Vascular tree reconstruction with discrete tomography: intensity based camera correction for 3D reconstruction

  • C. Bodensteiner
  • C. Darolti
  • A. Schweikard
Original Article



This paper is concerned with the reconstruction of vascular trees from few projections using discrete tomography. However, its computational cost is high and it lacks robustness when the data are inconsistent. We improve robustness by incorporating an intensity-based camera-correction method. The proposed approach is also capable of handling small motion artifacts by modeling them as repositionings of a virtual X-ray camera. We also present a parallel implementation which substantially reduces reconstruction time.


We propose a data-driven reduction of positional inconsistencies by minimizing the reconstruction residual to increase the robustness. Inspired by motion compen-sation algorithms in SPECT imaging, we combine an intensity-based 2D/3D-registration method with itera-tive reconstruction methods. Our objective is the robust vascular-tree reconstruction from positionally inconsistent data. The speed of the reconstruction is substantially increased by a volume-splitting scheme that allows parallel processing.


Vascular trees in the liver can be accurately reconstructed from few positionally inconsistent projections using digitally reconstructed radiographs. We have tested the proposed method on synthetic projection data and on objects imaged with a new robotized C-arm. We measured a decrease in the average reconstruction residual of about 13% for real data compared to projection data without preprocessing. Over 4,600 reconstruction experiments were conducted to evaluate the speed-up obtained when employing the volume-splitting scheme. Reconstruction time decreased linearly with increased number of processor-cores, both for real and synthetic data.


The proposed method reduces inconsistencies caused by positioning errors and small motion artifacts. No prior segmentation or detection of correspondences between projections is necessary, because all algorithms are intensity-based. As a result, the proposed method allows for robust, high-quality reconstructions, while reducing radiation dose substantially.


3D Reconstruction Digital subtraction angiography Algebraic reconstruction 2D/3D-registration Camera calibration 


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© CARS 2009

Authors and Affiliations

  1. 1.Institute of Robotics and Cognitive SystemsUniversity of LuebeckLuebeckGermany

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