Image Halftoning with Turing Patterns

Atsushi Nomura


This paper presents an image halftoning algorithm with a reaction-diffusion system in which periodic patterns called Turing patterns autonomously emerge. Image halftoning refers to conversion of a gray level image to a binary image so that the human visual system can perceive the original gray level image from the converted binary one. The reaction-diffusion system has activator and inhibitor distributions, and creates the Turing type periodic patterns in the distributions from an initial noisy distributions under the condition of long-range inhibition. Characteristics of the Turing patterns depend on a parameter of the reaction-diffusion system. Thus, by modulating the parameter distribution according to an image brightness distribution, the proposed algorithm creates Turing patterns of which characteristics distribute spatially; the human visual system can perceive distribution of the Turing patterns as the original image. Application of the proposed algorithm to a test image demonstrates its qualitative performance and convergence.


  1. Crounse, K. R., Roska, T., and Chua, L. O. (1993). Image halftoning with cellular neural networks. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 40(4):267-283.
  2. Kawasaki, J., Hayashi, A., and Iijima, T. (2002). Evaluation method of picture quality by two dimensional vissual model and verification of its theory using various modulated images. IEICE Transactions on Information and Systems, J85-D-II(2):228-241. [in Japanese].
  3. Kuhnert, L., Agladze, K. I., and Krinsky, V. I. (1989). Image processing using light-sensitive chemical waves. Nature, 337:244-247.
  4. Lau, D. L. and Arce, G. R. (2008). Modern Digital Halftoning. CRC Press, New York, USA, second edition.
  5. Schmaltz, C., Gwosdek, P., Bruhn, A., and Weickert, J. (2010). Electrostatic halftoning. Computer Graphics Forum, 29(8):2313-2327.
  6. Schnakenberg, J. (1979). Simple chemical reaction systems with limit cycle behaviour. Journal of Theoretical Biology, 81:389-400.
  7. Shoji, H., Iwasa, Y., Mochizuki, A., and Kondo, S. (2002). Directionality of stripes formed by anisotropic reaction-diffusion models. Journal of Theoretical Biology, 214:549-561.
  8. Turing, A. M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237:37-72.
  9. Wakin, M. (2003). Standard test images - Lena/Lenna.Ëśwakin/images/.
  10. Witkin, A. and Kass, M. (1991). Reaction-diffusion textures. In Proceedings of the 18th annual conference on Computer Graphics and Interative Techniques, pages 299-308, Las Vegas, US. ACM.

Paper Citation

in Harvard Style

Nomura A. (2012). Image Halftoning with Turing Patterns . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 286-289. DOI: 10.5220/0004149202860289

in Bibtex Style

author={Atsushi Nomura},
title={Image Halftoning with Turing Patterns},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)},

in EndNote Style

JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)
TI - Image Halftoning with Turing Patterns
SN - 978-989-8565-33-4
AU - Nomura A.
PY - 2012
SP - 286
EP - 289
DO - 10.5220/0004149202860289