multiplication Time. In: Proceedings of the 27th annual symposium on computational geometry (SoGC’11), pp. 216–225. ACM, New York, NY (2011)
Zheng, J., et al.: ZM-CTC: covert timing channel construction method based on zigzag matrix. Comput. Commun. 182(15), 212–222 (2022)
Rakotomalala, M., Rakotondraina, T.E., Rakotodramanana, S.: Contribution for improvement of image scrambling technique based on zigzag matrix reodering. Int. J. Comput. Trends Technol. 61(1), 10–17 (2018)
Thefreedictionary, Raster Scan. https://encyclopedia.thefreedictionary.com/raster+scan. Last accessed 20 Mar 2023
Kinoshita, J., et al.: Nonuniformity measurement of image resolution under effect of color speckle for raster-scan RGB laser mobile projector. IEICE Trans. Electr. E105/C(2), 86–94 (2022)
Rashmi, P., Supriya, M.C.: Optimized Chaotic encrypted image based on continuous raster scan method. Global Transitions Proc. 2(2), 589–593 (2021)
Chai, X., Wu, H., Gan, Z., et al.: An efficient visually meaningful image compression and encryption scheme based on compressive sensing and dynamic LSB embedding. Opt. Lasers Eng. 124(1), 105837 (2020)
Wang, H., Xiao, D., Li, M., et al.: A visually secure image encryption scheme based on parallel compressive sensing. Signal Process. 155, 218–232 (2019)
Cui, T., et al.: An efficient zigzag scanning and entropy coding architecture design. In: Huet, B., Ngo, C.-W., Tang, J., Zhou, Z.-H., Hauptmann, A.G., Yan, S. (eds.) PCM 2013. LNCS, vol. 8294, pp. 350–358. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03731-8_33
Ding, J.-J., Lin, P., Chen, H.: Generalized zigzag scanning algorithm for non-square blocks. In: Lee, K.-T., Tsai, W.-H., Mark Liao, H.-Y., Chen, T., Hsieh, J.-W., Tseng, C.-C. (eds.) MMM 2011. LNCS, vol. 6524, pp. 252–262. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-17829-0_24
Thefreedictionary, parallel processing. https://www.thefreedictionary.com/parallel+processing. Last accessed 20 Mar 2023
Sur, S., Koop, M., Panda, D.: High-performance and scalable mpi over infiniband with reduced memory usage: an in-depth performance analysis. In: Proceedings of the 2006 ACM/IEEE Conference on Supercomputing, pp. 105–117. ACM, New York, NY (2006)
Thefreedictionary, OpenMP. https://encyclopedia.thefreedictionary.com/OpenMP. Last accessed 20 Mar 2023
Openmp.org, OpenMP Compilers & Tools. https://www.openmp.org/resources/openmp-compilers-tools/. Last accessed 20 Mar 2023
An, D., et al.: A novel fast DCT coefficient scan architecture. In: Proceedings of the 27th Conference on Picture Coding Symposium, pp. 273–276. ACM, New York, NY (2009)
Gu, T.: Compression algorithm for electric field data based on two-dimensional lifting wavelet-discrete cosine transform. Comput. Eng. Des. 41(6), 1652–1657 (2020)
Ramanjaneyulu, K., et al.: Robust and oblivious watermarking based on swapping of DCT coefficients. Int. J. Appl. Innov. Eng. Manag. 2(7), 445–452 (2013)
Kong, F., et al.: Learning whole heart mesh generation from patient images for computational simulations. IEEE Trans. Med. Imaging 42(2), 533–545 (2022)
Acknowledgments
This work is supported financially by the National Natural Science Foundation of China (NSFC) under grant 61471306 and 61672438. The Natural Science Foundation of Sichuan Province under grant 2022NSFSC0548 and 2023NSFSC 1966, Smart Education Research Fund of Southwest University of Science and Technology under grant 22ZHJYZD02 and 22SXB004, the Education and Teaching Research Project of Sichuan Provincial Education Department under grant JG2021-1414, and the Key R&D Projects of Sichuan Province under grant 2020YFS0360.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Li, L. et al. (2023). The Optimization and Parallelization of Two-Dimensional Zigzag Scanning on the Matrix. In: Iliadis, L., Papaleonidas, A., Angelov, P., Jayne, C. (eds) Artificial Neural Networks and Machine Learning – ICANN 2023. ICANN 2023. Lecture Notes in Computer Science, vol 14257. Springer, Cham. https://doi.org/10.1007/978-3-031-44216-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-031-44216-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-44215-5
Online ISBN: 978-3-031-44216-2
eBook Packages: Computer ScienceComputer Science (R0)