Image Enhancement Method based on 1:1 Resonant Hopf Bifurcation in Time-Delay Neural Networks
This paper investigates the 1:1 resonant Hopf bifurcation characteristics of a class of time-delay neural network models and their application in low-light image enhancement. By analyzing the characteristic equation of the linearized system, the conditions for the asymptotic stability of the equilibrium point and the critical delay for the Hopf bifurcation are derived. It is further obtained that at the critical delay, the system undergoes a 1:1 resonant Hopf bifurcation, and the amplitude of the periodic solution grows at a rate of μ16 . Based on this amplitude amplification mechanism, a time-delay neural network image enhancement algorithm is constructed: the pixel values of the low-light image are assigned as the initial values of neuron u1 , and contrast enhancement is achieved by utilizing the periodic solution outputs of neuron u2 or u3 through the selection of appropriate delay parameters and evolution time t . Experiments were conducted using 10 real low-light images from the LIME dataset, and quantitative comparisons were made with the linear grayscale enhancement method and the gamma transformation method. The results indicate that the proposed algorithm significantly outperforms the comparison methods in terms of image mean, standard deviation, and information entropy, effectively improving image brightness, contrast, and detail richness. It performs moderately on the NIQE index, suggesting a compromise in naturalness when intensely stretching the grayscale range, yet the overall enhancement performance remains outstanding. This paper provides a new approach with a clear mathematical mechanism for image enhancement.
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