Pozícióbecslési módszerek elemző összehasonlítása orvosi ... · Pozícióbecslési...
Transcript of Pozícióbecslési módszerek elemző összehasonlítása orvosi ... · Pozícióbecslési...
-
Presented by Márton Kelemen
Advisor: Tamás HaideggerBudapest University of Technology and Economics, Hungary
-
ØCIS, MIS, IGSØ Surgical tracking systems
Ø OpticalØ OpticalØ ElectromagneticØ Other modalities
ØPre-operative 3D-model of the patient(mostly MRI- or CT-based)
-
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)
-
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
-
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)
-
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°
-
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
-
ØLPF, where span ~ cut-off frequencyØWider window -> smoother signal,
but worse dinamic characteristics(slow response time)
ØConclusion: only for stationary signals
-
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
-
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
-
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
-
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
-
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
-
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
-
Thank you for your attention!
Any questions?