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Motion capture system validation with surveying techniques
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 26501–26506
www.materialstoday.com/proceedings
DAS_2017
Motion capture system validation with surveying techniques Gergely Nagymátéa, Rita M. Kissa* a
Budapest University of Technology and Economics, Faculty of Mechanical Engineering Dept of Mechatronics, Optics and Mechanical Engineering Informatics, Műegyetem rkp 3., Budapest 1111, Hungary
Abstract Motion capture systems are widely used in biomechanics, thus users must consider system errors when evaluating their results. The usually applied validation techniques of these systems are based on relative distance measurements. In contrast, our study aimed to analyse the absolute volume accuracy of an optical motion capture system composed of 18 OptiTrack Flex13 cameras with external reference points that were calibrated using surveying methods. Calibration was based on a geodetic reference network. We demonstrated the benefits of using this method compared to the validation based on relative distance measurements, and we determined the absolute accuracy that describes the difference between the reference and measured coordinates of the markers from the geodetic and OptiTrack coordinate systems, respectively. Camera number dependency of precision expressed by the static detection noise of the marker coordinates was also quantified. The absolute accuracy provided a root-mean-square error (RMSE) of 1.735 mm owing to improper extrinsic calibration, a scaling error that is undetected by conventional validation techniques. The observed noise was in a sub-millimeter range, and showed progressive improvement up to 15 cameras. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of the Committee Members of 34th DANUBIA ADRIA SYMPOSIUM on Advances in Experimental Mechanics (DAS 2017). Keywords: motion capture; validation; absolute accuracy; scale error
* Corresponding author. Tel.: +36 20 458 7518. E-mail address: [email protected] 2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of the Committee Members of 34th DANUBIA ADRIA SYMPOSIUM on Advances in Experimental Mechanics (DAS 2017).
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Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
1. Introduction Optical motion capture systems are widely used in biomechanics. Studies with motion capture measurements should always consider system errors when evaluating their results, but it is rarely done. Validation studies evaluate the accuracy of motion capture systems in the form of measuring the detected deviations of coordinate distances of rigidly fixed markers at various places of the measuring volume [1-4], or by measuring small relative translations [5] performed by robotic equipment. These first methods are capable to detect dynamic errors around the capture volume while the latter method is capable to quantify the precision of the motion capture system at small distances. None of the known methods are suitable to measure the absolute accuracy of a motion capture system in large measurement volumes. The present study aims to analyze the absolute volume accuracy of an 18 camera OptiTrack Flex13 motion capture system using geodetic-surveying techniques. 2. Methods 2.1. Setup The evaluated system consists of 18 Optitrack Flex13 cameras (NaturalPoint, Corvallis, OR, USA) connected to a computer via three USB hubs. The cameras were equidistantly located around a room using a wall-mounted console at 3 m above the floor (Fig. 1.). The field of view of each camera was aligned to the floor. We operated the camera system for recording data and calibration with an OptiTrack 500 mm standard calibration wand and the Motive v1.10.3 software (NaturalPoint, Corvallis, OR, USA) for 30s at 120 Hz. The experimental setup was employed in the Motion Analysis Laboratory of the Department of Mechatronics, Optics and Mechanical Engineering Informatics at the Budapest University of Technology and Economics in Hungary. The room where the OptiTrack system was installed has permanently darkened windows to avoid infrared (IR) interference caused by sunlight. The independent control network used for the quality control of the OptiTrack system was created as a 0.5m raster grid with the total dimension of 4m x 2.5m. The grid points of the control network were set by using a Leica TS15i 1” Total station. The local coordinate system was aligned with the orientation of the grid. We considered it important to check the marked control points with independent measurements. The coordinates of the two independent observations were compared, and the mean three dimensional coordinate residual between the two measurements was 0.758 (SD: 0.315) mm. The final coordinates of the control points were calculated as the mean value of the two coordinate measurements. Thus it can be stated that the accuracy of the coordinates of the control network is below 1mm. The complete setup with the camera arrangement and the geodetic reference points is shown in Fig. 1., where the values indicate the number of cameras pointing at the corresponding geodetic points.
