Bayesian epipolar geometry estimation from tomographic projections

Sami Sebastian Brandt; Katrine Hommelhoff Jensen; Francois Bernard Lauze

doi:10.1007/978-3-642-37447-0_18

Bayesian epipolar geometry estimation from tomographic projections

Sami Sebastian Brandt, Katrine Hommelhoff Jensen, Francois Bernard Lauze

Department of Computer Science

Abstract

In this paper, we first show that the affine epipolar geometry can be estimated by identifying the common 1D projection from a pair of tomographic parallel projection images and the 1D affine transform between the common 1D projections. To our knowledge, the link between the common 1D projections and the affine epipolar geometry has been unknown previously; and in contrast to the traditional methods of estimating the epipolar geometry, no point correspondences are required. Using these properties, we then propose a Bayesian method for estimating the affine epipolar geometry, where we apply a Gaussian model for the noise and non-informative priors for the nuisance parameters. We derive an analytic form for the marginal posterior distribution, where the nuisance parameters are integrated out. The marginal posterior is sampled by a hybrid Gibbs-Metropolis-Hastings sampler and the conditional mean and the covariance over the posterior are evaluated on the homogeneous manifold of affine fundamental matrices. We obtained promising results with synthetic 3D Shepp-Logan phantom as well as with real cryo-electron microscope projections.

Original language	English
Title of host publication	Computer Vision – ACCV 2012 : 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part IV
Editors	Kyoung Mu Lee, Yasuyuki Matsushita, James M. Rehg, Zhanyi Hu
Number of pages	12
Publisher	Springer
Publication date	2013
Pages	231-242
ISBN (Print)	978-3-642-37446-3
ISBN (Electronic)	978-3-642-37447-0
DOIs	https://doi.org/10.1007/978-3-642-37447-0_18
Publication status	Published - 2013
Event	The 11th Asian Conference on Computer Vision - Daejeon, Korea, Republic of Duration: 5 Nov 2012 → 9 Nov 2012 Conference number: 11

Conference

Conference	The 11th Asian Conference on Computer Vision
Number	11
Country/Territory	Korea, Republic of
City	Daejeon
Period	05/11/2012 → 09/11/2012

Series	Lecture notes in computer science
Volume	7727
ISSN	0302-9743

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10.1007/978-3-642-37447-0_18

http://www.ee.oulu.fi/~sbrandt/publications/ACCV2012.pdfLicence: Other

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Brandt, S. S., Jensen, K. H., & Lauze, F. B. (2013). Bayesian epipolar geometry estimation from tomographic projections. In K. M. Lee, Y. Matsushita, J. M. Rehg, & Z. Hu (Eds.), Computer Vision – ACCV 2012: 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part IV (pp. 231-242). Springer. https://doi.org/10.1007/978-3-642-37447-0_18

Bayesian epipolar geometry estimation from tomographic projections. / Brandt, Sami Sebastian; Jensen, Katrine Hommelhoff; Lauze, Francois Bernard.
Computer Vision – ACCV 2012: 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part IV. ed. / Kyoung Mu Lee; Yasuyuki Matsushita; James M. Rehg; Zhanyi Hu. Springer, 2013. p. 231-242 (Lecture notes in computer science, Vol. 7727).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Brandt, SS, Jensen, KH & Lauze, FB 2013, Bayesian epipolar geometry estimation from tomographic projections. in KM Lee, Y Matsushita, JM Rehg & Z Hu (eds), Computer Vision – ACCV 2012: 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part IV. Springer, Lecture notes in computer science, vol. 7727, pp. 231-242, The 11th Asian Conference on Computer Vision , Daejeon, Korea, Republic of, 05/11/2012. https://doi.org/10.1007/978-3-642-37447-0_18

Brandt SS, Jensen KH, Lauze FB. Bayesian epipolar geometry estimation from tomographic projections. In Lee KM, Matsushita Y, Rehg JM, Hu Z, editors, Computer Vision – ACCV 2012: 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part IV. Springer. 2013. p. 231-242. (Lecture notes in computer science, Vol. 7727). doi: 10.1007/978-3-642-37447-0_18

Brandt, Sami Sebastian ; Jensen, Katrine Hommelhoff ; Lauze, Francois Bernard. / Bayesian epipolar geometry estimation from tomographic projections. Computer Vision – ACCV 2012: 11th Asian Conference on Computer Vision, Daejeon, Korea, November 5-9, 2012, Revised Selected Papers, Part IV. editor / Kyoung Mu Lee ; Yasuyuki Matsushita ; James M. Rehg ; Zhanyi Hu. Springer, 2013. pp. 231-242 (Lecture notes in computer science, Vol. 7727).

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AB - In this paper, we first show that the affine epipolar geometry can be estimated by identifying the common 1D projection from a pair of tomographic parallel projection images and the 1D affine transform between the common 1D projections. To our knowledge, the link between the common 1D projections and the affine epipolar geometry has been unknown previously; and in contrast to the traditional methods of estimating the epipolar geometry, no point correspondences are required. Using these properties, we then propose a Bayesian method for estimating the affine epipolar geometry, where we apply a Gaussian model for the noise and non-informative priors for the nuisance parameters. We derive an analytic form for the marginal posterior distribution, where the nuisance parameters are integrated out. The marginal posterior is sampled by a hybrid Gibbs-Metropolis-Hastings sampler and the conditional mean and the covariance over the posterior are evaluated on the homogeneous manifold of affine fundamental matrices. We obtained promising results with synthetic 3D Shepp-Logan phantom as well as with real cryo-electron microscope projections.

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ER -

Bayesian epipolar geometry estimation from tomographic projections

Abstract

Conference

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