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Technical Brief

Effect of Calibration Error on Bone Tracking Accuracy With Fluoroscopy

[+] Author and Article Information
Luca Tersi

Health Sciences and Technologies - Interdepartmental
Center for Industrial Research (HST - ICIR),
University of Bologna,
Via Cavalcavia 797,
Cesena (FC) 47521, Italy
e-mail: luca.tersi@unibo.it

Rita Stagni

Assistant Professor
Health Sciences and Technologies - Interdepartmental
Center for Industrial Research (HST - ICIR),
University of Bologna,
Via Cavalcavia 797,
Cesena (FC) 47521, Italy;
Department of Electric,
Electronic and Information Engineering,
“Guglielmo Marconi” (DEI),
University of Bologna,
Viale Risorgimento 2,
Bologna 40136, Italy
e-mail: rita.stagni@unibo.it

1Corresponding author.

Manuscript received September 20, 2013; final manuscript received February 3, 2014; accepted manuscript posted March 6, 2014; published online April 10, 2014. Assoc. Editor: Paul Rullkoetter.

J Biomech Eng 136(5), 054502 (Apr 10, 2014) (5 pages) Paper No: BIO-13-1438; doi: 10.1115/1.4027058 History: Received September 20, 2013; Revised February 03, 2014; Accepted March 06, 2014

Model-based 3D-fluoroscopy can quantify joint kinematics with 1 mm and 1 deg accuracy level. A calibration based on the acquisition of devices of known geometry is usually applied to size the system. This study aimed at quantifying the sensitivity of the fluoroscopic pose estimation accuracy specifically to errors in the calibration process, excluding other sources of error. X-ray focus calibration error was quantified for different calibration setups, and its propagation to the pose estimation was characterized in-silico. Focus reference position influenced the calibration error dispersion, while calibration cage pose affected its bias. In the worst-case scenario, the estimation error of the principal point and of the focus distance was lower than 1 mm and 2 mm, respectively. The consequent estimation of joint angles was scarcely influenced by calibration errors. A linear trend was highlighted for joint translations, with a sensitivity proportional to the distance between the model and the image plane, resulting in a submillimeter error for realistic calibration errors. The biased component of the error is compensated when computing relative joint kinematics between two segments.

FIGURES IN THIS ARTICLE
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Copyright © 2014 by ASME
Topics: Bone , Calibration , Errors
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Figures

Grahic Jump Location
Fig. 1

reverse engineered cage model (a) with fiducial markers on the green plane, and control markers on blue plane. Panel (b) shows the cage markers projections, perturbed with Poisson noise. Black circles are the markers centers detected by Hough transform.

Grahic Jump Location
Fig. 2

Fluoroscope virtual outline (a), 3D bone model (humerus) is placed in reference pose (Pref), the relevant projected contour is generated from the focus Fref. Panel (b) represents the scene viewed from Fref (perfect correspondence between contour and bone model). The same scene is viewed from Fper (panel (c)), the matching is lost and automatic alignments will introduce pose estimation error.

Grahic Jump Location
Fig. 3

Box & whiskers plot of the calibration error grouped by focus reference position and cage pose. The whiskers extend to the most extreme data points not considered outliers.

Grahic Jump Location
Fig. 4

Box & whiskers plot of the translation estimation errors with respect to focus position perturbations (radius, worst-case scenario) for the reference poses with Tz = 200 mm. The whiskers extend to the most extreme data points not considered outliers. A linear correlation was highlighted along concordant directions (sensitivity in Table 3).

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