Fig.1. Camera system layout and geodetic reference points (left), where the values indicate the number of cameras pointing at each location. Real camera system setup (right)
Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
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2.2. Measurement protocol The system was warmed up for 30 minutes before each measurement, and then it was calibrated using the standard 500 mm OptiTrack calibration wand (CW-500) and the OptiTrack Motive 1.10.3 software. The calibration proceeded until each camera acquired at least 2000 samples and the calibration quality feedback in the software indicated an excellent calibration. Measurements were taken using these individual calibrations. Given that the OptiTrack system only detects IR light and the cameras are equipped with IR illumination, we used brand new OptiTrack retro reflective markers with a diameter of 8 mm for all the measurements. These markers were placed on the geodetic reference points onto their bore on the bottom with the largest possible human precision to measure the reference positions by the OptiTrack system (Fig. 2.). However, this process includes human inaccuracy on the placement of the markers. Therefore - to give a statistical basis for marker placement - the whole process was repeated by four people, 10 repetitions each. The average coordinates of the 40 repetitions of each calibrated reference point will approach the true position of the reference points. Measurements were recorded in the Motive software (NaturalPoint, OR, USA) for 30 seconds, at 120 Hz.
Fig.2. IR marker placed on the geodetic reference point.
2.3. Determination of absolute accuracy The absolute accuracy of the system is characterized by the mean standard deviation of the distance and RMSE between the geodetic reference coordinates and the mean of the repeatedly measured coordinates by the OptiTrack camera system. Hence, this comparison requires the geodetic and the OptiTrack coordinates to be represented in the same system. The OptiTrack coordinate system can be arbitrarily located using three markers: one that determines the origin, another located on the X axis, and the third on the X–Z plane. Thus, we used three of the geodetic reference points to define a simple transformation between the geodetic and the OptiTrack coordinate systems. For the geodetic raster grid to be aligned with the geodetic coordinate system, we performed two translations and a –90° rotation around the X axis. We calculated the RMSE as
RMSE
1 m geo opt 2 xi xi yigeo yiopt m i1
2
(1)
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Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
where xgeo and ygeo are the coordinates of the reference points determined by the geodetic method, ݔҧ opt and ݕതopt are the mean measured coordinates by the OptiTrack system represented in the common coordinate system, and m is the number of measured points. 2.4. Analysis of precision and its camera number dependency Precision is related to the coordinate fluctuation of the markers at rest over time. It is defined by the standard deviation of the 3D marker position. It is further characterized by the largest instantaneous deviations from the mean of static marked coordinate detections, also referenced as the largest 3D deviation. The camera number dependency of precision was analyzed on a single trial. In post processing, unused cameras were disabled and a 3D reconstruction of the markers was performed on a limited number of cameras. The reconstructions were performed from two to eighteen cameras, re-enabling the cameras in reconstruction in an order to possibly always earn uniform camera distribution around the studied points. In this context, the average largest 3D displacement for 8 points was calculated as a measure of camera dependent precision. The eight points were selected because those were visible by all the 18 cameras. Therefore, camera number dependency could be tested up to 18 cameras. In contrast, the least visible unused reference points were seen by 12 cameras on the corners of the measurement area. 3. Results 3.1. Absolute accuracy Results of the comparison of reference coordinates and measured average coordinates of the markers showed significantly larger deviations than the reliability of the reference coordinates. The errors are characterized by RMS deviation: 1.735 mm, average deviation: 1.576 (SD: 0.733 mm) and maximum deviation: 3.072 mm. Deviations of the marker coordinates from the reference coordinates showed strong correlation to their distance from the reference frame origin (correlation: 0.81). This highly positive correlation suggested that there must be a scaling factor behind the observed errors as seemingly the virtual space is a bit larger than the real space. The observed average error vectors of each measured point are indicated in Fig. 3. Error vectors are displayed in hundredfold magnification for sufficient visibility.
