Model of Brightness Perception: Understanding Hermann Grid Illusion with Turing Scenario

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In this research work we proposed an algorithm which converts a gray level image into a binary one. The algorithm utilizes a Schnakenberg type reaction-diffusion equation with activator and inhibitor distributions under a Turing condition; a periodic spatial pattern is self-organized in the reaction-diffusion equation under the Turing condition. We numerically confirmed that the spatial wave length of the self-organized periodic pattern depends on a parameter value of the equation. Thus, by modulating the parameter value with the gray level of an input image, we converted the image into a binary image. By applying the proposed algorithm to several real images, we confirmed that the algorithm successfully produces binary images which are perceptually equivalent to their input images. We also confirmed the convergence of the algorithm.