The role of relaxation oscillator models in application fields such as modeling dynamic systems and image analysis is discussed. A short review of the Van der Pol, Wilson-Cowan and Terman-Wang relaxation oscillators is given. The key property of such nonlinear oscillators, i.e., the oscillator phase shift (called the Phase Response Curve) as a result of external pulse stimuli is indicated as a fundamental mechanism to achieve and sustain synchrony in networks of coupled oscillators. It is noted that networks of such oscillators resemble a variety of naturally occurring phenomena (e.g., in electrophysiology) and dynamics arising in engineering systems. Two types of oscillator networks exhibiting synchronous behaviors are discussed. The network of oscillators connected in series for modeling a cardiac conduction system is used to explain causes of important cardiac abnormal rhythms. Finally, it is shown that a 2D network of coupled oscillators is an effective tool for segmenting image textures in biomedical images.
@article{bwmeta1.element.bwnjournal-article-amcv16i4p513bwm,
author = {Strumi\l \l o, Pawe\l\ and Strzelecki, Micha\l },
title = {Application of coupled neural oscillators for image texture segmentation and modeling of biological rhythms},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {16},
year = {2006},
pages = {513-523},
zbl = {1112.92038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv16i4p513bwm}
}
Strumiłło, Paweł; Strzelecki, Michał. Application of coupled neural oscillators for image texture segmentation and modeling of biological rhythms. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) pp. 513-523. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv16i4p513bwm/
[000] Cesmeli E. and Wang D. (2001): Texture segmentation using Gaussian-Markov random fields and neural oscillator networks. - IEEE Trans. Neural Netw., Vol. 12, No. 3, pp. 394-404.
[001] Eckhorn R., Bauer R., Jordan W., Brosch M., Kruse W., Munk M. and Retbock H.J. (1988): Coherent oscillations: A mechanism of feature linking in the visual cortex? - Biol. Cybern., Vol. 60, No. 2, pp. 265-280.
[002] Freeman W.J. (1978): Spatial properties of an EEG event in the olfactory bulb and cortex. - Electroenceph. Clin. Neurophysiol., Vol. 44,No. 5, pp. 586-605.
[003] Glass L. and Mackey M.C. (1990): From Clocks to Chaos: The Rhythms of Life. - New York: Princeton University Press. | Zbl 0705.92004
[004] Guevara M., Shrier A. and Glass L. (1990): Chaotic and complex cardiac rhythms, In: Cardiac Electrophysiology: From Cell to Bedside, (Zipes D.D. and Jalife J., Eds.). - Philadelphia: W.B. Saunders Company, pp. 192-200.
[005] Hu Y.H. and Hwang J.-N. (2001): Handbook of Neural Network Signal Processing. - Boca Raton, FL: CRC Press.
[006] Jain A.K., Duin R.P.W. and Mao J. (2000): Statistical pattern recognition: A review. - IEEE Trans. Pattern Anal. Mach. Intell., Vol. 22, No. 1, pp. 4-37.
[007] Konig P. and Schillen T.B. (1991): Stimulus-dependent assembly formation of oscillatory responses: I. Synchronization. - Neural Comput., Vol. 3,No. 2, pp. 155-166.
[008] Korbicz J., Koscielny J.M., Kowalczuk Z. and Cholewa W. (2004): Fault Diagnosis: Models, Artificial Intelligence, Applications. - Berlin: Springer-Verlag. | Zbl 1074.93004
[009] Kowalski J. and Strzelecki M. (2005): CMOS VLSI chip for segmentation of binary images. - Proc. IEEE Workshop Signal Processing, Poznań, Poland, pp. 251-256.
[010] Linsay P. and Wang D. (1998): Fast numerical integration of relaxation oscillator networks based on singular limit solutions. - IEEE Trans. Neural Netw., Vol. 9, No. 3, pp. 523-532.