Fig. 3. 2D deviation vectors of the detected average marker coordinates and of the geodetic references. Vector magnitudes are scaled with 100% for visibility.
Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
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3.2. Camera number dependency of precision Epipolar geometry allows the coordinate calculation of markers from two camera images, but this results in significantly larger mean and maximal deviation values in the coordinate fluctuation. Maximum 3D coordinate deviation progressively improves by increasing the camera number up to 15 cameras. The graphical representation of camera dependent values is displayed in Fig. 4. The total largest deviation can be observed with only 2 cameras; it is larger than 0.35 mm (Fig. 4., right), but this is the most extreme deviation from 28,800 samples (8 points, 30 second measurements at 120 Hz). The average largest deviations are below 0.15 mm starting from 3 cameras (Fig. 4., right). Precision - that is, the standard deviation of 3D coordinate deviations from the average coordinates shows a similarly improving trend along with the camera number, but the curve is flatter and far below the former maximum deviations. Precision in the worst case - as the largest standard deviation of the detected 3D displacement of motionless markers - is below 0.1 mm with every camera number, and the average standard deviation is below 0.05 mm (Fig. 4., left).
Fig. 4. Average camera dependent precision, also known as 3D standard deviation (left), and the largest instantaneous deviations from the mean of static marked coordinate detections, also known as the largest 3D deviation (right) with ranges for eight markers. Dots are to mark the average value for the eight markers.
4. Discussion The study analyzed the absolute accuracy of a 18 camera OptiTrack Flex 13 motion capture system using geodetic reference points, which method is capable to detect inaccuracies of the system that are undetectable using conventional camera system validation methods. A distance dependent distortion in the measurement volume was detected that is owed to scaling errors that can be compensated after detection. Compared to the geodetic reference network, methods based on computer-controlled motorized relativedisplacement measurement might be more precise, but they are usually applicable for small-scale motions [5, 6]. Aurand et al. [6] studied precision in a large measurement volume. However, they only performed relative motions along one axis and no longer than 100 mm at different locations of the capture volume. No validation for largerscale measurements has been presented in the literature. In contrast, our method is suitable to analyse the absolute accuracy of an optical motion capture system in both small and large capture volumes. Another contribution of the proposed method for absolute accuracy measurement is the capability to evince system scale errors that cannot be detected with other available methods. Furthermore, our method provides the error vectors for the measurement area in a single measurement. Thus, the position-dependent accuracy of the capture volume can be really observed as emphasised by Eichelberger et al. [7] and Windolf et al. [5]. For relative distance error measurements [1 - 4], the same distortion applies to both markers; and the scale error in measurements of large volumes cannot be detected. This is also valid for small-scale relative displacement
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Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
measurements [5, 6], where the measurement positions are evenly distorted, and thus, the corresponding error is not detectable from the marker coordinates. In our study we measured this static coordinate noise of single markers as a function of the number of cameras used. While the precision improved up to 15 cameras (Fig. 4.), there is an observable decrease of precision when further cameras are introduced. The most likely explanation for this is that the sixteenth camera was slightly out of calibration, and negatively influenced the whole system. Both average noise and largest deviations from the average coordinates were sub-millimeter ranges, consequently representing a quite negligible static noise for both human motion capture and robotic applications. The limitations of the study are that the measurements only studied the coordinate of markers in a single plane, and the 3D characteristics of scale error have not yet been studied. Another limitation is the human error of marker placement. 