On using the Microsoft Kinect TM sensors to determine the lengths of the arm and leg bones of a human subject in motion
aa r X i v : . [ phy s i c s . m e d - ph ] M a y On using the Microsoft Kinect TM sensors todetermine the lengths of the arm and legbones of a human sub ject in motion M.J. Malinowski a , E. Matsinos ∗ a a Institute of Mechatronic Systems, School of Engineering, Zurich University ofApplied Sciences (ZHAW), Technikumstrasse 5, CH-8401 Winterthur, Switzerland ∗ E-mail: evangelos[DOT]matsinos[AT]zhaw[DOT]ch,evangelos[DOT]matsinos[AT]sunrise[DOT]ch
Abstract
The present study is part of a broader programme, exploring the possibility of in-volving the Microsoft Kinect TM sensor in the analysis of human motion. We examinethe output obtained from the two available versions of this sensor in relation to thevariability of the estimates of the lengths of eight bones belonging to the subject’sextremities: of the humerus (upper arm), ulna (lower arm, forearm), femur (upperleg), and tibia (lower leg, shank). Large systematic effects in the output of the twosensors have been observed. PACS:
Key words:
Biomechanics, motion analysis, treadmill, Kinect
In a previous study [1], we established the theoretical background neededfor the comparison of the output of measurement systems used in capturingdata for the analysis of human motion. We developed our methodology fora direct application in case of the two versions of the Microsoft Kinect TM (hereafter, simply ‘Kinect’) sensor [2], a low-cost, portable motion-sensinghardware device, developed by the Microsoft Corporation (Microsoft, USA)as an accessory to the Xbox 360 video-game console (2010). The sensor is awebcamera-type, add-on peripheral device, enabling the operation of Xboxvia gestures and spoken commands. The first upgrade of the sensor (‘Kinectfor Windows v2’), both hardware- and software-wise, tailored to the needs ofbox One, became available for general development and use in July 2014.In Ref. [3], we applied our methodology [1] to a comparative study of the twoKinect sensors and drew attention to significant differences in their output.Previous attempts to validate the Kinect sensor for various medical/health-relating applications have been discussed in Ref. [1]. The present study is partof our research programme, investigating the possibility of involving (eitherof) the Kinect sensors in the analysis of the motion of subjects walking or run-ning ‘in place’, e.g., on commercially-available treadmills. If successful, Kinectcould become an interesting alternative to marker-based systems (MBSs) incapturing data for motion analysis, one with an incontestably high benefit-to-cost ratio.Studied herein is the dependence of the evaluated lengths of eight bones of thesubject’s extremities on the kinematical variables pertaining to the viewing ofthese bones by the sensor. The bones are: humerus (upper arm), ulna (lowerarm, forearm), femur (upper leg), and tibia (lower leg, shank). The evaluatedlengths of the subject’s left and the right extremities are separately analysed .Ideally, the lengths of the bones of the subject’s extremities should comeout constant, irrespective of the orientation of these bones in space and ofthe viewing angle by the sensor. In reality, a departure from constancy isinevitable, given that the Kinect nodes represent centroids in the probabilitymaps obtained from the captured data in each frame separately [4]; as such, thenode-extraction process is subject to statistical fluctuations and is affected bydifferent systematic effects in the three spatial directions. In the present work,we first examine the variability of the evaluated bone lengths with the variationof two angles describing the orientation of the bones in space, to be denotedhereafter as θ and φ ; θ is the angle of the bone with the vertical, whereas φ is the angle between the bone projection on the (anatomical) transverseplane and the z axis (the direction associated with the depth in the imagesobtained with the sensors). Subsequently, we investigate the dependence ofthe evaluated lengths of these bones on the inclination angle with respect toKinect’s viewing direction. We pursue the determination of systematic effectsin the Kinect-captured data, placing emphasis on establishing the similaritiesand the differences in the behaviour of the two sensors; in this respect, thepresent paper constitutes another comparative study of the two Kinect sensors,albeit from a perspective different to the one of Refs. [1,3].The material in the present paper has been organised in four sections. InSection 2, we provide the details needed in the evaluation and in the analysisof the bone lengths. The results of the study are contained in Section 3. Wediscuss the implications of our findings in the last section. The subject’s left and right parts refer to what the subject perceives as the leftand right parts of his/her body. On the evaluation and analysis of the bone lengths
