IJMNTA  Vol.5 No.2 , June 2016
Discrete-Time Dynamic Image Segmentation Using Oscillators with Adaptive Coupling
Abstract: In this study, we propose a novel discrete-time coupled model to generate oscillatory responses via periodic points with a high periodic order. Our coupled system comprises one-dimensional oscillators based on the Rulkov map and a single globally coupled oscillator. Because the waveform of a one-dimensional oscillator has sharply defined peaks, the coupled system can be applied to dynamic image segmentation. Our proposed system iteratively transforms the coupling of each oscillator based on an input value that corresponds to the pixel value of an input image. This approach enables our system to segment image regions in which pixel values gradually change with respect to a connected region. We conducted a bifurcation analysis of a single oscillator and a three-coupled model. Through simulations, we demonstrated that our system works well for gray-level images with three isolated image regions.
Cite this paper: Kobayashi, M. and Yoshinaga, T. (2016) Discrete-Time Dynamic Image Segmentation Using Oscillators with Adaptive Coupling. International Journal of Modern Nonlinear Theory and Application, 5, 93-103. doi: 10.4236/ijmnta.2016.52010.

[1]   Mesejo, P., et al. (2016) A Survey on Image Segmentation Using Metaheuristic-Based Deformable Models: State of the Art and Critical Analysis. Applied Soft Computing, 44, 1-29.

[2]   Pal, N.R. and Pal, S.K. (1993) A Review on Image Segmentation Techniques. Pattern Recognition, 26, 1277-1294.

[3]   Ghosh, P., Mitchell, M., Tanyi, J.A. and Hung, A.Y. (2016) Incorporating Priors for Medical Image Segmentation Using a Genetic Algorithm. Original Research Article Neurocomputing, 195, 181-194.

[4]   Terman, D. and Wang, D.L. (1995) Global Competition and Local Cooperation in a Network of Neural Oscillatros. Physica D, 81, 148-176.

[5]   Wang, D.L. and Terman, D. (1995) Locally Excitatory Globally Inhibitory Oscillator Networks. IEEE Transactions on Neural Networks, 6, 283-286.

[6]   Liu, X. and Wang, D.L. (1999) Rnage Image Segmentation Using a LEGION Network. IEEE Transactions on Neural Networks, 10, 564-573.

[7]   Shareef, N., Wang, D.L. and Yagel, R. (1999) Segmentation of Medical Images Using LEGION. IEEE Transactions on Medical Imaging, 18, 74-94.

[8]   Zhao, L., et al. (2003) A Network of Coupled Chaotic Maps for Adaptive Multi-Scale Image Segmentation. International Journal of Neural Systems, 13, 129-137.

[9]   Fujimoto, K., Musashi, M. and Yoshinaga, T. (2008) Discrete-Time Dynamic Image Segmentation System. Electronics Letters, 44, 727-729.

[10]   Kobayashi, M., Fujimoto, K. and Yoshinaga, T. (2011) Bifurcations of Oscillatory Responses Observed in Discrete-Time Coupled Neuronal System for Dynamic Image Segmentation. Journal of Signal Processing, 15, 145-153.

[11]   Aihara, K. (1989) Chaotic Neuronal Networks. In: Kawakami, H., Ed., Bifurcation Phenomena in Nonlinear System and Theory of Dynamical System, Vol. 710, World Scientific, Singapore, 143-161.

[12]   Aihara, K., Takabe, T. and Toyoda, M. (1990) Chaotic Neural Networks. Physics Letters A, 144, 333-340.

[13]   Rulkov, N.F. (2001) Regularization of Synchronized Chaotic Bursts. Physical Review Letters, 86, 183-186.

[14]   Fujimoto, K., Kobayashi, M. and Yoshinaga, T. (2011) Discrete-Time Dynamic Image Segmentation Based on Oscillations by Destabilizing a Fixed Point. IEEJ Transactions on Electrical and Electronic Engineering, 6, 468-473.

[15]   Fujimoto, K., Musashi, M. and Yoshinaga, T. (2009) Reduced Model of Discrete-Time Dynamic Image Segmentation System and Its Bifurcation Analysis. International Journal of Imaging Systems and Technology, 19, 283-289.

[16]   Musashi, M., Fujimoto, K. and Yoshinaga, T. (2009) Bifurcation Phenomena of Periodic Points with High Order of Period Observed in Discrete-Time Two-Coupled Chaotic Neurons. Journal of Signal Processing, 13, 311-314.

[17]   Kawakami, H. (1984) Bifurcation of Periodic Responses in Forced Dynamic Nonlinear Circuits: Computation of Bifurcation Values of the System Parameters. IEEE Transactions on Circuits and Systems, 31, 248-260.