Biomedical Imaging Group

Wavelet-based monogenic analysis

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MONOGENIC |

Download Plugin for ImageJ [Version 21.09.2009] |

The software package MonogenicJ performs multiresolution monogenic analyses of 2D images. It extracts wavelet-domain features that characterize the local orientation, the phase and the dominant frequency of an image patch at various levels of resolution. The package is available for download as a Java plugin for ImageJ.

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Experiment: scaled values, J=5, σ=1

H: Orientation S:Coherency B:Input

MonogenicJ has the ability to compute and display Riesz and Laplace wavelet components, structure-tensor descriptors, and monogenic features in a dyadic multiresolution framework. It offers two modes of analysis:

- pyramid, in which the low resolution wavelet channels are critically sampled;
- redundant where all features maps are displayed at the same resolution as the original image.

The Riesz-Laplace wavelet analysis decomposition provides three multiscale monogenic components:

- Laplace (Quasi-isotropic wavelet analysis)
- Riesz X and Riesz Y (Riesz components of order 1)

These are used to build the tensor matrix **J** which is used to extract the following image descriptors:

- Orientation
- Coherency
- Energy

Note that the tensor matrix is computed for each wavelet cell using a local averaging scheme (Gaussian window).

The next step is the wavelet-domain monogenic analysis which is equivalent to performing a 1D analytic signal analysis along the dominant orientation. This is achieved via a steering mechanism and leads to the extraction of the following local features.

- Wavenumber (an estimate of the local dominant frequency)
- Modulus (amplitude of the analytic signal)
- Phase (phase of the the analytic signal)
- Directional Hilbert (Hilbert transform along the dominant orientation)

The complete technical details together with some examples of applications are given in the publication below.

M. Unser, D. Sage, D. Van De Ville, "Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform," IEEE Transactions on Image Processing, vol. 18, no. 11, pp. 2402-2418, November 2009.

Free and easy-to-use software

The software is a plugin for ImageJ, a general purpose image-processing package. ImageJ has a public domain licence; it runs on several plateforms: Unix, Linux, Windows, Mac OSX.

Quick installation

- Get a copy of ImageJ
- Download the file MonogenicJ_.jar [Version 21.09.2009] and put it into the "plugins" folder of ImageJ. Restart ImageJ

The whole process should not take more than a couple of minutes.

How to perform the monogenic analysis of an image

- Open the input to analyze (only grayscale image).
- Launch the plugin MonogenicJ.
- Choose the type of the wavelet transformation: dyadic pyramid or full redundant
- Select the number of scale J (the width and the height should be a multiple of 2^
^{J}). - Choose the size of the weighted window of the structure tensor. It is a Gaussian window defined by its standard deviation σ.
- Click on Run.

Display of the features

- Select the type the features to display or click on the corresponding Show button.
- True values: shows the computed values, in 32-float format.
- Scaled values: shows the a rescale [0..255] version of the computed values in each sub-bands.
- Stacked presentation: shows the sub-bands as stack of images.
- Horizontal Flatten: maps horizontally the sub-bands in one image.
- Vertical Flatten: maps vertically the sub-bands in one image.
- Color Map: nice way to shows several features at once by assigning at most three features in color channels. MonogenicJ has a HSB color representation, the hue (H) is often used to display angle (Orientation). Any computed feature map (in addition to the input image and a constant) can be assigned in the hue (H), saturation (S), or brigthness (B) channels.
- Click on Run.

Screenshot

- You are free to use this software for research purposes, but you should not redistribute it without our consent.
- In addition, we expect you to include adequate citations and acknowledgments whenever you present or publish results that are based on it.

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