In the original sensor, the skeletal data (‘stick figure’) of the output comprises20 time series of three-dimensional (3D) vectors of spatial coordinates, i.e.,estimates of the ( x , y , z ) coordinates of the 20 nodes which the sensor associateswith the axial and appendicular parts of the human skeleton. While walkingor running, the subject faces the Kinect sensor. In coronal (frontal) view ofthe subject (sensor view), the Kinect coordinate system is defined with the x axis (medial-lateral) pointing to the left (i.e., to the right part of the bodyof the subject being viewed), the y axis (vertical) upwards, and the z axis(anterior-posterior) away from the sensor, see Fig. 1. In the upgraded sensor,five new nodes have been appended at the end of the list: one is a body node,whereas the remaining nodes pertain to the subject’s hands. In both versions,parallel to the video image, Kinect captures an infrared image, which enablesthe extraction of information on the depth z . The sampling rate in the Kinectoutput (for the video and the skeletal data, in both versions of the sensor) is30 Hz. As the Kinect output has already been detailed twice, in Sections 2.1of Refs. [1,3], there is no need to further describe it here.The ‘upper’ endpoint (upper or proximal extremity) of each bone will be iden-tified by the subscript S , the ‘lower’ endpoint (lower or distal extremity) by E . The upper and lower endpoints of the bones refer to the upright (erect)standing (rest) position of the subject (standard anatomical position); in thisposition, y S > y E in all cases. The four bones pertaining to the upper extrem-ities (arms) are defined on the basis of the Kinect nodes SHOULDER LEFT,ELBOW LEFT, and WRIST LEFT (left side); SHOULDER RIGHT, EL-BOW RIGHT, and WRIST RIGHT (right side). The four bones pertainingto the lower extremities (legs) are defined using the Kinect nodes HIP LEFT,KNEE LEFT, and ANKLE LEFT (left side); HIP RIGHT, KNEE RIGHT,and ANKLE RIGHT (right side).Denoting the bone length as L = q ( x S − x E ) + ( y S − y E ) + ( z S − z E ) , theangle θ is estimated via the expression y S − y E ≡ ∆ y = L cos θ . (1)Evidently, θ ∈ [0 , π ]; in the standard anatomical position, θ = 0 ◦ (ideally).Additionally, x S − x E ≡ ∆ x = L sin θ sin φ (2)and z S − z E ≡ ∆ z = L sin θ cos φ . (3)Obviously, φ = 0 ◦ when the bone projection on the transverse plane ( x , z )is antiparallel to the z axis (i.e., when the projection of the vector −→ SE onthat plane points in the direction of the sensor). Denoting the projected bone3ength on the transverse plane as L xz = q (∆ x ) + (∆ z ) = L sin θ , we obtainthe relation: cos φ = ∆ zL xz (4)for all θ values, exempting θ = 0 and θ = π where the projected length L xz vanishes; although cases in the data where θ comes out identical to 0 or π havenot been found, we will assign (for the sake of mathematical completeness)the value of 0 to φ in both cases. Evidently, φ ∈ [0 , π ). In the present study,we will assume left/right symmetry (in the description of the motion of thebones) and restrict the angle φ in the [0 , π ] domain.Of relevance in the context of the present work is the angle at which theKinect sensor views a bone. The inclination angle is obtained from the dataas follows. Referring to Fig. 1, we define the position vectors pertaining to thebone endpoints as ~r S = ( x S , y S , z S ) and ~r E = ( x E , y E , z E ). The unit vector,normal to the KSE plane, is obtained via the expression:ˆ u N = ~r E × ~r S k ~r E × ~r S k . (5)(We have not found instances in the data involving parallel or antiparallelvectors ~r S and ~r E .) The position vector of the midpoint M of the SE segmentis given by ~r M = ~r S + ~r E u R = ~r M k ~r M k . (7)The unit vector ˆ u , on the KSE plane, orthogonal to ˆ u R , is obtained by theexpression ˆ u = ˆ u R × ˆ u N k ˆ u R × ˆ u N k = ˆ u R × ˆ u N . (8)The inclination ω is the angle between −→ SE ≡ ~r E − ~r S and ˆ u ; evidently,cos ω = ( ~r E − ~r S ) · ˆ u k ~r E − ~r S k . (9)As we are interested in the inclination of each bone, not in its orientation withrespect to the unit vector ˆ u , we will use | cos ω | as free variable. It is expectedthat the reliability of the Kinect-evaluated bone lengths should increase withincreasing | cos ω | . 4 Results
