The Hessian of Axially Symmetric Functions on SE(3) and Application in 3D Image Analysis
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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 language | English |
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Title of host publication | Scale Space and Variational Methods in Computer Vision : 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 2017, Proceedings |
Editors | François Lauze, Yiqui Dong, Anders Bjorholm Dahl |
Number of pages | 13 |
Publisher | Springer |
Publication date | 2017 |
Pages | 643-655 |
ISBN (Print) | 978-3-319-58770-7 |
ISBN (Electronic) | 978-3-319-58771-4 |
DOIs | |
Publication status | Published - 2017 |
Externally published | Yes |
Event | 6th International Conference on Scale Space and Variational Methods in Computer Vision - Kolding, Denmark Duration: 4 Jun 2017 → 8 Jun 2017 Conference number: 6 |
Conference
Conference | 6th International Conference on Scale Space and Variational Methods in Computer Vision |
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Nummer | 6 |
Land | Denmark |
By | Kolding |
Periode | 04/06/2017 → 08/06/2017 |
Series | Lecture notes in computer science |
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Volume | 10302 |
ISSN | 0302-9743 |
ID: 195286618