Symmetry prior for epipolar consistency

  • Alexander PreuhsEmail author
  • Andreas Maier
  • Michael Manhart
  • Markus Kowarschik
  • Elisabeth Hoppe
  • Javad Fotouhi
  • Nassir Navab
  • Mathias Unberath
Original Article



For a perfectly plane symmetric object, we can find two views—mirrored at the plane of symmetry—that will yield the exact same image of that object. In consequence, having one image of a plane symmetric object and a calibrated camera, we automatically have a second, virtual image of that object if the 3-D location of the symmetry plane is known.


We propose a method for estimating the symmetry plane from a set of projection images as the solution of a consistency maximization based on epipolar consistency. With the known symmetry plane, we can exploit symmetry to estimate in-plane motion by introducing the X-trajectory that can be acquired with a conventional short-scan trajectory by simply tilting the acquisition plane relative to the plane of symmetry.


We inspect the symmetry plane estimation on a real scan of an anthropomorphic human head phantom and show the robustness using a synthetic dataset. Further, we demonstrate the advantage of the proposed method for estimating in-plane motion using the acquired projection data.


Symmetry breakers in the human body are widely used for the detection of tumors or strokes. We provide a fast estimation of the symmetry plane, robust to outliers, by computing it directly from a set of projections. Further, by coupling the symmetry prior with epipolar consistency, we overcome inherent limitations in the estimation of in-plane motion.


Symmetry Consistency conditions Cone-beam CT Motion compensation Data completeness Tomographic reconstruction 


Compliance with ethical standards

Conflict of interest

M. Unberath, J. Fotouhi, N. Navab and A. Maier have no conflict of interest. A. Preuhs and E. Hoppe are funded by Siemens Healthcare GmbH, Forchheim Germany. M. Kowarschik and M. Manhart are employees of Siemens Healthcare GmbH, Forchheim Germany

Informed consent

This article does not contain patient data.


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Copyright information

© CARS 2019

Authors and Affiliations

  1. 1.Pattern Recognition LabFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany
  2. 2.Siemens Healthcare GmbHForchheimGermany
  3. 3.Department of Computer ScienceJohns Hopkins UniversityBaltimoreUSA

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