图像局部弹性变换中径向基函数紧支撑集的选取

Compact Support Analysis of Radial Basis Function in Image Local Elastic Transformation

弹性图像配准中常常需要采用紧支撑的径向基函数来实现局部弹性变换,径向基函数的支撑集大小决定了图像局部扭曲的范围,而如何选取基函数的支撑集大小是一个一直没有解决的问题。该文利用弹性变换模型,针对Wendland基函数,从理论上分析了双标志点空间位置与基函数支撑集的关系,并对任意标志点集合通过构造Delaunay三角剖分来确定基函数支撑集大小,文中给出了径向基函数支撑集的选取原则。人工网格图像和医学图像的局部弹性变换实验验证了该文的结论。

In image local elastic transformation, compact support radial basis functions are used to implement local elastic deformation transformation. The elastic deformation area is related to the support of radial basis function. However, how to choose the support size of the radial basis function based on space distribution of landmarks still is an unresolved doubt. In this paper, choosing the support of Wendland basis functions based on the space distribution of two landmarks is analyzed in detail. For the landmarks set, Delaunay triangle is constructed to obtain the optimal distance between landmarks, and support is chosen correspondingly. The principle of choosing the support size of radial basis functions in image local elastic transformation is given also. Experiments of the artificial images and medial images show the feasibility of this conclusion.