An analytical geometric calibration method for circular cone-beam geometry

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This work is a continuation of our previous work on geometric calibration in the circular cone-beam geometry. It is well known that seven parameters completely describe such a geometry in either flat-panel X-ray computed tomography or single pinhole SPECT imaging. Previously we developed a graphical procedure to determine the detector in-plane rotation angle independently of the other six parameters. Using the discovered geometrical relationships, in this paper we determine the remaining six parameters using the cone-beam projections of a minimum of three point objects. Our method is analytical. It makes use of the parameters of the fitted ellipse from the calibration data. The parameter estimation is accurate in the noise-free case or when there is moderate projection data truncation or shorter calibration scan range ({\leq} 360^\circ). We perform numerical evaluations to study the robustness of the proposed method under different projection noise levels and using different data acquisition ranges. Using a full 360^\circ scan range, the estimation accuracy and precision of our method are comparable or superior to previous methods. Using a shorter acquisition range, there may be bias in the ellipse parameters obtained by simple algebraic fitting methods. This bias will propagate to the estimated geometric parameters. Such bias can be mostly eliminated by using a more sophisticated fitting algorithm. At the same noise level, the geometric parameter estimation accuracies are comparable, but the estimation precision degrades, as the acquisition range becomes shorter.

Original languageEnglish (US)
Article number6530715
Pages (from-to)1731-1744
Number of pages14
JournalIEEE transactions on medical imaging
Issue number9
StatePublished - 2013


  • Ellipse fitting
  • flat-panel X-ray computed tomography (CT)
  • geometric calibration
  • homogeneous representation
  • image reconstruction
  • multi-pinhole
  • pinhole SPECT
  • projective geometry

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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