Narrow Results

Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention, for instance, works on directional wavelets, steerable filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets, etc. In general, features that are best represented are straight lines or smooth curves as those defining contours of objects (e.g. in curvelets processing) or oriented textures (e.g. wave atoms, ridgelet packets). However, real images present also a set of details less oriented and more isotropic, like corners, spots, texture components, etc. This paper develops an adaptive representation for all these image elements, ranging from highly directional ones to fully isotropic ones. This new tool can indeed be tuned relatively to these image features by decomposing them into a Littlewood–Paley frame of directional wavelets with variable angular selectivity. Within such a decomposition, 2D wavelets inherit some particularities of the biorthogonal circular multiresolution framework in their angular behavior. Our method can therefore be seen as an angular multiselectivity analysis of images. Two applications of the proposed method are given at the end of the paper, namely, in the fields of image denoising and N-term nonlinear approximation.

This paper focuses on the development of a new two-dimensional representation for images that can capture different features in images, ranging from highly directional ones to fully isotropic ones. We propose a multiselectivity analysis, defined by combining an isotropic multiscale and multidirection decomposition. The result is new half-continuous frame for each selectivity level. The angular selectivity of these frames grows with selectivity level. This selectivity level can be adapted locally to the content of the image; so it can be seen as an adaptive selectivity representation, which present adaptively isotropic, directional and intermediary features in images. The numerical experiments presented in this paper demonstrate that the adaptive selectivity approach is very competitive in image denoising and enhancement.

In this paper, the general idea of the fringe detection which using wavelet analysis were put forward. By the study of the detection for image fringe of heterogeneity (such as mechanical image and medical image), the maximum module method of wavelet transform and the directional method of wavelet were used to carry out detection. The design was practical through the certification of the theoretical analysis and the experimental result. Furthermore, the contrasting effect of the algorithm illustrated that the better effect would be got if the different algorithm was adopted.