The data acquisition involved one male adult (ZHAW employee), with noknown motion problems, walking and running on a commercially-availabletreadmill (Horizon Laufband Adventure 5 Plus, Johnson Health Tech. GmbH,Germany). The placement of the treadmill in the laboratory of the Institute ofMechatronic Systems (School of Engineering, ZHAW), where the data acqui-sition took place, was such that the subject’s motion be neither hindered norinfluenced in any way by close-by objects. Prior to the data-acquisition ses-sions, the Kinect sensors were properly centred and aligned. The sensors werethen left at the same position, untouched throughout the data acquisition.It is worth mentioning that, as we are interested in capturing the motion ofthe subject’s lower-leg parts (i.e., of the ankle and foot nodes), the Kinectsensors must be placed at such a height that the number of lost lower-legsignals be kept reasonably small. Our past experience dictated that the Kinectsensor should be placed close to the minimal height recommended by themanufacturer, namely around 2 ft off the (treadmill-belt) floor. Placing thesensor higher (e.g., around the midpoint of the recommended range of values,namely at 4 ft off the treadmill-belt floor) leads to many lost lower-leg signals(the ankle and foot nodes are not properly tracked), as the lower leg is notvisible by the sensor during a sizeable fraction of the gait cycle, shortly aftertoe-off.The Kinect sensor may lose track of the lower parts of the subject’s extremities(wrists, hands, ankles, and feet) for two reasons: either due to the particular-ity of the motion of the extremity in relation to the position of the sensor(e.g., the identification of the elbows, wrists, and hands becomes problematicin some postures, where the Kinect viewing angle of the ulnar bone is small)or due to the obstruction of the extremities of the human body (behind thesubject) for a fraction of the gait cycle. Assuming that these instances remainrare (e.g., below about 3% of the available data in each time series, i.e., nomore than one lost frame in 30), the missing values may be reliably obtained(interpolated) from the well-determined (tracked) data. Although, when nor-malised to the total number of available values, the untracked signals usuallyappear ‘harmless’, particular attention was paid in order to ensure that nonode be significantly affected.Five velocities were used in the data acquisition: walking-motion data wereacquired at 5 km/h; running-motion data at 8, 9, 10, and 11 km/h. At eachvelocity setting, the subject was given 1 min to adjust his movements comfort-ably to the velocity of the treadmill belt. The Kinect output spanned slightlyover 2 min at each velocity. The variation of the distance between the subjectand the Kinect sensors was monitored during the data acquisition; it ranged5etween about 2 . . θ , cos φ ) cells; the same values werealso histogrammed in bins of | cos ω | . Twenty bins per angular direction wereused in the former case, forty in the latter. Averages, as well as the standarderrors of the means, were calculated in all cells/bins containing at least tenentries; cells/bins with fewer entries were ignored.Techniques yielding accurate results for in-vivo measurements of the humanlong bones include conventional (planar) radiography, CT scanning (e.g., seeRef. [5]), Raman spectroscopy [6], and ultrasonic scanning [7]. Unwilling orunable to use any of these techniques, we obtained static measurements ofthe subject’s bone lengths with an MBS (AICON 3D Systems GmbH, Ger-many) [8]. Our system features two digital cameras, a control unit, and ahigh-end personal computer (where the visualisation software is installed).The MoveInspect Technology HF | HR reconstructs the 3D coordinates of thecentres of markers (adhesive targets, reflective balls) which are simultaneouslyviewed by the two cameras; the typical uncertainty in the determination of the3D coordinates of each marker centre is below 100 µ m, i.e., negligible whencompared to other uncertainties, namely to those pertaining to the placementof the markers and to skin motion. The bone lengths, not to be identifiedherein with the suprema of the distances of any two points belonging to thebones regarded as 3D objects, were defined as follows. • Humerus: from the centre of the humeral greater tubercle (‘coinciding’ withthe Kinect shoulder node) to the humeral lateral epicondyle. As it is notstraightforward to identify the centre of the humeral greater tubercles, flatmarkers were placed on the greater tuberosities and the resulting humeral-bone lengths were reduced by 39 mm. • Ulna: from just below the humeral medial epicondyle, on top of the humeraltrochlea, to the ulnar styloid process. The description of the algorithm, used in the determination of the 3D positions ofthe skeletal joints of the subject being viewed with Kinect, may be found in Ref. [4].The ‘3D positions of the joints’ of Ref. [4] are essentially produced from the ‘3Dpositions of the projections of the joints onto the front part of the subject’s body’after applying a ‘shift’ in depth (i.e., from the surface to the interior of the subject’sbody), namely a constant offset ( ζ c ) of 39 mm (see end of Section 3 of Ref. [4]).We will assume that the same correction is also applied to the infrared image inthe vertical ( y ) direction (and, albeit not relevant herein, also in the medial-lateral( x ) direction), in order to yield the y (and x ) coordinates of the shoulder joints.Therefore, when comparing it with the Kinect-evaluated humeral-bone length, theMBS-evaluated length will be reduced by ζ c . Femur: from the centre of the femoral head to just below the femoral medialcondyle, on top of the medial meniscus. As the identification of the cen-tres of the femoral heads, using a non-invasive anthropometric technique,is neither easy nor accurate, we obtained the hip positions by following theindirect approach of Ref. [9], featuring four flat markers on the surface ofthe subject’s body (see Subsection 2.2 of Ref. [1]). The knee positions wereidentified in two ways: either using ∅ • Tibia: from just below the femoral medial condyle, on top of the medialmeniscus, to the medial malleolus.All measurements were acquired in the upright position. The extracted valuesof the subject’s bone lengths are listed in Table 1.The average values, along with the rms (root-mean-square) values of the cor-responding distributions, of the Kinect-evaluated bone lengths are shown inTable 2, separately for the two Kinect sensors. A noticeable difference be-tween the two sets of values occurs in the femoral-bone lengths, the valuesof which come out, in all cases, significantly smaller when using the data ofthe upgraded sensor; this underestimation is equivalent to an effect between1 .
69 and 2 .
42 standard deviations in the normal distribution. The quoted un-certainties in Table 2 are large, indicating that systematic effects come intoplay, thus suggesting further analysis of the bone lengths, in terms of thekinematical variables θ , φ , and ω . cos θ , cos φ ) cells Walking and running motions have different signatures; the differences areboth quantitative and qualitative: the ranges of motion in running are larger,generally expected to increase with increasing velocity; qualitatively, the walk-ing motion is characterised by extended elbow joints, the running motion byflexed ones. This last dissimilarity affects the detection of the elbows and ofthe wrists at several postures in running motion, inevitably introducing sys-tematic effects in the evaluation of the humeral- and ulnar-bone lengths.Our first study of the systematic effects in the evaluation of the bone lengthsinvolved profile scatter plots in (cos θ ,cos φ ) cells. For convenience, the follow-ing definitions will be used in the short description of the results obtained inthis part of the analysis. • Forward (ventral) placement of a bone corresponds to a position of its lower-7ndpoint joint more proximal to the Kinect sensor than the mid-coronalplane; ‘very forward’ placement refers to cos φ > . • Backward (dorsal) placement of a bone corresponds to a position of itslower-endpoint joint more distal to the Kinect sensor than the mid-coronalplane; ‘very backward’ placement refers to cos φ < − . θ values; only in the caseof the ulna does the motion extend to θ ≈ ◦ . The humeral-bone lengths cameout cos φ -dependent; systematically smaller values were extracted in forwardplacement, larger in backward. Regarding the ulna, the θ domain is somewhatenlarged in very forward placement, when the elbow joint is (usually) flexed.Regarding the tibia, a significant dependence of the evaluated length on cos φ was seen in very backward placement; the effect was maximal around themost distal position of the ankle (with respect to the Kinect sensor), wherethe shank is not viewed sufficiently well by the sensor.Compared to walking motion, the domain of the θ values is significantly en-hanced in running (as expected). The evaluated humeral-bone lengths were(again) found cos φ -dependent. Regarding the ulna, the cos φ values were large(restriction of the motion to very forward placement). For the tibial bones, theevaluated lengths in very backward placement were found to be significantlylarger than those obtained elsewhere. Again, the largest bone lengths wereextracted for large θ and φ values (large dorsal elevation of the lower leg),where the tibial bone is not viewed sufficiently well by the Kinect sensor.In all cases, the relative minimax variation d r = 2( M − m ) / ( M + m ) (where M and m stand for corresponding maximal and minimal values, respectively)of the extracted values of the bone lengths was large. The d r ranges (over allvelocities) were: for the humerus, 3-22% (original sensor) and 4-20% (upgradedsensor); for the ulna, 7-29% (original sensor) and 8-35% (upgraded sensor);for the femur, 4-13% (original sensor) and 7-17% (upgraded sensor); and forthe tibia, 18-24% (original sensor) and 24-26% (upgraded sensor). Overall,the matching of the results between the two sensors in the case of runningmotion was not satisfactory; the values of Pearson’s correlation coefficient (onthe d r values of the eight bone lengths at fixed velocity) showed a pronouncedvelocity dependence, ranging from 0 .
