The Hessian of Axially Symmetric Functions on SE(3) and Application in 3D Image Analysis

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  • Michiel H. J. Janssen
  • Tom Dela Haije
  • Frank C. Martin
  • Erik J. Bekkers
  • Remco Duits

We propose a method for computation of the Hessian of axially symmetric functions on the roto-translation group SE(3). Eigendecomposition 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. Implementations are available at: http://lieanalysis.nl/orientationscores.html

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision : 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings
EditorsFrançois Lauze, Yiqui Dong, Anders Bjorholm Dahl
Number of pages13
PublisherSpringer
Publication date2017
Pages 643-655
ISBN (Print)978-3-319-58770-7
ISBN (Electronic)978-3-319-58771-4
DOIs
Publication statusPublished - 2017
Externally publishedYes
Event6th International Conference on Scale Space and Variational Methods in Computer Vision - Kolding, Denmark
Duration: 4 Jun 20178 Jun 2017
Conference number: 6

Conference

Conference6th International Conference on Scale Space and Variational Methods in Computer Vision
Nummer6
LandDenmark
ByKolding
Periode04/06/201708/06/2017
SeriesLecture notes in computer science
Volume10302
ISSN0302-9743

ID: 195286618