title: Guided ultrasound calibration: where, how, and how many calibration fiducials.
abstract: OBJECTIVE
  Many image-guided interventions rely on tracked ultrasound where the transducer is augmented with a tracking device. The relationship between the ultrasound image coordinate system and the tracking sensor must be determined accurately via probe calibration. We introduce a novel calibration framework guided by the prediction of target registration error (TRE): Between successive measurements of the calibration phantom, our framework guides the user in choosing the pose of the calibration phantom by optimizing TRE.
  
  
  METHODS
  We introduced an oriented line calibration phantom and modeled the ultrasound calibration process as a point-to-line registration problem. We then derived a spatial stiffness model of point-to-line registration for estimating TRE magnitude at any target. Assuming isotropic, identical localization error, we used the model to estimate TRE for each pixel using the current calibration estimate. We then searched through the calibration tool space to find the pose for the next fiducial which maximally minimized TRE.
  
  
  RESULTS
  Both simulation and experimental results suggested that TRE decreases monotonically, reaching an asymptote when a sufficient number of measurements (typically around 12) are made. Independent point reconstruction accuracy assessment showed sub-millimeter accuracy of the calibration framework.
  
  
  CONCLUSIONS
  We have introduced the first TRE-guided ultrasound calibration framework. Using a hollow straw as an oriented line phantom, we virtually constructed a rigid lines phantom and modeled the calibration process as a point-to-line registration. Highly accurate calibration was achieved with minimal measurements by using a spatial stiffness model of TRE to strategically choose the pose of the calibration phantom between successive measurements.
authors.affiliation: Robarts Research Institute, Western University, London, ON, Canada. chene@robarts.ca.
authors.forename: Elvis C S
authors.initials: EC
authors.lastname: Chen
authors.affiliation: Robarts Research Institute, Western University, London, ON, Canada.
authors.forename: Terry M
authors.initials: TM
authors.lastname: Peters
authors.affiliation: Department of Electrical Engineering and Computer Science, York University, Toronto, ON, Canada.
authors.forename: Burton
authors.initials: B
authors.lastname: Ma
mesh_terms: D000465:Algorithms; D002138:Calibration; D057918:Fiducial Markers; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D025321:Surgery, Computer-Assisted / Q000379:methods*; D014463:Ultrasonography / Q000379:methods*
keywords: Calibration; Fiducial localization error; Guidance; Spatial stiffness model; Target registration error; Ultrasound; Virtual rigid lines phantom