CLOSED FORM OF THE STEERED ELONGATED HERMITE-GAUSS WAVELETS

Giuseppe Papari*, Patrizio Campisi, Nicolai Petkov

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Abstract

We provide a closed form, both in the spatial and in the frequency domain, of a family of wavelets which arise from steering elongated Hermite-Gauss filters. These wavelets have interesting mathematical properties, as they form new dyadic families of eigenfunctions of the 2D Fourier transform, and generalize the well known Laguerre-Gauss harmonics. A special notation introduced here greatly simplifies our proof and unifies the cases of even and odd orders. Applying these wavelets to edge detection increases the performance of about 12.5% with respect to standard methods, in terms of the Pratt’s figure of merit, both for noisy and noise-free input images.
Original languageEnglish
Title of host publication2010 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING
Place of PublicationNEW YORK
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Pages377-380
Number of pages4
ISBN (Electronic)9781424479931
ISBN (Print)9781424479924
Publication statusPublished - 2010
EventIEEE International Conference on Image Processing -
Duration: 26-Sep-201029-Sep-2010

Publication series

NameIEEE International Conference on Image Processing ICIP
PublisherIEEE
ISSN (Print)1522-4880

Other

OtherIEEE International Conference on Image Processing
Period26/09/201029/09/2010

Keywords

  • Edge features
  • Fourier analysis
  • Steerable filters
  • EDGE-DETECTION
  • EARLY VISION
  • DESIGN
  • DECOMPOSITION
  • KERNELS

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