[011] Materka A. (2002): MaZda User's Manual. - Availablelinebreak at: http://www.eletel.p.lodz.pl/cost/progr_mazda_eng.html
[012] Michalewicz Z. (1996): Genetic Algorithms + Data Structures = Evolution Programs. - Berlin: Springer. | Zbl 0841.68047
[013] Mucciardi A. and Gose E. (1971): A comparison of seven techniques for choosing subsets of patter recognition properties. - IEEE Trans. Comput., Vol. C-20, No. 9, pp. 1023-1031. | Zbl 0222.68044
[014] Narenda K.S. and Parthasarathy K. (1990): Identification and control of dynamical systems using neural networks. - IEEE Trans. Neural Netw., Vol. 1,No. 1, pp. 4-27.
[015] Rutkowski L. (2004): Flexible Neuro-Fuzzy Systems. - Boston: Kluwer. | Zbl 1080.93014
[016] Shareef N., Wang D. and Yagel R. (1999): Segmentation of medical images using LEGION. - IEEE Trans. Med. Imag., Vol. 18, No. 1, pp. 74-91.
[017] Somers D. and Kopell N. (1993): Rapid synchrony through fast threshold modulation. - Biol. Cybern., Vol. 68, No. 5, pp. 393-407.
[018] Strumiłło P. (1993) Neurodynamic Modelling of the Human Heartbeat. - Ph.D.Thesis, Univ. Strathcyle, UK.
[019] Strumiłło P. and Durrani T.S. (1991): Simulations of cardiac arrhythmias based on dynamical interactions between neural models of cardiac pacemakers. - Proc. 2nd Int. Conf. Artificial Neural Networks, Bornemouth, UK, pp. 195-199.
[020] Strumiłło P. and Durrani T.S. (1996): Spiral waves in a 2-D model of fibrillating heart and a new way to break them. - Med. Science Mon., Vol. 2,No. 4, pp. 495-504.
[021] Strzelecki M. (2002): Segmentation of MRI trabecular-bone images using network of synchronised oscillators. - Mach. Graph. Vis., Vol. 11, No. 1, pp. 77-100.
[022] Strzelecki M. (2004a): Segmentation of image texture using network of synchronised oscillators and statistical methods. - Sci. Lett., No. 946, Technical University of Łódź, (in Polish).
[023] Strzelecki M. (2004b): Texture boundary detection using network of synchronized oscillators. - Electron. Lett., Vol. 40, No. 8, pp. 466-467.
[024] Strzelecki M., Materka A., Drozdz J., Krzemińska-Pakula M. and Kasprzak J.D. (2006): Classification and segmentation of intracardiac masses in cardiac tumour echocardiograms. - Comp. Med. Imag. Graph., (in print).
[025] Tadeusiewicz R. (1993): Neural Networks. - Warsaw: Akademicka Oficyna Wydawnicza, (in Polish).
[026] Terman D. and Wang D.L. (1995): Global competition and local cooperation in network of neural oscillators. - Phys. D, Vol. 81,Nos. 1-2, pp. 148-176. | Zbl 0882.68153
[027] Van der Pol B. and Van der Mark J. (1928): The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. - London, Edinburgh, and Dublin Philosoph. Mag., and J. Sci., Ser. 7, Vol. 6, pp. 763-775.
[028] Von der Malsburg C. and Schneider W. (1986): A neural cocktail-party processor. -Biol. Cybern., Vol. 54, pp. 29-40.
[029] Wang D. (1995): Emergent Synchrony in Locally Coupled Neural Oscillators. - IEEE Trans. Neural Netw., Vol. 4, No. 6, pp. 941-948.
[030] Wang D. (2005): The time dimension for scene analysis. - IEEE Trans. Neural Netw., Vol. 16, No. 6, pp. 1401-1426.
[031] Wilson H.R. and Cowan J.D. (1972): Excitatory and inhibitory interactions in localized populations of model neurons. - Biophys. J., Vol. 12,No. 1, pp. 1-24.
[032] Winfree A.T. (1967): Biological rhythms and the behaviour of populations of coupled oscillators. - J. Theoret. Biol., Vol. 16,No. 1, pp. 15-42.