Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames
A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two class...
| Publié dans: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 25(2016), 5 vom: 01. Mai, Seite 2275-87 |
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| Auteur principal: | |
| Autres auteurs: | , |
| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2016
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| Accès à la collection: | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
| Sujets: | Journal Article Research Support, Non-U.S. Gov't |
| Résumé: | A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones |
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| Description: | Date Completed 02.08.2016 Date Revised 25.07.2016 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1941-0042 |
| DOI: | 10.1109/TIP.2016.2545301 |