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Presented by Márton Kelemen
Advisor: Tamás HaideggerBudapest University of Technology and
Economics, Hungary
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ØCIS, MIS, IGSØ Surgical tracking systems
Ø OpticalØ OpticalØ ElectromagneticØ Other modalities
ØPre-operative 3D-model of the patient(mostly MRI- or
CT-based)
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ØProvides a feedback to the surgeon
Ø If robot operates: the joint-variablesØ If robot operates: the
joint-variablesare well-known -> just for control(detect the
crash of incrementalencoders or the drift from the
initialregistration)
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1) To find the „optimal” representationfor
coordinate-transformation
2) Elaboration of a method, whichmakes us able to be more
precise bythe pose-estimation of the end-the pose-estimation of the
end-effector during the operation
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Ø Translation + rotation -> homogeneoustransformation
matrix
Ø Comparison between 4 well-knownrepresentations (Euler, RPY,
axis-angle and quaternion-based)quaternion-based)
Ø Examined their sensitivity for disturbancesand non-linear
distortions deriving + abilityfor interpolation (linear or
SLERP)
Ø Result: there aren’t significant differences, but the
quaternions are mathematically more favourable (matrix-operations,
no gimballock)
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0.3
0.35
0.4
0.45Euler-rotáció esetén a phi-szög átlagtól való eltérése és
szórása különböző nagyságú phi-szögekre, a zaj szórásának
függvényében
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.05
0
0.05
0.1
0.15
0.2
0.25
Normális eloszlású zaj szórása az elfordulási szögekre terhelve,
%-ban megadva
Phi
szö
g je
llem
zői [
°]
átlag, phi=0.5°szórás, phi=0.5°regressziós egyenes,
phi=0.5°átlag, phi=5°szórás, phi=5°regressziós egyenes,
phi=5°átlag, phi=45°szórás, phi=45°regressziós egyenes, phi=45°
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ØProblem: coupled disturbances can’tbe removed from useful
signal
ØGoal: increased accuracy of theestimated pose -> rise of
SNR
ØConsiderations:ØConsiderations:Ø Noise modeled with
Gaussian
distributionØ Process can be stationary or dinamicØ Filter
specification in the time domain
Ø 2 methods were examined:Ø Moving average smoothingØ Kalman
filtering
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ØLPF, where span ~ cut-off frequencyØWider window -> smoother
signal,
but worse dinamic characteristics(slow response time)
ØConclusion: only for stationary signals
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63.725
63.73
63.735
green = samples of a 7 Hz signalmagenta = averaged 7Hz signalred
= on value-changes
100 101 102 103 104 105 106 107 108 109 11063.7
63.705
63.71
63.715
63.72
changesaveraged 7 Hz signalblue = 60 Hz interpolated
redsignal
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Ø Optimal linear estimator, one-step predictor-corrector
algorithm
Ø Weighting between actual measured and formerly estimated value
during the Kalman gain
Ø State space modelState space modelØ Succeed in tracking
dinamic signals too, but with
overshoots can’t be admitted in surgicalapplications
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63.8
63.85
63.8
63.85
black = original signalblue = filtered signalred =
pre-estimatedsignal
15.5 16 16.5 17 17.5 18 18.563.6
63.65
63.7
63.75
15.5 16 16.5 17 17.5 18 18.563.6
63.65
63.7
63.75
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ØNot steadily acquired dataØLow resolution camera ->
certain
values exist during more samples (see 50100
150
200
250
50
100
150
200
250
values exist during more samples (seehistogram)
Ø Solution: only the value-changes aretaken into
consideration
ØRate changing (interpolation and decimation) – not integer
factor
0 5 10 15 20 25 30 35 40 45 5000 5 10 15 20 25 30 35 40 45
50
0
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ØEKF, UKF, Markov-chains, Monte Carlo simulation
Ø Sensor fusion, hybrid systemsØDevelopment of an intelligent
filter byØDevelopment of an intelligent filter by
means of a filter bank (event-basedestimation)
ØPhysical modelling (noise still can be removed?) – e.g. with
finite elementmethod by electromagneticdisturbances
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Ø Lantos – Robot control; Academic Publisher, Budapest 2001
Ø B. Danette Allen, Gary Bishop and Greg Welch – „Tracking:
Beyond 15 Minutes of Thought”; SIGGRAPH 2001, Course 11
Ø P. Grunnert, K. Darabi, j. Espinosa, R. Filippi –
„Computer-aidednavigation in neurosurgery”; Neurosurg Rev (2003)
26:73-99
Ø Andreas Tobergte, Mihai Pomarlan and Gerd Hirzinger – „Robust
Multi Sensor Pose Estimation for Medical Applications”; 2009 Multi
Sensor Pose Estimation for Medical Applications”; 2009 IEEE/RSJ
International Conference on Intelligent Robots and Systems
Ø Russell H. Taylor, Fellow, IEEE and Dan Stoianovici –
„MedicalRobotics in Computer-Integrated Surgery”; IEEE Transactions
OnRobotics And Automation, Vol. 19, Nr. 5., October 2003
Ø Gregory Scott Fischer – „Electromagnetic Tracker
Characterizationand Optimal Tool Design (with Applications to Ent
Surgery)”; John Hopkins University MSc Thesis, Baltimore, Maryland,
2005
Ø Verena Elisabeth Kremer – „Quaternions and SLERP”;
SeminarCharacter Animation, University of Saarbrücken, 2008
Ø http://www.ndigital.com/medical
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Thank you for your attention!
Any questions?
[email protected]
