The Hough-Based Multibeamlet Transform

There are plenty of geometrical multiresolution transforms devoted to efficient edge representation. However, they have two drawbacks. The first one is that such transforms represent mono edge models. And the second one is that they are often based on approximations which are optimal according to the Mean Square Error what does not necessarily lead to optimal edge approximation. In this paper the multibeamlet transform based on the Hough transform is proposed. This transform is defined to properly detect multiedges present in images. Next, the method of image approximation with the use of the multibeamlet transform is described. Additionally, the modified bottom-up tree pruning algorithm is presented in order to properly approximate images with the use of multibeamlets. As follows from the performed experiments, this approach leads to image approximations with better quality than the state-of-the-art geometrical multiresolution transforms.