The multiselectivity scheme: A pyramidal organization of wavelets with variable angular selectivity

During the last ten years, many techniques have been devised to add directionality in image processing. We may cite, for instance, directional wavelets [1], steerable filters [8], curvelets [2], contourlets [5], …. This has opened the door to new ways for efficiently representing objects by oriented atoms. Real images, however, contain more than just smooth curves and straight lines defining contours of objects. They can present also details that are less oriented and more isotropic (like corners, spots, texture elements, …). We present in this paper a tool which can be tuned relatively to these image features by decomposing them into a (linear) frame of directional wavelets with variable angular selectivity. To obtain such a decomposition, these new functions exploit some particularities of the (biorthogonal) circular multiresolution framework in the frequency domain. This link suggests the name of our method, ‘multiselectivity analysis’.