The hessian of axially symmetric functions on SE(3) and application in 3D image analysis

M.H.J. Janssen, T.C.J. Dela Haije, F.C. Martin, E.J. Bekkers, R. Duits

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

2 Citaten (Scopus)

Samenvatting

We propose a method for computation of the Hessian of axially symmetric functions on the roto-translation group SE(3). Eigen decomposition of the resulting Hessian is then used for curvature estimation of tubular structures, similar to how the Hessian matrix of 2D or 3D image data can be used for orientation estimation. This paper focuses on a new implementation of a Gaussian regularized Hessian on the roto-translation group. Furthermore we show how eigenanalysis of this Hessian gives rise to exponential curve fits on data on position and orientation (e.g. orientation scores), whose spatial projections provide local fits in 3D data. We quantitatively validate our exponential curve fits by comparing the curvature of the spatially projected fitted curve to ground truth curvature of artificial 3D data. We also show first results on real MRA data.

Originele taal-2Engels
TitelScale Space and Variational Methods in Computer Vision
Subtitel6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings
RedacteurenF. Lauze, Y. Dong, A. Bjorholm Dahl
Plaats van productieDordrecht
UitgeverijSpringer
Pagina's643-655
Aantal pagina's13
ISBN van elektronische versie978-3-319-58771-4
ISBN van geprinte versie978-3-319-58770-7
DOI's
StatusGepubliceerd - 2017
Evenement6th International Conference on Scale Space and Variational Methods in Computer Vision, (SSVM 2017), June 4-8, 2017, Kolding, Denmark - Kolding, Denemarken
Duur: 4 jun 20178 jun 2017
http://ssvm2017.compute.dtu.dk/

Publicatie series

NaamLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10302 LNCS
ISSN van geprinte versie0302-9743
ISSN van elektronische versie1611-3349

Congres

Congres6th International Conference on Scale Space and Variational Methods in Computer Vision, (SSVM 2017), June 4-8, 2017, Kolding, Denmark
Verkorte titelSSVM 2017
LandDenemarken
StadKolding
Periode4/06/178/06/17
Internet adres

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  • Citeer dit

    Janssen, M. H. J., Dela Haije, T. C. J., Martin, F. C., Bekkers, E. J., & Duits, R. (2017). The hessian of axially symmetric functions on SE(3) and application in 3D image analysis. In F. Lauze, Y. Dong, & A. Bjorholm Dahl (editors), Scale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings (blz. 643-655). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10302 LNCS). Springer. https://doi.org/10.1007/978-3-319-58771-4_51