Decoupling Respiratory and Angular Variation in Rotational X-ray Scans Using a Prior Bilinear Model

  • Tobias GeimerEmail author
  • Paul Keall
  • Katharina Breininger
  • Vincent Caillet
  • Michelle Dunbar
  • Christoph Bert
  • Andreas Maier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11269)


Data-driven respiratory signal extraction from rotational X-ray scans is a challenge as angular effects overlap with respiration-induced change in the scene. In this paper, we use the linearity of the X-ray transform to propose a bilinear model based on a prior 4D scan to separate angular and respiratory variation. The bilinear estimation process is supported by a B-spline interpolation using prior knowledge about the trajectory angle. Consequently, extraction of respiratory features simplifies to a linear problem. Though the need for a prior 4D CT seems steep, our proposed use-case of driving a respiratory motion model in radiation therapy usually meets this requirement. We evaluate on DRRs of 5 patient 4D CTs in a leave-one-phase-out manner and achieve a mean estimation error of \(3.01\%\) in the gray values for unseen viewing angles. We further demonstrate suitability of the extracted weights to drive a motion model for treatments with a continuously rotating gantry.


Bilinear model Motion model Respiratory signal X-ray projection Feature extraction 



This work was partially conducted at the ACRF Image X Institute as part of a visiting research scholar program. The authors gratefully acknowledge funding of this research stay by the Erlangen Graduate School in Advanced Optical Technologies (SAOT).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Pattern Recognition Lab, Department of Computer ScienceFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Erlangen Graduate School in Advanced Optical Technologies (SAOT)Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  3. 3.Department of Radiation OncologyUniversitätsklinikum Erlangen, Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  4. 4.ACRF Image X InstituteThe University of SydneySydneyAustralia

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