MARKERLESS TRACKING ERROR OF A BI-PLANAR X-RAY MOTION CAPTURE SYSTEM 1
1
Daniel L. Miranda, 2Joel B. Schwartz, 2Megan M. Dawson, 2Braden C. Fleming, and 2Joseph J. Crisco
Brown University and 2Department of Orthopaedics, The Warren Alpert Medical School of Brown University and Rhode Island Hospital, Providence, RI, USA email:
[email protected], web: http://www.brownbiomechanics.org
INTRODUCTION Three-dimensional (3-D) skeletal motion capture technology, such as X-ray Reconstruction of Moving Morphology (XROMM; Brown University, Providence, RI), currently employs a combination of bi-planar x-ray video and computed tomography (CT) to track dynamic 3-D skeletal movement in vivo with high accuracy [1]. Current tracking algorithms can be classified as markerbased tracking or markerless tracking. The invasive nature of marker-based tracking limits its applicability for studying in vivo human joint motion. Markerless tracking eliminates implantation of markers and uses tracking algorithms designed to match 3-D bone volumes to the bi-planar x-ray videos. Employing this technology to obtain quantitative data on human joint motion requires an understanding of its systematic error, herein referred to as “kinematic error”. The purpose of this study was to evaluate the kinematic error of a bi-planar x-ray motion capture system using a markerless tracking algorithm under static and dynamic motion conditions. METHODS The bi-planar XROMM facility consists of two Varian model G-1086 x-ray tubes, two EMD Technologies model EPS 45-80 pulsed x-ray generators, two 16” Dunlee model TH9447QXH590 image intensifiers (IIs), and two Phantom v9.1 highspeed digital video cameras. The resolution of the imaging chain is approximately 2 line pairs/mm. Markerless XROMM uses an auto-registration algorithm based on the work of You et al. [2] and Bey et al. [3] to recover the 3-D pose of the bones from the bi-planar x-ray videos using a clinical CT scan. Static error was evaluated by translating and rotating a set of human cadaver bones (distal femur, distal radius, and distal ulna) by known increments with high precision linear (RT-3 Series; Newmark
Systems, Mission Viejo, CA) and rotary (NB4 Series; Newmark Systems) positioning stages with accuracies of 0.001 mm and 0.002° (Fig. 1A). Figure. 1: A. Static accuracy testing jig including the specimen (i), mount plate (ii), rotary stage (iii), and linear stage (iv). The static stage assembly was rigidly fixed to a concrete pedestal for all static testing. B. Dynamic accuracy testing jig including the ADT (i), pendulum arm (ii), and rubber impact bumper (iii). The specimen displayed in A.i is attached to the far end of the pendulum arm. The pedulum arm is able to spin along the same axis as the mechanical axis of the ADT. The dynamic testing apparatus was rigidly fixed to a concrete pedestal. During testing, the rubber bumper impacted the concrete pedestal.
For each bone specimen, twenty trials of 15 linear motion steps (0.000, 0.001, 0.010, 0.100, 1.000, 10.000, 10.100, 25.000, 25.100, 50.000, 50.100, 75.000, 75.100, 100.000, and 100.100 mm) and 15 rotational motion steps (0, 0.002, 0.010, 0.100, 1.000, 10.000, 10.100, 25.000, 25.100, 50.000, 50.100, 75.000, 75.100, 100.000, and 100.100°) were performed. A reference position for the linear and rotational tests was determined at 0.000 mm and 0.000°, respectively. Dynamic error was evaluated using the specimens previously described. A pendulum was fabricated using a high precision (±0.06°) angular displacement transducer (ADT; Series 600 Angular Displacement Transducer, Trans-Tek Incorperated, Ellington, CT) (Fig. 1B). Five pendulum drop trials were performed for each trial where the pendulum arm was accelerated from rest. As the arm fell, it entered the field of view and impacted a concrete pedestal. The motion
of the arm and attached specimen were recorded. Additionally, an average reference position for each specimen was determined by collecting a stationary trial at the final resting position. The x-ray tube voltage and current were set at 70 kVp and 200 mA and the source to image distance (SID) was set to ~140 cm. For all static testing, the XROMM system recorded in pulsed (4 ms) x-ray generation mode at 60 frames-per-second (fps). During dynamic testing, the XROMM system recorded in continuous x-ray generation mode at 250 fps. Each high-speed video camera was shuttered between 1/1300 and 1/2000 s depending on the specimen. Kinematic error, defined as the difference between the measured rigid body motion (XROMM) and the true value of the parameter being measured (stages or ADT), was determined for every static and dynamic data point. These data are summarized using sample median, 25-75 percentile, and range statistics. Additionally, absolute error data are summarized using sample mean and standard deviation (SD) statistics. RESULTS
Figure 2: Left column Box and whiskers rotational (top) and linear (bottom) plot displaying range, 25-75 percentile, and median static error for each specimen. Right column Mean (+1 SD) rotational (top) and linear (bottom) absolute static error for each specimen.
The overall mean static rotational absolute error was estimated to be 0.30±0.18°, 0.39±0.32°, and 0.44±0.26° for the distal femur, distal radius, and distal ulna, respectively (Fig. 2). The overall mean static linear absolute error was estimated to be 0.25±0.16mm, 0.33±0.27mm, and 0.30±0.30mm for the distal femur, distal radius, and distal ulna, respectively (Fig. 2). The overall mean dynamic error was estimated to be 0.14±0.09°, 0.10±0.09°, and 0.14±0.12° for
the distal femur, distal radius, and distal ulna, respectively (Fig. 3).
Figure 3: Left column Box and whiskers plot displaying range, 25-75 percentile, and median dynamic error for each specimen. Right column Mean (+1 SD) absolute dynamic error for each specimen.
DISCUSSION Understanding the systematic error of individual bi-planar x-ray motion capture systems is important for understanding each system’s capabilities. Creating a method for quantifying error allows investigators to more easily determine study specific limitations. We determined that the overall dynamic error for the system lies between 0.1° and 0.15°, under the given testing conditions. We unexpectedly observed worse error for the static testing protocol as compared to the dynamic testing protocol. We postulate that is a result of the initialguess position required as input to the markerless tracking algorithm. During static testing, each frame (or trial) is tracked independent of the previous and succeeding trial. During dynamic testing, each frame uses position information from the previous (or succeeding) frame to determine the bone position at the current frame. Overall, these results are consistent with those of other 3-D skeletal motion capture technologies [3]. The markerless XROMM system that combines bi-planar x-ray video and CT data for measuring dynamic 3-D in vivo skeletal motion will permit novel, non-invasive studies on human joint function during dynamic tasks. Studies quantifying systematic error are critical first steps. REFERENCES 1. Brainerd EL, et al. J Exp Zool A Ecol Genet Physiol. 313(5), 262-79, 2010. 2. You BM, et al. IEEE Trans Med Imaging. 20(6), 514-25, 2001. 3. Bey MG, et al. J Biomech Eng. 128(4), 604-9, 2006. ACKNOWLEDGEMENTS This study was funded by the W.M. Keck Foundation.
