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This website presents the main results of a research work conducted in the 2010s by Raphaël Soulard and Philippe Carré in the XLIM laboratory (UMR CNRS 7252), University of Poitiers, France.

About

Our general topic is about designing numerical representation methods providing intuitive handling of the visual content in color images. Representation tools usually come as the first stage of higher level image processing procedures, such as pattern recognition or enhancing. Typical methods are wavelet transforms, that separate coarse information from details through several scales. The topic also includes feature extraction such as contour analysis and particular point detection.

In practice, color images are often either reduced to their luminance, or analyzed through their separate color channels, which is impeding for proper color analysis. The literature reveals a strong lack of mathematical tools for the handling of color images, due to higher dimensional complexity compared to greyscale.

Our goal is to find suitable mathematical extensions of the fundamental signal and image processing tools to higher dimensions so that the color and geometric information can be intuitively represented. Our main result, the Elliptical Monogenic Wavelet Transform, is able to separate the information in terms of shape and color features.

This website aims at making our work accessible to researchers and engineers, particularly for the development of the applicative side. In particular, we provide the Matlab code associated to every section, so that all technical details of our methods and experiments are reproducible. The reader should be familiar with the basics of signal and image processing (Fourier transform and 2d filtering). For theoretical details, we refer the reader to our main articles:

Soulard & Carré, ...Monogenic maxima... IEEE TPAMI 2017

Soulard & Carré, Elliptical Monogenic Wavelets... IEEE TSP 2015

Soulard, Carré & Fernandez, Vector extension of monogenic wavelets... IEEE TIP 2013