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

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

3 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision
Subtitle of host publication6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings
EditorsF. Lauze, Y. Dong, A. Bjorholm Dahl
Place of PublicationDordrecht
PublisherSpringer
Pages643-655
Number of pages13
ISBN (Electronic)978-3-319-58771-4
ISBN (Print)978-3-319-58770-7
DOIs
Publication statusPublished - 2017
Event6th International Conference on Scale Space and Variational Methods in Computer Vision, (SSVM 2017), June 4-8, 2017, Kolding, Denmark - Kolding, Denmark
Duration: 4 Jun 20178 Jun 2017
http://ssvm2017.compute.dtu.dk/

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10302 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Conference on Scale Space and Variational Methods in Computer Vision, (SSVM 2017), June 4-8, 2017, Kolding, Denmark
Abbreviated titleSSVM 2017
CountryDenmark
CityKolding
Period4/06/178/06/17
Internet address

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