Application of radial basis functions to evolution equations arising in image segmentation

Abstract

In this paper, radial basis functions are used to obtain the solution of evolution equations which appear in variational level set method based image segmentation. In this method, radial basis functions are used to interpolate the implicit level set function of the evolution equation with a high level of accuracy and smoothness. Then, the original initial value problem is discretized into an interpolation problem. Accordingly, the evolution equation is converted into a set of coupled ordinary differential equations, and a smooth evolution can be retained. Compared with finite difference scheme based level set approaches, the complex and costly re-initialization procedure is unnecessary. Numerical examples are also given to show the efficiency of the method.

A meshless algorithm with moving least square approximations for elliptic Signorini problems

“…Besides, the MLS shape functions Φ i (𝑦 j ) used in Eqs. ( 16), ( 17), (21), and ( 23) can also be computed only once, then the matrices 𝑀 1 , 𝑀 2 , and 𝑀 3 at each iteration can be assembled easily.…”

“…Some MLS-based meshless methods, such as the element-free Galerkin method, the h-p meshless method, and the meshless local Petrov-Galerkin method have been developed and achieved remarkable success in solving a broad range of physical problems. [18][19][20][21] They are the domain type, as the FEM, in which the problem domain is discretized by nodes.…”