958 at 5 km/h to 0 .
260 at 11 km/h. | cos ω | bins The analysis described in the previous subsection is suggestive of the directionwhich the investigation must next turn to. In short, it appears plausible toassume that the goodness of the evaluation of the bone lengths does not dependseparately on the angles θ and φ , but on another quantity, namely on the8iewing angle of the particular bone by the Kinect sensor. It is reasonable toexpect that the accuracy in the evaluation of each bone length depends on theinclination of that bone with respect to the Kinect viewing direction; when abone is viewed by the Kinect sensor at almost right angle, its length shouldbe evaluated more reliably. The appropriate free variable in this investigation, | cos ω | , is obtained via Eq. (9).The results, obtained from the data analysis, are shown in Figs. 2, 4, 6, and8 for the original sensor; in Figs. 3, 5, 7, and 9 for the upgraded sensor. Wenow discuss these plots. • Humerus . There can be little doubt that both Kinect sensors systemati-cally underestimate the humeral-bone length regardless of the type of themotion (walking or running). Only in the case | cos ω | → | cos ω | → • Ulna . In the data obtained with the original sensor, some left/right asym-metry in the results is visible. The range of variation of the ulnar-bonelength was found maximal (about 10 cm) in the case of the original sensor,for the right ulna. Regarding the walking-motion data for | cos ω | →
1, theextracted values do not disagree with the results of the static measurements. • Femur . The femoral-bone length, obtained with the original sensor, is se-riously overestimated in all cases. The hip positions are mostly responsiblefor this discrepancy. (In Ref. [3], we reported that the waveforms for thehips, obtained from the two versions of the sensor, do not match well.) • Tibia . In all cases, both sensors seriously overestimate the tibial-bone lengthsfor small viewing angles and underestimate them for | cos ω | →
1. The rangeof variation of the tibial-bone length was found sizeable, namely between 9and 11 cm. On the other hand, a nearly monotonic behaviour is observedin Figs. 8 and 9, and the results from the walking- and the running-motiondata generally appear to be consistent between the two sensors.It must be mentioned that the dependence of the bone lengths L on | cos ω | isexpected to be monotonic. Visual inspection of Figs. 2-9 reveals that this isnot always the case. One reason for the observed departure from a monotonicbehaviour (yet not the only one) is that the inclination ω is estimated fromthe Kinect-captured data; systematic effects also affect this estimation.The results, reported in the present section, have also been checked againstinfluences from ‘cross-talk’, which might be present in the output of the two9inect sensors. Both sensors use reflected infrared light in order to yield in-formation on the depth in the captured images; one might thus argue that, incase of a simultaneous data acquisition, they distort one another’s recording.To clarify this issue, data (using the same subject and velocity settings) wereacquired with the two measurement systems ‘serially’, first with the originalsensor, subsequently with the upgraded one; in both cases, the second sensorwas switched off (but was not removed from the mount). The differences to theresults reported herein were inessential. Our conclusion is that the aforemen-tioned discrepancies cannot be due to an interaction between the two sensors. The present paper addressed one use of the output of the two MicrosoftKinect TM (hereafter, simply ‘Kinect’) sensors, namely the evaluation of thelengths of eight bones pertaining to the extremities of one subject walkingand running on a treadmill: of the humerus (upper arm), ulna (lower arm,forearm), femur (upper leg), and tibia (lower leg, shank). For comparison,static measurements of these bone lengths were obtained with a marker-basedsystem.The evaluated lengths of the left and right parts of the subject’s extremitieshave been separately analysed. The constancy of the lengths of these eightbones in terms of the variation of the two angles involved in the viewing, θ ofEq. (1) and φ of Eq. (4), was examined. We have also investigated the depen-dence of the bone lengths on the inclination angle ω of Eq. (9) with respect toKinect’s viewing direction. We pursued the analysis of systematic effects in theoutput, emphasising on the similarities and the differences between the twosensors; in this respect, the present study is another comparative study of thetwo Kinect sensors, albeit from a perspective different to that of Refs. [1,3].The walking motion is characterised by extended elbow joints and small θ values in the case of the humerus and of the femur; in the case of the ulna,the θ values reached about 60 ◦ . The running motion is characterised by flexedelbow joints and (compared to the walking motion) extends more in θ . Themotion of the ulnar bones is different in walking and running; in the lattercase, the ulnar motion extends in θ , rather than in φ . A major overestimationof the tibial-bone lengths occurs in very backward placement, where thesebones cannot be viewed sufficiently well by the Kinect sensors.The analysis of the arm-bone lengths in terms of the inclination angle ω demonstrated that the results obtained with both sensors do not agree wellwith those of the static measurements; agreement occurs only in the walking-motion data for | cos ω | →