5. Conclusion This study analysed the absolute accuracy and precision of a motion capture system consisting of 18 OptiTrack Flex13 cameras. Precision was expressed by the static noise of marker coordinates and was studied with respect to camera numbers. The observed noise was in a sub-millimeter range, and showed progressive improvement up to 15 cameras. We used geodetic surveying methods for large-scale absolute accuracy measurements. Using the proposed method, scale errors in the millimeter range can be detected. These errors are undetectable by using other conventional validation methods. Similar validations should be performed on every camera system that is used for precise robotic or human motion analysis. Acknowledgements This work was supported by the Hungarian Scientific Research Fund OTKA [grant number K115894]; and the New National Excellence Program of the Hungarian Ministry of Human Resources [grant number ÚNKP-17- 3-I]. References [1] B. Carse, B. Meadows, R. Bowers, and P. Rowe, Affordable clinical gait analysis: An assessment of the marker tracking accuracy of a new low-cost optical 3D motion analysis system, Physiother. (United Kingdom), vol. 99, no. 4, pp. 347–351, 2013. [2] Y. Ehara, H. Fujimoto, S. Miyazaki, M. Mochimaru, S. Tanaka, and S. Yamamoto, Comparison of the performance of 3D camera systems II, Gait Posture, vol. 5, no. 3, pp. 251–255, 1997. [3] Y. Ehara, H. Fujimoto, S. Miyazaki, S. Tanaka, and S. Yamamoto, Comparison of the performance of 3D camera systems, Gait Posture, vol. 3, no. 3, pp. 166–169, 1995. [4] D. Thewlis, C. Bishop, N. Daniell, and G. Paul, Next-generation low-cost motion capture systems can provide comparable spatial accuracy to high-end systems, J. Appl. Biomech., vol. 29, no. 1, pp. 112–117, 2013. [5] M. Windolf, N. Götzen, and M. Morlock, Systematic accuracy and precision analysis of video motion capturing systems-exemplified on the Vicon-460 system, J. Biomech., vol. 41, no. 12, pp. 2776–2780, 2008. [6] Aurand, A.M., Dufour, J.S., Marras, W.S., 2017. Accuracy map of an optical motion capture system with 42 or 21 cameras in a large measurement volume. J. Biomech. 58, 237–240. [7] Eichelberger, P., Ferraro, M., Minder, U., Denton, T., Blasimann, A., Krause, F., Baur, H., 2016. Analysis of accuracy in optical motion capture – A protocol for laboratory setup evaluation. J. Biomech. 49, 2085–2088
ScienceDirect Materials Today: Proceedings 5 (2018) 26501–26506
www.materialstoday.com/proceedings
DAS_2017
Motion capture system validation with surveying techniques Gergely Nagymátéa, Rita M. Kissa* a
Budapest University of Technology and Economics, Faculty of Mechanical Engineering Dept of Mechatronics, Optics and Mechanical Engineering Informatics, Műegyetem rkp 3., Budapest 1111, Hungary
Abstract Motion capture systems are widely used in biomechanics, thus users must consider system errors when evaluating their results. The usually applied validation techniques of these systems are based on relative distance measurements. In contrast, our study aimed to analyse the absolute volume accuracy of an optical motion capture system composed of 18 OptiTrack Flex13 cameras with external reference points that were calibrated using surveying methods. Calibration was based on a geodetic reference network. We demonstrated the benefits of using this method compared to the validation based on relative distance measurements, and we determined the absolute accuracy that describes the difference between the reference and measured coordinates of the markers from the geodetic and OptiTrack coordinate systems, respectively. Camera number dependency of precision expressed by the static detection noise of the marker coordinates was also quantified. The absolute accuracy provided a root-mean-square error (RMSE) of 1.735 mm owing to improper extrinsic calibration, a scaling error that is undetected by conventional validation techniques. The observed noise was in a sub-millimeter range, and showed progressive improvement up to 15 cameras. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of the Committee Members of 34th DANUBIA ADRIA SYMPOSIUM on Advances in Experimental Mechanics (DAS 2017). Keywords: motion capture; validation; absolute accuracy; scale error
* Corresponding author. Tel.: +36 20 458 7518. E-mail address: [email protected] 2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of the Committee Members of 34th DANUBIA ADRIA SYMPOSIUM on Advances in Experimental Mechanics (DAS 2017).
