Application of the Monogenic Image Analysis

Virginie Uhlmann

Semester Project

Life Science, EPFL

January 2010

Abstract

The aim of this semester project was to find some applications of the multiresolution monogenic signal analysis. The monogenic signal is a 3 component signal composed of the wavelet transform of an original image as well as the real and imaginary part of the Riesz transform of the wavelet transform of the latter original image. This analysis was refined by using isotropic wavelets (Shannon and Simoncelli wavelets) instead of the initial polyharmonic wavelets. These two wavelets have the advantage of being truly isotropic, and they allow for an easy reconstruction of the image. We first implemented Shannon and Simoncelli wavelet decomposition and reconstruction, and then we included them in an existing plugin called MonogenicJ that implements the whole analysis as initially proposed.
The monogenic signal can be used to compute rotation invariant features (the monogenic modulus, phase and instantaneous frequency) describing the image. We combined the information given by these features to process the monogenic signal in different ways, yielding four different "applied" plugins. A first plugin is able to demodulate an image, another performs a "directional smoothing" of the image (i.e. simplifying the overall image but keeping the most oriented structures intact), a third allows a specific processing of the frequencies contained in the image (by keeping or removing frequencies lying in a given range), and the last one gives an insight of what could be done in the field of keypoints detection using the monogenic signal. Examples of two of these possible applications are shown in Fig. 1 and 2.

Fig. 1: Specific frequency selection (middle) and removal (left) on the Barbara image using the Monogenic wavenumber (instantaneous frequency).

Fig. 2: Directional Smoothing of collagen fibers using the Monogenic features (source: Rana Rezakhaniha, Laboratory of Hemodynamics and Cardiovascular Technology, Institute of Bioengineering, EPFL, Lausanne, Switzerland.)