Invertible orientation scores of 3D images

M.H.J. Janssen, R. Duits, M. Breeuwer

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Abstract

The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical applications. To handle complex crossing structures in 2D images, 2D orientation scores U:R2×S1¿R were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores U:R3×S2¿R . First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake-wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. For efficient implementation of the different steps in the wavelet creation we use a spherical harmonic transform. Finally, we show some first results of practical applications of 3D orientation scores. Keywords: Orientation scores; Reproducing kernel spaces; 3D wavelet design; Scale spaces on SE(3); Coherence enhancing Diffusion on SE(3)
Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision (5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31-June 4, 2015, Proceedings)
EditorsJ.-F. Aujol, M. Nikolova, N. Papadakis
PublisherSpringer
Pages563-575
ISBN (Print)978-3-319-18460-9
DOIs
Publication statusPublished - 2015

Publication series

NameLecture Notes in Computer Science
Volume9087
ISSN (Print)0302-9743

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Janssen, M. H. J., Duits, R., & Breeuwer, M. (2015). Invertible orientation scores of 3D images. In J-F. Aujol, M. Nikolova, & N. Papadakis (Eds.), Scale Space and Variational Methods in Computer Vision (5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31-June 4, 2015, Proceedings) (pp. 563-575). (Lecture Notes in Computer Science; Vol. 9087). Springer. https://doi.org/10.1007/978-3-319-18461-6_45