Nonuniform mesh generation for images via moving mesh equation

An efficient nonuniform mesh generation method is proposed based on the information provided by digital images. In our scheme, the mesh nodes are continuously moved according to an elliptic partial differential equation, namely, the moving mesh equation, where a monitor function ω is responsible for controlling the density of mesh nodes. A general form for ω is suggested based on the gradient and the grey values of the images, and the Monte Carlo Method is utilized to evaluate ω efficiently. The moving mesh equation can be solved with several steps Gauss-Sediel iterations. Numerical experiments on various images illustrate the effectiveness of the proposed method.