The purpose of this study was to control two variables of the nonlinear camera calibration  to evaluate if they affect the 3D undewater accuracy. Two cameras (GoPro, 60 Hz) were  fixed in the swimming pool. In order to evaluate the influence of a distance constrain (1  and 2 markers) and the movement of the wand calibration, we performed three different  movements: M1 (zig zag), M2 (circular) and M3 (up and down). In each condition the 3D  accuracy were assessed in seven trials of a dynamic rigid bar test (ANOVA, 

Bernardina, Gustavo R. D.

Cerveri, Pietro

de Barros, Ricardo M. L.

Silvatti, Amanda P.

English

ISBS (International Society of Biomechanics in Sports): Conference Proceedings Archive

33rd International Conference on Biomechanics in Sports, Poitiers, France, June 29 - July 3, 2015Floren Colloud, Mathieu Domalain & Tony Monnet (Editors)Equipment / Instrumentation529THE INFLUENCE OF TWO VARIABLES OF THE NONLINEAR CAMERA CALIBRATIONON THE 3D UNDERWATER ACCURACYGustavo R. D. Bernardina1, Pietro Cerveri2, Ricardo M. L. de Barros3 and Amanda P. Silvatti1              Department of Physical Education, Universidade Federal de Viçosa, Viçosa, Brazil1Biomedical Engineering Department, Politecnico di Milano, Milano, Italy2Faculty of Physical Education, Universidade Estadual de Campinas, São Paulo, Brazil3The purpose of this study was to control two variables of the nonlinear camera calibrationto evaluate if they affect the 3D undewater accuracy. Two cameras (GoPro, 60 Hz) werefixed in the swimming pool. In order to evaluate the influence of a distance constrain (1and 2 markers) and the movement of the wand calibration, we performed three differentmovements: M1 (zig zag), M2 (circular) and M3 (up and down). In each condition the 3Daccuracy were assessed in seven trials of a dynamic rigid bar test (ANOVA, p<0.05). Thebest accuracy results were found in the M1. In this movement  the wand spread more theacquisition volume. No significant difference was found when we compare this movementusing or not the distance constrain, however if the movement did not spread very well thevolume the usages of the distance constrain improved significantly the results.KEY WORDS: accuracy analysis, nonlinear camera calibration, 3D underwater analysis.INTRODUCTION:  In an attempt to solve the problems of high cost of  3D motion analysissystems, some commercial  cameras have been tested  (Silvatti  et  al.  2012;  Silvatti  et  al.2013; Chong e al. 2011). These commercial cameras have two main features that allowstheir usage for biomechanics analysis: high resolution images and high speed records. Theaction sports cameras are an example,  and their  advantages are  low cost,  compared tooptoelectronics cameras specially designed for 3D motion analysis, small size and portability.Acceptable accuracy results for underwater analysis, with this kind of camera, were found inprevious work (Bernardina et al. 2014). Since the camera calibration is strictly related to theresults of  the 3D accuracy it  is  necessary to investigate the variables that  can influencenegatively or positively this step in order to improve the reability of the 3D data obtained withthe  action  sports  cameras.  So,  the  purpose  of  this  study  was  to  control  two  variables(different wand movements and a distance constrain in the wand) of the nonlinear cameracalibration to evaluate if they affect the 3D undewater accuracy.METHODS: The  data  acquisition  was  performed in  a  vinyl  swimming  pool.  The  volumeacquisition was defined by 4x1x1.5m3.  Two action sports cameras (GoPro, Hero 3, blackedition) with 2 m distance between them were fixed with suction cups on the wall  of  theswimming pool. We used the GoPro app (cell phone Galasy S4 active) to set the cameraposition, view and configuration: 1920x1080 (image resolution), 127o (view angle) and 60Hz(acquisition frequency). A wifi remote was used to start all the cameras. The images wereconverted to AVI in the GoPro studio software. The Dvideo software (Figueroa et al. 2003)was used to track the markers. An orthogonal waterproof triad (1x1x1m) with nine spherical black markers (35mm) was usedto determine  initial extrinsic and intrinsic  parameters using DLT equations and defines theaxes X, transversal, Y longitudinal and Z vertical directions (Silvatti et al. 2012). In order tocalculate the nonlinear camera calibration (Cerveri et al. 1998) a rigid bar was moved in thevolume (4x1x1.5m3)  during  20 seconds.  