Quaternionic Wavelets for Texture Classification

4 pagesInternational audienceThis paper proposes a new texture classifier based on the Quaternionic Wavelet Transform (QWT). This recent transform separates the informations contained in the image better than a classical wavelet transform (DWT), and provides a multiscale image analysis which coefficients are 2D analytic, with one near-shift invariant magnitude and a phase, that is made of three angles. The interpretation and use of the QWT coefficients, especially the phase, are discussed, and we present a texture classifier using both the QWT magnitude and the QWT phase of images. Our classifier performs a better recognition rate than a standard wavelet based classifier

Ondelettes monogènes couleur pour l'analyse d'image

4 pagesNational audienceNous proposons une transformée en ondelettes monogène couleur, basée sur une récente transformée monogène et une extension non marginale pour la couleur. Les schémas de traitement d'image couleur utilisant les ondelettes correspondent souvent à l'application d'un outil " niveaux de gris " sur chaque canal couleur séparément. Cela peut entraîner des effets indésirables sur la couleur lorsque ces schémas marginaux ne sont pas justifiés. Dans ce papier nous proposons une définition qui prends en compte une image couleur (vectorielle) dès le début de la construction mathématique, pour amener à une " vraie " transformée couleur. On obtient une analyse géométrique couleur multirésolution prometteuse pour l'image couleur

Ondelettes Quaternioniques pour la Classification de Textures

8 pagesNational audienceThis paper proposes a new texture classifier based on the Quaternionic Wavelet Transform (QWT). This recent transform separates the informations contained in the image better than a classical wavelet transform (DWT), and provides a multiscale image analysis which coefficients are 2D analytic, with one near-shift invariant magnitude and a phase, that is made of three angles. The interpretation and use of the QWT coefficients, especially the phase, are discussed, and we present a texture classifier using both the QWT magnitude and the QWT phase of images. Our classifier performs a better recognition rate than a standard wavelet based classifier

Color monogenic wavelets for image analysis

4 pagesInternational audienceWe define a color monogenic wavelet transform. This is based on the recent grayscale monogenic wavelet transform and a non-marginal extension to color signals. To our knowledge, wavelet based color image processing schemes have always been made by using a grayscale tool separately on color channels. This may have some unexpected effect on colors because those marginal schemes are not necessarily justified. Here we propose a definition that considers a color (vector) image right at the beginning of the mathematical definition and so brings an actual color wavelet transform - which has not been done so far to our knowledge. This so provides a promising multiresolution color geometric analysis of images

Color monogenic wavelet representation based on a tensor-like use of the riesz transform: application to image coding

11 pagesInternational audienceWe propose a new extension of monogenic analysis to multi-valued signals like color images. This generalization is based on an analogy between the Riesz transform and structure tensors and takes advantage of the well defined vector differential geometry. Our color wavelet transform is non-marginal and its coefficients - separated into amplitude, phase, orientation and local color axis - have interesting physical interpretation in terms of local energy, contour model, and colorimetric features. An image coding application is proposed as a practical study

Tensor based generalization of monogenic wavelets for coherent multiscale local phase analysis of color images

4 pagesInternational audienceWe propose a new color extension of the monogenic wavelet transform. Monogenic wavelets give a coherent representation of scalar images through a local phase concept and an underlying orientation analysis. We here define a color extension of the monogenic framework. The underlying local geometric analysis and phase concept are generalized by using the color structure tensor. Resulting transform appears to be a clear improvement of our previous work - that is the only proposition of color monogenic wavelets to our knowledge. This is shift and rotation invariant and efficiently represents multiscale color lines and edges

Elliptical Monogenic Wavelets for the analysis and processing of color images

International audienceThis paper studies and gives new algorithms for image processing based on monogenic wavelets. Existing greyscale monogenic filterbanks are reviewed and we reveal a lack of discussion about the synthesis part. The monogenic synthesis is therefore defined from the idea of wavelet modulation, and an innovative filterbank is constructed by using the Radon transform. The color extension is then investigated. First, the elliptical Fourier atom model is proposed to generalize theanalytic signal representation for vector-valued signals. Then a color Riesz-transform is defined so as to construct color elliptical monogenic wavelets. Our Radon-based monogenic filterbank can be easily extended to color according to this definition. The proposed wavelet representation provides efficient analysis of local features in terms of shape and color, thanks to the concepts of amplitude, phase, orientation, and ellipse parameters. The synthesis from local features is deeply studied. We conclude the article by defining the color local frequency, proposing an estimation algorithm

A discrete approach to monogenic analysis through Radon transform

8 pagesInternational audienceMonogenic analysis is gaining interest in the image processing community as a true signal processing tool for 2D signals. Unfortunately, it is only defined in the continuous case. We address this issue by proposing an innovative scheme that uses a discrete Radon transform based on discrete geometry. Radon domain signal processing and monogenic analysis is studied and performance is shown to be equivalent to the usual FFT-based algorithms. The advantage is that extensions to filterbanks and to higher dimensions are facilitated, thanks to the perfect invertibility and computational simplicity of the used Radon algorithm

Color Extension of Monogenic Wavelets with Geometric Algebra : Application to Color Image Denoising

10 pagesInternational audienceWe define a color monogenic wavelet transform. This is based on the recent grayscale monogenic wavelet transform and an extension to color signals aimed at defining non-marginal tools. Wavelet based color image processing schemes have mostly been made by using a grayscale tool separately on color channels. This may have some unexpected effect on colors because those marginal schemes are not necessarily justified. Here we propose a definition that considers a color (vector) image right at the beginning of the mathematical definition so we can expect to bring an actual color wavelet transform - which has not been done so far to our knowledge. This so provides a promising multiresolution color geometric analysis of images. We show an application of this transform with a statistical modeling of coefficients for color denoising issue

Elliptical monogenic representation of color images and local frequency analysis

International audienceWe define a new color extension for the monogenic representation of images by using an elliptical tri-valued oscillation model jointly with the vector structure tensor formalism. The proposed method provides a rich local colorimetric and geometric analysis, in particular a color phase concept, which can be computed by a numerically stable algorithm. This representation is finally used to estimate the local frequency of color images