Moments-Based Fast Wedgelet Transform

Abstract

In the paper the moments-based fast wedgelet transform has been presented. In order to perform the classical wedgelet transform one searches the whole wedgelets’ dictionary to find the best matching. Whereas in the proposed method the parameters of wedgelet are computed directly from an image basing on moments computation. Such parameters describe wedgelet reflecting the edge present in the image. However, such wedgelet is not necessarily the best one in the meaning of Mean Square Error. So, to overcome that drawback, the method which improves the matching result has also been proposed. It works in the way that the better matching one needs to obtain the longer time it takes. The proposed transform works in linear time with respect to the number of pixels of the full quadtree decomposition of an image. More precisely, for an image of size N ×N pixels the time complexity of the proposed wedgelet transform is O(N2 log2 N).