In  order  to  evaluate  the influence  of  the  wandmovement on the 3D underwater accuracy we performed three different wand movements:M1 (zig zag),  M2 (circular)  and M3 (up and down).  We also evaluate the influence of  adistance constrain  in  the  wand on the 3D accuracy using  the rigid  bar  with  one or  two33rd International Conference on Biomechanics in Sports, Poitiers, France, June 29 - July 3, 2015Floren Colloud, Mathieu Domalain & Tony Monnet (Editors)Equipment / Instrumentation530markers.  Thus,  we obtained five situations  of  calibration:  M1-1 (one marker),  M1-2 (twomarkers), M2-1 (one marker), M2-2 (two markers), M3-1 (one marker).  400 useful frameswere opportunely extracted from the whole sequence to  refine the initial parameters  into abundle  adjustment  nonlinear  optimization.  The  distortion  was  taken  into  account  in  thecamera model adopting a radial model with 1 parameter. The  accuracy  values  were  assessed  in  seven  trials  of  a  dynamic  rigid  bar  test  in  allconditions (M1, M2 and M3). The rigid bar (two markers) was moved within the workingvolume  during  about  20s.  The  real  size  of  the  rigid  bar  was  determined  by  computernumerical  control  machine  (CNC) with  an  accuracy  of  about  10μm  (nominal  value  D:250.00mm).  The distance between the markers was obtained as a function of  time.  Thefollowing variables were calculated: a) minimum, mean and maximum value of the distancebetween the markers, b) the standard deviation and c) the mean absolute error.As  data  assumed  normality  assumptions,  we  applied  the  analysis  of  variance  (ANOVA,p<0,05) to determine if the wand movements and a distance constrain in the wand affectedthe accuracy results. We used the post hoc Tukey (p<0,05) to find the statistical significancebetween the five situations (Matlab® 2012).RESULTS AND DISCUSSION: Table 1 shows the variables calculated.Table 1: Minimum, mean and maximum results of the 7 trials of dynamic rigid bar test for each situationsof calibration and results of post hoc Tukey.  D: 250mm. Values expressed in millimeter (mm).  CalibrationDistance MeanAbsoluteErrorComparison PMinimum Mean MaximumM1-1 249,31 249.46 249,60 1.21M1-2   0.389M2-1 0.000*M2-2 0.000*M3-1 0.000*M1-2 249,07 249.19 249,38 1.32M2-1 0.000*M2-2   0.046*M3-1 0.000*M2-1 248,54 248.63 248,92 1.83M2-2 0.000*M3-1 0.000*M2-2 248,90 248.99 249,17 1.51 M3-1 0.000*M3-1 247,92 248.20 248,72 2.65*p<0.05; M1-1 (Movement 1 – 1 marker); M1-2 (Movement 1 – 2 markers); M2-1 (Movement 2 – 1 marker); M2-2 (Movement 2 – 2 markers); M3-1 (Movement 3 – 1 marker)There is  a  significal  effect  between  the five  situations  of  calibration,  F(4,30)  =  168,294,p<0,001,  ω=0,97.  Since  the  M1 spread  more the acquisition  volume we found the  bestaccuracy  results  in  the  M1-1  (1.21mm).  No  significant  difference  was  found  when  wecompare  the  same  movement  using  or  not  the  distance  constrain  (Table1).  When  themovement  did  not  spread  very  well  the  volume  the  usages  of  the  distance  constrainimproved  significantly  the  accuracy  results  (M2-2  =  1.51mm;  M2-1 =  1.83mm,  p<0.001)(Table1).Previous works, that evaluated the accuracy out of the water, found values that ranged from0.58mm to 0.75mm (Pribanic et al., 2008; Silvatti et al. 2013). However, on the market, thereare commercials systems for 3D underwater analysis that report a relative accuracy of 2mm33rd International Conference on Biomechanics in Sports, Poitiers, France, June 29 - July 3, 2015Floren Colloud, Mathieu Domalain & Tony Monnet (Editors)Equipment / Instrumentation531at 10 meters distance (Oqus – Underwater,  Qualysis,  Sweden). In this work, in all  trials,using two cameras, the mean absolute error ranged from 1.09mm to 2.91mm in 4 meters.Our best accuracy result (1.09mm M1-1 to 1.45mm M1-2) are comparable with the valuesreported by others works that used the wand calibration (Silvatti et al. 2012; Bernardina et al.2014). It  is important to highlight the mainly benefit  to use this kind of camera. In this work, wepresented an alternative to obtain accurate 3D data with low cost and flexibility.  