Bayesian epipolar geometry estimation from tomographic projections

TY - GEN

T1 - Bayesian epipolar geometry estimation from tomographic projections

AU - Brandt, Sami Sebastian

AU - Jensen, Katrine Hommelhoff

AU - Lauze, Francois Bernard

N1 - Conference code: 11

PY - 2013

Y1 - 2013

N2 - 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.

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.

U2 - 10.1007/978-3-642-37447-0_18

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

M3 - Article in proceedings

SN - 978-3-642-37446-3

T3 - Lecture notes in computer science

SP - 231

EP - 242

BT - Computer Vision – ACCV 2012

A2 - Lee, Kyoung Mu

A2 - Matsushita, Yasuyuki

A2 - Rehg, James M.

A2 - Hu, Zhanyi

PB - Springer

T2 - The 11th Asian Conference on Computer Vision

Y2 - 5 November 2012 through 9 November 2012

ER -