基于紧支径向基函数内插的图像修复算法

该文提出一种基于紧支径向基函数插值的图像修复算法，该算法将图像看成残缺的三维散乱点集，将图像修复问题转化为三维数据的曲面重建问题。采用径向基函数曲面重建的方法构造出逼近三维点集的隐函数曲面，实现对残缺部分的插值，并对重构曲面采样得到残缺部分的像素值。紧支径向基函数可使求解权系数的线性系统的系数矩阵具有稀疏带状结构，从而降低算法的复杂度。实验结果表明，该算法是一种实用对图像修复算法，可得到良好的修复效果。

Novel Image Inpainting Algorithm Based on CSRBF Interpolation

A novel algorithm for image inpainting based on Compactly Supported Radial Basis Functions(CSRBF) interpolation is proposed. The algorithm looks an image as an incomplete 3D points set. The 2D image inpainting problem is converted into implicit surface reconstruction problem from 3D points set. To construct the implicit surface for approximating the points set by using Radial Basis Functions(RBF) can interpolate the points in absent portion, and then resample from the constructed surface can calculate the pixels' value of damaged or removed portion on the image. Using CSRBF, the matrix of corresponding system of the linear algebraic equations is spare and bounded. So it can decrease the complexity of RBF algorithm. A number of examples on image inpainting demonstrates that the algorithm is an practical one and using the algorithm can obtain good results.