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Digital stereophotogrammetry based on circular markers and zooming cameras: evaluation of a method for 3D analysis of small motions in orthopaedic research.

Bobrowitsch E, Hurschler C, Olender G, Plaass C, Waizy H, Arnold H, Stukenborg-Colsman C - Biomed Eng Online (2011)

Bottom Line: The first experiment of the 10 mm distances measurement showed a total accuracy of 0.0086 mm and precision of ± 0.1002 mm.In the second experiment, translations from 0.5 mm to 5 mm were measured with total accuracy of 0.0038 mm and precision of ± 0.0461 mm.The rotations of 2.25° amount were measured with the entire accuracy of 0.058° and the precision was of ± 0.172°.

View Article: PubMed Central - HTML - PubMed

Affiliation: Laboratory for Biomechanics and Biomaterials, Department of Orthopaedic Surgery, Hannover Medical School, Germany. evgenij.bobrowitsch@yahoo.de

ABSTRACT

Background: Orthopaedic research projects focusing on small displacements in a small measurement volume require a radiation free, three dimensional motion analysis system. A stereophotogrammetrical motion analysis system can track wireless, small, light-weight markers attached to the objects. Thereby the disturbance of the measured objects through the marker tracking can be kept at minimum. The purpose of this study was to develop and evaluate a non-position fixed compact motion analysis system configured for a small measurement volume and able to zoom while tracking small round flat markers in respect to a fiducial marker which was used for the camera pose estimation.

Methods: The system consisted of two web cameras and the fiducial marker placed in front of them. The markers to track were black circles on a white background. The algorithm to detect a centre of the projected circle on the image plane was described and applied. In order to evaluate the accuracy (mean measurement error) and precision (standard deviation of the measurement error) of the optical measurement system, two experiments were performed: 1) inter-marker distance measurement and 2) marker displacement measurement.

Results: The first experiment of the 10 mm distances measurement showed a total accuracy of 0.0086 mm and precision of ± 0.1002 mm. In the second experiment, translations from 0.5 mm to 5 mm were measured with total accuracy of 0.0038 mm and precision of ± 0.0461 mm. The rotations of 2.25° amount were measured with the entire accuracy of 0.058° and the precision was of ± 0.172°.

Conclusions: The description of the non-proprietary measurement device with very good levels of accuracy and precision may provide opportunities for new, cost effective applications of stereophotogrammetrical analysis in musculoskeletal research projects, focusing on kinematics of small displacements in a small measurement volume.

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Schematic diagram of the circle centre determination. Elliptical projection Π of the real imaged circle Kr and imaginary circle Ki on the XY-image plane with correspondent centres in cr and ci, /AB/ = 2a, /CD/ = 2b, ∠ABA' = ∠BAB' = γ, the distance between the projection centre O and the XY-plane is equal to d. The bisecting line of the cone with the basis Π on the XY-plane and the top in the perspective projection centre O coincided with the Z-axis. See the text for explanation.
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Figure 2: Schematic diagram of the circle centre determination. Elliptical projection Π of the real imaged circle Kr and imaginary circle Ki on the XY-image plane with correspondent centres in cr and ci, /AB/ = 2a, /CD/ = 2b, ∠ABA' = ∠BAB' = γ, the distance between the projection centre O and the XY-plane is equal to d. The bisecting line of the cone with the basis Π on the XY-plane and the top in the perspective projection centre O coincided with the Z-axis. See the text for explanation.

Mentions: When considering the cone with the basis Πi on the image plane and the top in the perspective projection centre O, was defined as the unit vector of the bisecting line of this cone from O to Πi. We rotated the cone about O till the cone bisecting line coincided with the image Z-axis. The rotation matrix described this rotation, where was the unit vector derived from the cross product of with the image Z-axes and β was the angle between them. The intersection of the rotated cone with the image XY-plane was an ellipse Π(c,a,b,α) (Figure 2). If a = b the ellipse Π was a circle and the normal vector of the circle-plane was the same as the image Z-axis. The angle γ between the circle-plane and the image XY-plane was in this case equal to zero.


