The Generation Of Diffusion Curve With The Control Of Diffusion Coefficients

Diffusion curve is a new method of image vectorization, which holds the advantages of both the bitmap and vector graph. That is, it not only remains the rich color, like the bitmap, but also is easy to modify, store, and able to zoom without any distortion, similar as the vector graph.This paper focuses on the diffusion phase of diffusion curve, and studies how the diffusion equation with diffusion coefficients affects the richness of the diffusion image. We concentrate on how to generate the diffusion coefficients of a given image and how to use them.Calculating the diffusion coefficients of a diffusion image is an inverse problem.In this problem, a diffusion image is input and the diffusion coefficients of the diffusion equation are calculated according to this input image. This problem can be classified into the parameter identification problem which knows the source positions and diffusion results, and calculates the diffusion coefficients. In our implementation, a B-spline function is employed to fit the unknown parameters. And the inverse problem is solved by minimizing a target function with regularization.To study the diffusion coefficient’s effect on the diffusion image, we adopt a diffusion equation with diffusion coefficients. Then several kinds of diffusion coefficients are developed to control the diffusion results, and the relationship between the coefficients and the diffusion results is analyzed. Moreover, some beautiful images generated from diffusion equation with different kinds of diffusion coefficients are demonstrated in this paper, which shows that diffusion coefficients can lead to richer pictures.