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Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
1. Introduction Optical motion capture systems are widely used in biomechanics. Studies with motion capture measurements should always consider system errors when evaluating their results, but it is rarely done. Validation studies evaluate the accuracy of motion capture systems in the form of measuring the detected deviations of coordinate distances of rigidly fixed markers at various places of the measuring volume [1-4], or by measuring small relative translations [5] performed by robotic equipment. These first methods are capable to detect dynamic errors around the capture volume while the latter method is capable to quantify the precision of the motion capture system at small distances. None of the known methods are suitable to measure the absolute accuracy of a motion capture system in large measurement volumes. The present study aims to analyze the absolute volume accuracy of an 18 camera OptiTrack Flex13 motion capture system using geodetic-surveying techniques. 2. Methods 2.1. Setup The evaluated system consists of 18 Optitrack Flex13 cameras (NaturalPoint, Corvallis, OR, USA) connected to a computer via three USB hubs. The cameras were equidistantly located around a room using a wall-mounted console at 3 m above the floor (Fig. 1.). The field of view of each camera was aligned to the floor. We operated the camera system for recording data and calibration with an OptiTrack 500 mm standard calibration wand and the Motive v1.10.3 software (NaturalPoint, Corvallis, OR, USA) for 30s at 120 Hz. The experimental setup was employed in the Motion Analysis Laboratory of the Department of Mechatronics, Optics and Mechanical Engineering Informatics at the Budapest University of Technology and Economics in Hungary. The room where the OptiTrack system was installed has permanently darkened windows to avoid infrared (IR) interference caused by sunlight. The independent control network used for the quality control of the OptiTrack system was created as a 0.5m raster grid with the total dimension of 4m x 2.5m. The grid points of the control network were set by using a Leica TS15i 1” Total station. The local coordinate system was aligned with the orientation of the grid. We considered it important to check the marked control points with independent measurements. The coordinates of the two independent observations were compared, and the mean three dimensional coordinate residual between the two measurements was 0.758 (SD: 0.315) mm. The final coordinates of the control points were calculated as the mean value of the two coordinate measurements. Thus it can be stated that the accuracy of the coordinates of the control network is below 1mm. The complete setup with the camera arrangement and the geodetic reference points is shown in Fig. 1., where the values indicate the number of cameras pointing at the corresponding geodetic points.
Fig.1. Camera system layout and geodetic reference points (left), where the values indicate the number of cameras pointing at each location. Real camera system setup (right)
Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
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2.2. Measurement protocol The system was warmed up for 30 minutes before each measurement, and then it was calibrated using the standard 500 mm OptiTrack calibration wand (CW-500) and the OptiTrack Motive 1.10.3 software. The calibration proceeded until each camera acquired at least 2000 samples and the calibration quality feedback in the software indicated an excellent calibration. Measurements were taken using these individual calibrations. Given that the OptiTrack system only detects IR light and the cameras are equipped with IR illumination, we used brand new OptiTrack retro reflective markers with a diameter of 8 mm for all the measurements. These markers were placed on the geodetic reference points onto their bore on the bottom with the largest possible human precision to measure the reference positions by the OptiTrack system (Fig. 2.). However, this process includes human inaccuracy on the placement of the markers. Therefore - to give a statistical basis for marker placement - the whole process was repeated by four people, 10 repetitions each. The average coordinates of the 40 repetitions of each calibrated reference point will approach the true position of the reference points. Measurements were recorded in the Motive software (NaturalPoint, OR, USA) for 30 seconds, at 120 Hz.
Fig.2. IR marker placed on the geodetic reference point.
