双变量Box样条小波在图像处理中的应用

APPLICATION OF BIVARIATE BOX SPLINE WAVELETS IN IMAGE PROCESSING

将单变量样条扩展到双变量 Box样条 ,并给出 Box样条在图像处理中极为有用的几条性质 .然后 ,提出了一个使用一类双变量 Box样条来计算滤波器库的方法 ,这样得到的滤波器库在 4频带分析 /综合框架中具有完全重构的性质 ,可用来十分有效地分解合成图像 .最后 ,给出应用此方法的一个实例 .

In this paper, univariate splines are extended to bivariate Box splines, and some properties of Box splines are given, which are valuable in image processing. Then a method of computing filter bank is presented by using a particular class of bivariate Box splines. This filter bank is a perfectly reconstructing one in the four band analysis/synthesis scheme. It can be used to decompose and reconstruct images efficiently. Finally, an example is given to demonstrate this method.