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

在这项研究工作中，我们提出了一种将灰度图像转换为二值化图像的算法。该算法利用图灵条件下具有激活剂和抑制剂分布的Schnakenberg型反应扩散方程；在图灵条件下，反应扩散方程中的周期空间模式是自组织的。我们数值地证实了自组织周期图案的空间波长依赖于方程的参数值。因此，通过将参数值与输入图像的灰度级进行调制，我们将图像转换为二值图像。通过将该算法应用于几幅真实图像，我们证实了该算法成功地生成了与其输入图像在视觉上等价的二值图像。同时也证实了该算法的收敛特性。

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.