Abstract: A numerical algorithm based on globally supported and positive definite radial basis functions is developed in this paper to solve evolution equations which arise in image segmentation using partial differential equation based level set methods. In this algorithm, radial basis functions are used to interpolate level set functions with a high level of precision and smoothness, and then the nonlinear evolution equation is cast into ordinary differential equations and Euler’s scheme is used. Compared with conventional level set methods, this algorithm is free from the initial contour, and completely eliminates the need of the complex and costly re-initialization procedure. Experimental results indicate that the presented algorithm is free of re-initialization, and can segment images quickly even without any initial contour.

Key words: image segmentation, radial basis function, partial differential equation, evolution equation, level set

摘要： 将全局正定径向基函数和图像分割中基于偏微分方程水平集方法的发展方程相结合，提出了一种基于全局正定径向基函数的图像分割算法。用全局正定径向基函数插值发展方程中的水平集函数，得到的插值函数具有较高的精度和光滑性，克服了传统水平集方法中复杂费时的重新初始化过程和水平集对初始轮廓位置敏感等缺点，非线性发展方程最终被转化成常微分方程组并用Euler法求解。实验结果表明该算法不需要重新初始化过程，并且在没有初始轮廓时也能够快速正确地分割图像。

关键词: 图像分割, 径向基函数, 偏微分方程, 发展方程, 水平集