A Framework for Calibration of Electromagnetic Surgical Navigation Systems

1
A Framework for Calibration of Electromagnetic
Surgical Navigation Systems

• Xiaohui Wu, Russell H. Taylor
• Peter Choe
• Paper Presentation
• Mentor Greg Fischer
• 4/1/2005

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Presentation Layout

• Project Recap
• Paper Selection
• Summary of Problem
• Background
• Papers Approach
• Mathematical Explanation
• Experimental Setup
• Results Conclusion

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Project Recap

• Characterization of Magnetic Distortion
• Optimal Aurora Sensor Orientations
• Construction of US Probe Sleeve w/ Aurora Sensors
  

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Paper Selection

• Reason
• Explains calibration techniques and mathematical
  approach
• Part of deliverables consist of distortion
  characterizations
• Experimental results show significant improvement
  in tracking accuracy for both position and
  orientation

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Background

• Why use Electromagnetic Trackers?
• No Line-of-Sight Restrictions
• Lightweight and Small
• Roughly Size of Volleyball
• Relatively Inexpensive Compared to Optical
  Tracker
• Small size of Sensors (Aurora)
• Ideal to be built in customized surgical
  instruments
• i.e. PICC (Peripherally Inserted Central
  Catheter)

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Summary of Problem

• Almost all electromagnetic trackers degraded by
  magnetic field distortions
• Use in OR difficult (metal objects)
• Most Calibration done in two methods
• Local Interpolation
• Faster
• Polynomial Fit (what our project does)
• Better overall Error Correction Quality

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Papers Approach

• Aim
• Present framework of calibrating Electromagnetic
  Tracker (Aurora)
• Mathematical Explanation
• Experiments / Results
• Future Aims / Problems
• What needs to be done and future studies

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Apparatus and Calibration

• Aurora Sensors Infrared light emitting diodes
  (IREDs)
• Aurora used with Optotrak
• Calibration (3 Steps)
• Optotrak Aurora Registration
• Aurora Error Field Construction
• Error Correction and Validation

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Mathematical Explanation

• Acquire multiple samples
• FOT(k) tranformation of Body IREDs wrt Aurora
  base
• Fm(i,k) 6DOF pos. orient of Aurora Sensor wrt
  Aurora Base
• Sample(k) FOT(k),FM(1,k),FM(1,NA)

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Calibration body calibration

• Purpose
• Determine coordinate transformation between
  coordinate system Aurora sensors on calibration
  body and coordinate system for IREDs
• FAreg Transformation between IREDs on Aurora
  base and base coordinate system wrt Aurora
  sensors
• FB(i) Transformation between body IRED coordinate
  system and individual Aurora sensors
• Relationship of between frames
• FAFm(i,k) FOT(k)FB(i)

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Mathematical Explanation
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Calibration Body Calibration

• Gather Data
• Acquire samples from NP different poses of
  calibration body
• System Simplification
• Define FC(i,k) FM(i,k)Fm(i,0)-1
• After simplification, FAFC(i,k) FD(k)FA
• RD(k)RA-1RC(i,k)RA
• Find an initial estimation of RA0 for RA
• Initial estimation of Ra can be computed
• Using Horns Quaternion method for point cloud
  registration
• q(k) RAr(k)

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Calibration Body Calibration

• Find accurate value of FA by iteration
• Compute FB(i)
• Horns Quaternion Point cloud registration

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Mathematical Registration Formulas
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Mathematical Registration Formulas
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Aurora Error Measurement

• For given measurement frame from Aurora
• Fi(Ri,Pi)
• Ground truth is Fi (Ri, Pi)
• Define error associated w/ Fi

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KD tree and Local Interpolation

• A lot like final programming assignment
• Bounding box
• First construct KD tree using calibration points
• Given Aurora position vector search the KD tree
  to find a cell containing the point
• Position error function and orientation error

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Polynomial Fit

• Just like Bernstein polynomial algorithms learned
  in class and Least Squares

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Experimental Setup
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Experimental Setup

• Optotrack
• Plastic Lego Robot
• Moves semi-statically within calibration space
• 3 DOF (x,y,z) usage to place combined rigid body
  in close to grid pattern.
• Rigid Body w/ 6 Optotrak IRED Markers
• 6D Aurora dynamic reference body

Pictures taken from 1 Optotrack picture taken
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Environmental Disturbances

• Equipment kept at least 1m away from Aurora base
  unit (specified by ND guideline)
• 10mm distance between Optotrack marker wires and
  Aurora sensors (noise below 0.1mm)

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Results

• Registration Results
• Semi-Static VS. Dynamic
• Latency between Optotrack and Aurora
• (operate on different frequencies)

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Results
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Importance

• Registration error proves that with latency
  compensation dynamic registration is almost as
  good as static.
• As polynomial order increases to 4 residual error
  decreases
• Afterwards holds steady
• Polynomial fit method yields more accurate
  results than KD tree local interpolation

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Problems

• Tracker calibration and dependance of tracker
  error on orientation
• Large amount of Data
• (to fully characterize this dependance, a 6D
  function will be needed for 6d sensors which is
  impractical)
• Experiments controlled static environment
• Real clinical scenario
• Electronic equipment, metal devices, etc.

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Next Steps

• Use similar setup suggested in the paper to do US
  probe tests
• Optotrack with Aurora in previously calibrated
  environment
• Registration methods (same will be used)
• Different orientations will be tested as well
  standard 6DOF used in paper.

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Conclusion / Assessment

• Very useful paper in understanding registration
  between Aurora/Optotrack and calibration
  techniques
• Magnetic Error still has yet to be characterized
  completely in real time situations (OR)
• Still hard to predict distortions in unknown
  situations

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References

• Xiaohui Wu, Russell H. Taylor, A Framework for
  Calibration of Electromagnetic Surgical
  Navigation Systems, Intelligent Robots and
  Systems, 2003. (IROS 2003). Proceedings. 2003
  IEEE/RSJ International Conference pg. 547 552
  Posted online 2003-12-08 103649.0
• N. Glossop, F. Banovac, E. Levy, D. Lindisch, K.
  Cleary, Accuracy Evaluation of the AURORA
  Magnetic Tracking System Presented at CARS 2001
  (Computer Assisted Radiology and Surgery), 15th
  International Congree and Exhibition, June 27-30,
  2001 ICC Berlin, Germany
• www.ahs.uwaterloo.ca/ carnahan/equipment.htm