2.3. Determination of absolute accuracy The absolute accuracy of the system is characterized by the mean standard deviation of the distance and RMSE between the geodetic reference coordinates and the mean of the repeatedly measured coordinates by the OptiTrack camera system. Hence, this comparison requires the geodetic and the OptiTrack coordinates to be represented in the same system. The OptiTrack coordinate system can be arbitrarily located using three markers: one that determines the origin, another located on the X axis, and the third on the X–Z plane. Thus, we used three of the geodetic reference points to define a simple transformation between the geodetic and the OptiTrack coordinate systems. For the geodetic raster grid to be aligned with the geodetic coordinate system, we performed two translations and a –90° rotation around the X axis. We calculated the RMSE as
RMSE
1 m geo opt 2 xi xi yigeo yiopt m i1
2
(1)
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Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
where xgeo and ygeo are the coordinates of the reference points determined by the geodetic method, ݔҧ opt and ݕതopt are the mean measured coordinates by the OptiTrack system represented in the common coordinate system, and m is the number of measured points. 2.4. Analysis of precision and its camera number dependency Precision is related to the coordinate fluctuation of the markers at rest over time. It is defined by the standard deviation of the 3D marker position. It is further characterized by the largest instantaneous deviations from the mean of static marked coordinate detections, also referenced as the largest 3D deviation. The camera number dependency of precision was analyzed on a single trial. In post processing, unused cameras were disabled and a 3D reconstruction of the markers was performed on a limited number of cameras. The reconstructions were performed from two to eighteen cameras, re-enabling the cameras in reconstruction in an order to possibly always earn uniform camera distribution around the studied points. In this context, the average largest 3D displacement for 8 points was calculated as a measure of camera dependent precision. The eight points were selected because those were visible by all the 18 cameras. Therefore, camera number dependency could be tested up to 18 cameras. In contrast, the least visible unused reference points were seen by 12 cameras on the corners of the measurement area. 3. Results 3.1. Absolute accuracy Results of the comparison of reference coordinates and measured average coordinates of the markers showed significantly larger deviations than the reliability of the reference coordinates. The errors are characterized by RMS deviation: 1.735 mm, average deviation: 1.576 (SD: 0.733 mm) and maximum deviation: 3.072 mm. Deviations of the marker coordinates from the reference coordinates showed strong correlation to their distance from the reference frame origin (correlation: 0.81). This highly positive correlation suggested that there must be a scaling factor behind the observed errors as seemingly the virtual space is a bit larger than the real space. The observed average error vectors of each measured point are indicated in Fig. 3. Error vectors are displayed in hundredfold magnification for sufficient visibility.
Fig. 3. 2D deviation vectors of the detected average marker coordinates and of the geodetic references. Vector magnitudes are scaled with 100% for visibility.
Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
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3.2. Camera number dependency of precision Epipolar geometry allows the coordinate calculation of markers from two camera images, but this results in significantly larger mean and maximal deviation values in the coordinate fluctuation. Maximum 3D coordinate deviation progressively improves by increasing the camera number up to 15 cameras. The graphical representation of camera dependent values is displayed in Fig. 4. The total largest deviation can be observed with only 2 cameras; it is larger than 0.35 mm (Fig. 4., right), but this is the most extreme deviation from 28,800 samples (8 points, 30 second measurements at 120 Hz). The average largest deviations are below 0.15 mm starting from 3 cameras (Fig. 4., right). Precision - that is, the standard deviation of 3D coordinate deviations from the average coordinates shows a similarly improving trend along with the camera number, but the curve is flatter and far below the former maximum deviations. Precision in the worst case - as the largest standard deviation of the detected 3D displacement of motionless markers - is below 0.1 mm with every camera number, and the average standard deviation is below 0.05 mm (Fig. 4., left).
Fig. 4. Average camera dependent precision, also known as 3D standard deviation (left), and the largest instantaneous deviations from the mean of static marked coordinate detections, also known as the largest 3D deviation (right) with ranges for eight markers. Dots are to mark the average value for the eight markers.
