APPROXIMATION OF AN ARBITRARY FILTER AND ITS RECURSIVE IMPLEMENTATION

Filtering is one of the important techniques in computer vision. It ha s been widely used in edge detection, image restoration, range image s egmentation, etc. However, the efficient implementation of an arbitrar y filter has been a challenging problem until now. In this paper, a no vel method is proposed to implement an arbitrary filter. Firstly, an e fficient recursive structure is proposed to implement any (polynomial) x (exponential)-type (PET) filter. The computational complexity and s tructure are independent of its filter mask size or its bandwidth. Sec ondly, a new method is proposed-Lagurre spectrum decomposition method- to obtain the PET approximation of any filters. As an example, the abo ve method is applied to the approximation and implementation of Gaussi an filters and experiments have shown that a perfect approximation can be obtained with only third-order Lagurre bases, and therefore only a fourth-order recursive filter is needed to implement Gaussian filters . Finally, the comparison of the present method with the known ones sh ows that (1) Lagurre polynomial bases are orthogonal with each other, so the filter approximation is simple, (2) the bases are complete and the completeness guarantees the approximation error can be reduced to zero, (3) the method can be used to design both Gaussian and any other filters.