ITERATIVE DISCRETE STEERING OF THREE-DIMENSIONAL RECONSTRUCTIONS FROM X-RAY IMAGES WITH LIMITED ANGLE

Anja Frost, Eike Renners, Michael Hötter

Abstract

Computer Tomography is aimed to calculate a three dimensional reconstruction of the inside of an object from series of X-ray images. This calculation corresponds to the solution of a system of linear equations, in which the equations arise from the measured X-rays and the variables from the voxels of the reconstruction volume, or more precisely, their density values. Unfortunately, some applications do not supply enough equations. In that case, the system is underdetermined. The reconstructed object, as only estimated, seems to be stretched. As there are a few voxels, that are already representing the object true to original, it is possible to exclude these variables from the system of equations. Then, the number of variables decreases. Ideally, the system gets solvable. In this paper we concentrate on the detection of all good reconstructed voxels i.e. we introduce a quality measure, called Accuratio, to evaluate the volume voxel by voxel. In our experi-mental results we show the reliability of Accuratio by applying it to an iterative reconstruction algorithm. In each iteration step the whole volume is evaluated, voxels with high Accuratio are excluded and the new system of equations is reconstructed again. Steadily the reconstructed object becomes “destretched”.

References

  1. Benameur, S., Mignotte, M., Labelle, H., De Guise, J.A., 2003. A hierarchical statistical modeling approach for the unsupervised 3-D biplanar reconstruction of the scoliotic spine. In IEEE Transactions of Biomedical Engineering, 52(12), 2041-2057.
  2. Sadowsky, O., Lee, J., Sutter, E. G., Wall, S. J., Prince, J. L., Taylor, R.H., 2011. Hybrid cone-beam tomographic reconstruction: incorporation of prior anatomical models to compensate for missing data. In IEEE Transactions on Medical Imaging, 30(1), 69-83.
  3. Varga, L., Balázs, P., Nagy, A., 2010. Projection selection algorithms for discrete tomography. In Advanced Concepts for Intelligent Vision Systems, Springer. pp. 390-401.
  4. Herman, G. T., Kuba, A., 2007. Advances in discrete tomography and its applications, Birkhäuser. Bosten.
  5. Kak, A. C., Slaney, M., 1988. Principles of computerized tomographic imaging, IEEE Press. New York.
  6. Gordon, R., Bender, R., Herman, G. T., 1970. Algebraic Reconstruction Techniques (ART) for threedimensional electron microscopy and X-ray photography. In Journal of Theoretical Biology, 29(3), pp. 471-481. Elsevier.
  7. Xu, F., Müller, K., 2007. Real-time 3D computed tomographic reconstruction using commodity graphics hardware. In Physics in Medicine and Biology. 52, pp. 3405-3419. IOP Publishing.
  8. Kunze, H., 2007. Iterative Rekonstruktion in der medizinischen Bildverarbeitung, Shaker.
  9. Batenburg, K. J., Sijbers, J., 2007. Dart: A Fast Heuristic Algebraic Reconstruction Algorithm for Discrete Tomography. In Image Processing, 4th IEEE Conference on Image Processing. doi: 10.1109/ICIP. 2007.4379972
  10. Kuba, A., Ruskó, L., Rodek, L., Kiss, Z., 2005. Preliminary studies of discrete tomography in neutron imaging. In IEEE Transactions on Nuclear Science. 52(1), pp. 380-385. IEEE Press.
  11. Censor, Y., 2001. Binary steering in discrete tomography reconstruction with sequential and simultaneous iterative algorithms. In Linear Algebra and its Applications (Vol. 339(1-3), pp. 111-124). Elsevier.
  12. Frost, A., Hötter, M., 2010. Discrete Steering: Eine statistisch orientierte Diskretisierung von dreidimensionalen Rekonstruktionen aus Röntgenaufnahmen. In Puente León, F. and Heizmann, M, Forum Bildverarbeitung: [2. - 3. Dezember 2010 in Regensburg] (pp. 365-376). KIT Scientific Publishing.
Download


Paper Citation


in Harvard Style

Frost A., Renners E. and Hötter M. (2012). ITERATIVE DISCRETE STEERING OF THREE-DIMENSIONAL RECONSTRUCTIONS FROM X-RAY IMAGES WITH LIMITED ANGLE . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012) ISBN 978-989-8565-03-7, pages 89-94. DOI: 10.5220/0003809200890094


in Bibtex Style

@conference{visapp12,
author={Anja Frost and Eike Renners and Michael Hötter},
title={ITERATIVE DISCRETE STEERING OF THREE-DIMENSIONAL RECONSTRUCTIONS FROM X-RAY IMAGES WITH LIMITED ANGLE},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)},
year={2012},
pages={89-94},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003809200890094},
isbn={978-989-8565-03-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)
TI - ITERATIVE DISCRETE STEERING OF THREE-DIMENSIONAL RECONSTRUCTIONS FROM X-RAY IMAGES WITH LIMITED ANGLE
SN - 978-989-8565-03-7
AU - Frost A.
AU - Renners E.
AU - Hötter M.
PY - 2012
SP - 89
EP - 94
DO - 10.5220/0003809200890094