4. Discussion The study analyzed the absolute accuracy of a 18 camera OptiTrack Flex 13 motion capture system using geodetic reference points, which method is capable to detect inaccuracies of the system that are undetectable using conventional camera system validation methods. A distance dependent distortion in the measurement volume was detected that is owed to scaling errors that can be compensated after detection. Compared to the geodetic reference network, methods based on computer-controlled motorized relativedisplacement measurement might be more precise, but they are usually applicable for small-scale motions [5, 6]. Aurand et al. [6] studied precision in a large measurement volume. However, they only performed relative motions along one axis and no longer than 100 mm at different locations of the capture volume. No validation for largerscale measurements has been presented in the literature. In contrast, our method is suitable to analyse the absolute accuracy of an optical motion capture system in both small and large capture volumes. Another contribution of the proposed method for absolute accuracy measurement is the capability to evince system scale errors that cannot be detected with other available methods. Furthermore, our method provides the error vectors for the measurement area in a single measurement. Thus, the position-dependent accuracy of the capture volume can be really observed as emphasised by Eichelberger et al. [7] and Windolf et al. [5]. For relative distance error measurements [1 - 4], the same distortion applies to both markers; and the scale error in measurements of large volumes cannot be detected. This is also valid for small-scale relative displacement
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Nagymáté et al. / Materials Today: Proceedings 5 (2018) 26501–26506
measurements [5, 6], where the measurement positions are evenly distorted, and thus, the corresponding error is not detectable from the marker coordinates. In our study we measured this static coordinate noise of single markers as a function of the number of cameras used. While the precision improved up to 15 cameras (Fig. 4.), there is an observable decrease of precision when further cameras are introduced. The most likely explanation for this is that the sixteenth camera was slightly out of calibration, and negatively influenced the whole system. Both average noise and largest deviations from the average coordinates were sub-millimeter ranges, consequently representing a quite negligible static noise for both human motion capture and robotic applications. The limitations of the study are that the measurements only studied the coordinate of markers in a single plane, and the 3D characteristics of scale error have not yet been studied. Another limitation is the human error of marker placement. 5. Conclusion This study analysed the absolute accuracy and precision of a motion capture system consisting of 18 OptiTrack Flex13 cameras. Precision was expressed by the static noise of marker coordinates and was studied with respect to camera numbers. The observed noise was in a sub-millimeter range, and showed progressive improvement up to 15 cameras. We used geodetic surveying methods for large-scale absolute accuracy measurements. Using the proposed method, scale errors in the millimeter range can be detected. These errors are undetectable by using other conventional validation methods. Similar validations should be performed on every camera system that is used for precise robotic or human motion analysis. Acknowledgements This work was supported by the Hungarian Scientific Research Fund OTKA [grant number K115894]; and the New National Excellence Program of the Hungarian Ministry of Human Resources [grant number ÚNKP-17- 3-I]. References [1] B. Carse, B. Meadows, R. Bowers, and P. Rowe, Affordable clinical gait analysis: An assessment of the marker tracking accuracy of a new low-cost optical 3D motion analysis system, Physiother. (United Kingdom), vol. 99, no. 4, pp. 347–351, 2013. [2] Y. Ehara, H. Fujimoto, S. Miyazaki, M. Mochimaru, S. Tanaka, and S. Yamamoto, Comparison of the performance of 3D camera systems II, Gait Posture, vol. 5, no. 3, pp. 251–255, 1997. [3] Y. Ehara, H. Fujimoto, S. Miyazaki, S. Tanaka, and S. Yamamoto, Comparison of the performance of 3D camera systems, Gait Posture, vol. 3, no. 3, pp. 166–169, 1995. [4] D. Thewlis, C. Bishop, N. Daniell, and G. Paul, Next-generation low-cost motion capture systems can provide comparable spatial accuracy to high-end systems, J. Appl. Biomech., vol. 29, no. 1, pp. 112–117, 2013. [5] M. Windolf, N. Götzen, and M. Morlock, Systematic accuracy and precision analysis of video motion capturing systems-exemplified on the Vicon-460 system, J. Biomech., vol. 41, no. 12, pp. 2776–2780, 2008. [6] Aurand, A.M., Dufour, J.S., Marras, W.S., 2017. Accuracy map of an optical motion capture system with 42 or 21 cameras in a large measurement volume. J. Biomech. 58, 237–240. [7] Eichelberger, P., Ferraro, M., Minder, U., Denton, T., Blasimann, A., Krause, F., Baur, H., 2016. Analysis of accuracy in optical motion capture – A protocol for laboratory setup evaluation. J. Biomech. 49, 2085–2088