Digital stereophotogrammetry based on circular markers and zooming cameras: evaluation of a method for 3D analysis of small motions in orthopaedic research.

Bobrowitsch E, Hurschler C, Olender G, Plaass C, Waizy H, Arnold H, Stukenborg-Colsman C - Biomed Eng Online (2011)

Schematic diagram of the circle centre determination. Elliptical projection Π of the real imaged circle Kr and imaginary circle Ki on the XY-image plane with correspondent centres in cr and ci, /AB/ = 2a, /CD/ = 2b, ∠ABA' = ∠BAB' = γ, the distance between the projection centre O and the XY-plane is equal to d. The bisecting line of the cone with the basis Π on the XY-plane and the top in the perspective projection centre O coincided with the Z-axis. See the text for explanation.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3038981&req=5

Figure 2: Schematic diagram of the circle centre determination. Elliptical projection Π of the real imaged circle Kr and imaginary circle Ki on the XY-image plane with correspondent centres in cr and ci, /AB/ = 2a, /CD/ = 2b, ∠ABA' = ∠BAB' = γ, the distance between the projection centre O and the XY-plane is equal to d. The bisecting line of the cone with the basis Π on the XY-plane and the top in the perspective projection centre O coincided with the Z-axis. See the text for explanation.
Mentions: When considering the cone with the basis Πi on the image plane and the top in the perspective projection centre O, was defined as the unit vector of the bisecting line of this cone from O to Πi. We rotated the cone about O till the cone bisecting line coincided with the image Z-axis. The rotation matrix described this rotation, where was the unit vector derived from the cross product of with the image Z-axes and β was the angle between them. The intersection of the rotated cone with the image XY-plane was an ellipse Π(c,a,b,α) (Figure 2). If a = b the ellipse Π was a circle and the normal vector of the circle-plane was the same as the image Z-axis. The angle γ between the circle-plane and the image XY-plane was in this case equal to zero.

Bottom Line: The first experiment of the 10 mm distances measurement showed a total accuracy of 0.0086 mm and precision of ± 0.1002 mm.In the second experiment, translations from 0.5 mm to 5 mm were measured with total accuracy of 0.0038 mm and precision of ± 0.0461 mm.The rotations of 2.25° amount were measured with the entire accuracy of 0.058° and the precision was of ± 0.172°.

View Article: PubMed Central - HTML - PubMed

Affiliation: Laboratory for Biomechanics and Biomaterials, Department of Orthopaedic Surgery, Hannover Medical School, Germany. evgenij.bobrowitsch@yahoo.de

ABSTRACT

Background: Orthopaedic research projects focusing on small displacements in a small measurement volume require a radiation free, three dimensional motion analysis system. A stereophotogrammetrical motion analysis system can track wireless, small, light-weight markers attached to the objects. Thereby the disturbance of the measured objects through the marker tracking can be kept at minimum. The purpose of this study was to develop and evaluate a non-position fixed compact motion analysis system configured for a small measurement volume and able to zoom while tracking small round flat markers in respect to a fiducial marker which was used for the camera pose estimation.

Methods: The system consisted of two web cameras and the fiducial marker placed in front of them. The markers to track were black circles on a white background. The algorithm to detect a centre of the projected circle on the image plane was described and applied. In order to evaluate the accuracy (mean measurement error) and precision (standard deviation of the measurement error) of the optical measurement system, two experiments were performed: 1) inter-marker distance measurement and 2) marker displacement measurement.

Results: The first experiment of the 10 mm distances measurement showed a total accuracy of 0.0086 mm and precision of ± 0.1002 mm. In the second experiment, translations from 0.5 mm to 5 mm were measured with total accuracy of 0.0038 mm and precision of ± 0.0461 mm. The rotations of 2.25° amount were measured with the entire accuracy of 0.058° and the precision was of ± 0.172°.

Conclusions: The description of the non-proprietary measurement device with very good levels of accuracy and precision may provide opportunities for new, cost effective applications of stereophotogrammetrical analysis in musculoskeletal research projects, focusing on kinematics of small displacements in a small measurement volume.

Show MeSH