Thus, wecould assert that 3D analysis of several underwater movements are potentials applications,as swimming, gait, water aerobics, Hydrospinning, water polo and etc.For  future  studies  is  necessary  to  research  variables  and  situations  that  can  affect  thenonlinear camera calibration. Possible questions to investigate could be the 1. reproducibilityto use the action cameras, 2. more cameras, 3. evaluate and compare their usage to outwater and underwater applications, 4. test others frequencies and 5. feasibility in differentswater sports.CONCLUSION:  We can assert  that the movement of the wand calibration influences theaccuracy results and the best accuracy results were found in the M1. In this movement  thewand spread more the acquisition volume. Furthermore, the results showed that the distanceconstrain  is  not  more  important  than  to  spread  the  volume  very  well.  However,  if  themovement  did  not  spread  very  well  the  volume  the  usages  of  the  distance  constrainimproved significantly the results.REFERENCES:Bernardina,  G.R.D.,  Silva,  R.G,  Cerveri,  P.,  Barros,  R.M.L,  &  Silvatti,  A.P.  (2014,  July).Accuracy of sport action cameras for 3d underwater motion analysis. Paper presented at themeeting of 32nd International Conference on Biomechanics in Sports, Johnson City, USA.Cerveri,  P.,  Borghese,  N.A.,  &  Pedotti,  A.  (1998).  Complete  calibration  of  a  stereophotogrammetric  system  through  control  points  of  unknown  coordinates.  Journal  ofBiomechanics, 31(10), 935-940. doi: http://dx.doi.org/10.1016/S0021-9290(98)00104-3Chong,  A.K.  (2011).  Low-cost  Compact  camera  for  CMT  Disorder  application.  ThePhotogrammetric Record, 26(133), 263-273.Figueroa, P.J., Leite, N.J., & Barros, R.M.L. (2003). A flexible software for tracking of markersused in human motion analysis.  Computer Methods and Programs in Biomedicine,  72(2),155-165. doi: http://dx.doi.org/10.1016/S0169-2607(02)00122-0Pribanić, T., Sturm, P., & Cifrek, M. (2008, July). Calibration of 3D kinematic systems using2D calibration  plate.  Paper  presented at  the meeting of  26th International  Conference onBiomechanics in Sport, Seoul, Korea. Qualysis  Sweden  (2014). Qualysis,  Oqus  Underwater.  Retrieved  fromhttp://www.qualisys.com/wp-content/uploads/2014/01/PI_Oqus_Underwater.pdfSilvatti,  A.P.,  Dias,  F.A.S.,  Cerveri,  P.,  &  Barros,  R.M.L.  (2012).  Comparison  of  differentcamera calibration approaches for  underwater applications.  Journal  of  Biomechanics.  45,1112-1116. doi: 10.1016/j.jbiomech.2012.01.004Silvatti,  A.P.,  Silva, A.J.,  Dias, F.A.S.,  Figueroa, P.J., Cerveri,  P.,  &  Barros, R.M.L. (2013,August).  Accuracy  analysis  of  a  non-commercial  3D kinematic  analysis  system (dvideo)using standard and industrial cameras.  Paper presented at the meeting of 24th  Congress ofthe International Society of Biomechanics, Natal, RN. Brazil.Zhang,  Z.  (2000).  A flexible new technique for  camera calibration.  IEEE Transactions onPattern Analysis and Machine Intelligence, 22(11), 1330-1334. doi: 10.1109/34.888718AcknowledgementsResearch  supported  by  FAPESP  (00/01293-1,  2006/02403-1  and  2009/09359-6,2012/07757-7), CNPq (473729/2008-3, 304975/2009-5; 478120/2011-7), CAPES (2011/10-7) and FAPEMIG.

THE INFLUENCE OF TWO VARIABLES OF THE NONLINEAR CAMERA CALIBRATION ON THE 3D UNDERWATER ACCURACY

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THE INFLUENCE OF TWO VARIABLES OF THE NONLINEAR CAMERA CALIBRATION ON THE 3D UNDERWATER ACCURACY

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