On the Introduction of Nonlinear Dynamics in Image Processing with Applications

摘要

We apply the concept of nonlinear dynamics to perform specific image processing tasks (e. g., enhancement, edge detection, de-noising, conversion to binary image, chaotic encryption, etc.). A class of oscillators is considered each of which is modeled by nonlinear differential equations. Based on these equations the nonlinear dynamical behavior of the oscillators is investigated. This investigation leads to the depiction/discovery of three main states of the oscillators namely, equilibrium, stationary, and chaotic states. The occurrence of these states is predicted and controlled through a bifurcation analysis. Using the bifurcation analysis, ranges/windows of parameters are derived under which each specific oscillator can exhibit the aforementioned states. In each state of the oscillators the image processing is carried out and the output images are obtained as results of processing. Comparing output- with input-images reveals the basic processing tasks performed (e. g., enhancement, edge detection, denoising, conversion to binary image, chaotic encryption, etc.).