Application of SGRBF for Level-Set Based Image Segmentation

In this study, the radial basis functions based SG algorithm (SGRBF) is applied for evolution of level sets in image segmentation. The implementation of level set method in image processing often involves solving partial differential equations (PDEs). Finite differences implicit scheme is a prevalent method to solve PDE for extending the evolution of level sets. Instead of using finite differences method, SGRBF is used in our study for evolving level sets. The SGRBF is a mathematical framework developed for function approximation using Gaussian RBFs. In SGRBF, the number and centers of the basis functions are determined in a systematic and mathematically sound way using a purely algebraic approach. The numerical results show that, except for a continuous representation of both the implicit function and its level sets, the algorithm we introduce here can reduce the computation cost by selecting the most contributive centers for radial basis functions.