Image Denoising Algorithm with a Three-dimensional Grid System of Coupled Nonlinear Elements

Atsushi Nomura, Yoshiki Mizukami, Koichi Okada

2014

Abstract

This paper presents an image denoising algorithm with a three-dimensional grid system of coupled nonlinear elements. The system consists of a two-dimensional image grid and a one-dimensional grid representing a quantized image brightness. At each grid point, a FitzHugh-Nagumo type nonlinear element is placed and coupled with other elements placed at its nearest neighboring grid points. The FitzHugh-Nagumo element is described with a set of time-evolving ordinary differential equations, and is tuned to be excitable. When we externally stimulate the grid system with an image brightness distribution, we could observe that noise in the distribution was reduced and signal was strengthened as time proceeds. Thus, the image denoising algorithm utilizes this property of the grid system, in which we propose to modify external stimuli so as to have broad Gaussian distributions. We confirm performance of the algorithm on artificial and real images in comparison with two classical algorithms of a diffusion equation and median filtering.

References

  1. Buades, A., Coll, B., and Morel, J. M. (2010). Image denoising methods. A new nonlocal principle. SIAM Review, 52:113-147.
  2. Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K. (2007). Image denoising by sparse 3-d transformdomain collaborative filtering. IEEE Transactions on Image Processing, 16:2080-2095.
  3. Eng, H.-L. and Ma, K.-K. (2001). Noise adaptive softswitching median filter. IEEE Transactions on Image Processing, 10:242-251.
  4. FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1:445-466.
  5. Gonzalez, R. C. and Woods, R. E. (1992). Digital Image Processing. Addison-Wesley, New York, USA.
  6. Guo, Z., Liu, Q., Sun, J., and Wu, B. (2011). Reactiondiffusion systems with p(x)-growth for image denoising. Nonlinear Analysis: Real World Applications, 12:2904-2918.
  7. Heath, M., Sarkar, S., Sanocki, T., and Bowyer, K. (confirmed on June 1st, 2014). Edge detector comparison. Available from: http://marathon.csee.usf.edu/edge/edge detection.html.
  8. Katkovnik, V., Foi, A., Egiazarian, K., and Astola, J. (2010). From local kernel to nonlocal multiple-model image denoising. International Journal of Computer Vision, 86:1-32.
  9. Koenderink, J. J. (1984). The structure of images. Biological Cybernetics, 50:363-370.
  10. Mrázek, P. and Navara, M. (2003). Selection of optimal stopping time for nonlinear diffusion filtering. International Journal of Computer Vision, 52:189-203.
  11. Murray, J. D. (1989). Mathematical Biology. SpringerVerlag, Berlin, Germany.
  12. Nagumo, J., Arimoto, S., and Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50:2061-2070.
  13. Nomura, A., Ichikawa, M., Okada, K., Miike, H., and Sakurai, T. (2011). Edge detection algorithm inspired by pattern formation processes of reaction-diffusion systems. International Journal of Circuits, Systems and Signal Processing, 5:105-115.
  14. Nomura, A., Okada, K., Mizukami, Y., Miike, H., Ichikawa, M., and Sakurai, T. (2012). Subpixel stereo disparity for surface reconstruction by utilising a threedimensional reaction-diffusion system. In Proceedings of the 27th Image and Vision Computing New Zealand Conference, pages 144-149, Dunedin, New Zealand.
  15. Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:629-639.
  16. Tomasi, C. and Manduchi, R. (1998). Bilateral filtering for gray and color images. In Proceedings of the 1998 IEEE International Conference on Computer Vision, pages 839-846, Bombay, India.
Download


Paper Citation


in Harvard Style

Nomura A., Mizukami Y. and Okada K. (2014). Image Denoising Algorithm with a Three-dimensional Grid System of Coupled Nonlinear Elements . In Proceedings of the 11th International Conference on Signal Processing and Multimedia Applications - Volume 1: SIGMAP, (ICETE 2014) ISBN 978-989-758-046-8, pages 220-225. DOI: 10.5220/0005119302200225


in Bibtex Style

@conference{sigmap14,
author={Atsushi Nomura and Yoshiki Mizukami and Koichi Okada},
title={Image Denoising Algorithm with a Three-dimensional Grid System of Coupled Nonlinear Elements},
booktitle={Proceedings of the 11th International Conference on Signal Processing and Multimedia Applications - Volume 1: SIGMAP, (ICETE 2014)},
year={2014},
pages={220-225},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005119302200225},
isbn={978-989-758-046-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th International Conference on Signal Processing and Multimedia Applications - Volume 1: SIGMAP, (ICETE 2014)
TI - Image Denoising Algorithm with a Three-dimensional Grid System of Coupled Nonlinear Elements
SN - 978-989-758-046-8
AU - Nomura A.
AU - Mizukami Y.
AU - Okada K.
PY - 2014
SP - 220
EP - 225
DO - 10.5220/0005119302200225