The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

The “Marr wavelet pyramid” is a wavelet decomposition that implements a multiscale version of the complex gradient-Laplace operator. It is closely linked to a multiresolution analysis of $L _{ 2 }$ $(\mathbb{R} ^{ 2 }$ ) and it has a fast filterbank implementation. We show how the Marr wavelets, which are essentially steerable, can be used to extract a multiscale version of the structure tensor. This yields a multiscale characterization of an image in terms of various features such as local gradient energy, orientation, and coherency. We provide an implementation of the proposed system as a Java plug-in for ImageJ, and we illustrate its applicability to directional image analysis which is useful in domains such as biological imaging and material science.