1, where the bones are viewed at almost right angle10y the sensor. We advanced an argument providing an explanation of thiseffect: it is mainly due to the systematic misplacement of the elbow nodes inthe running motion, where this joint is kept in flexed position throughout thegait cycle. Regarding the leg bones, there is no doubt that the original Kinectsensor seriously overestimates the femoral-bone length. Both sensors overesti-mate the tibial-bone lengths for small viewing angles and underestimate themfor large; discrepancies in the evaluated length of these bones lie in the vicinityof 9-11 cm, see Figs. 8 and 9.The present work corroborates earlier results [10], obtained with the originalsensor (the upgraded sensor was not available at the time that study wasconducted), that Kinect cannot be easily employed in medical/health-relatingapplications requiring high accuracy. In most cases, the results obtained withthe two sensors disagree with the static measurements and show a large rangeof variation within the gait cycle. The determination and application of cor-rections, needed in order to suppress these artefacts, comprises an interestingresearch subject.Finally, we would like to comment on one misconception in the field of Med-ical Physics, namely that the results of studies using one subject, or only afew subjects, are not reliable. In our opinion, there are studies which call forstatistics and studies in which statistics is superfluous. When comparing twomeasurement systems and the results (for a few subjects) come out sufficientlyclose, it does make sense to ‘pursue statistics’ and obtain reliable estimatesof averages, standard deviations, and ranges. On the contrary, there are occa-sions (in particular, in the validation of measurement systems) where seriousdiscrepancies are found in the output already obtained from the first subject.Unless one explains why the comparison of the output of the two measurementsystems failed for that one subject, one subject is sufficient in invalidating theapplication! Even in case that the tested measurement system failed for thespecific subject (and that it does not fail for the general subject), its valida-tion must be performed for every future subject separately, to guarantee thevalidity of the output on a case-by-case basis ; of course, this is not the essenceof validations of measurement systems.
Acknowledgements
The original idea of investigating the subject of the present study belongs toS. Roth and M. Regniet, who (along with R. Jain) had conducted a similaranalysis of data obtained with the original Kinect sensor.We are indebted to R. Guntersweiler and L. Lombriser for their support inthe measurements obtained with the AICON system.11ig. 1 has been produced with CaRMetal, a dynamic geometry free software(GNU-GPL license), first developed by R. Grothmann and recently underE. Hakenholz [11].
Conflict of interest statement
The authors certify that, regarding the material of the present paper, theyhave no affiliations with or involvement in any organisation or entity withfinancial or non-financial interest.
References [1] M.J. Malinowski, E. Matsinos,S. Roth, On using the Microsoft Kinect TM sensors in the analysis of humanmotion, arXiv:1412.2032 [physics.med-ph] TM sensor in regard to the analysis of human motion, arXiv:1504.00221 [physics.med-ph] able 1 The values of the subject’s bone lengths (in mm), obtained from a marker-basedsystem (see Section 3). To account for incorrect placement of the markers, an uncer-tainty of 10 mm is assumed in all cases, save for the femoral-bone lengths, where anoverall uncertainty of 20 mm is applicable (linear combination of the placement un-certainty of 10 mm and of a 10-mm uncertainty representing the systematic effectsof Ref. [9], as discussed in Section 2.2 of Ref. [1]). These values have been verifiedwith a non-stretchable tape measure.Left humerus 343Right humerus 344Left ulna 258Right ulna 271Left femur 434Right femur 436Left tibia 434Right tibia 427 able 2 The average values of the subject’s bone lengths (in mm), separately for the twoKinect sensors. 5 km/h 8 km/h 9 km/h 10 km/h 11 km/hOriginal Kinect sensorLeft humerus 278(23) 249(22) 245(16) 249(16) 250(14)Right humerus 284 . .
1) 239(12) 240(13) 244(18) 247(15)Left ulna 293(18) 271(27) 265(29) 253(24) 251(26)Right ulna 277(15) 282(24) 268(24) 249(30) 251(30)Left femur 531(29) 517(25) 513(30) 510(28) 503(30)Right femur 519(23) 512(17) 512(25) 508(25) 506(30)Left tibia 403(36) 431(35) 436(36) 440(38) 443(40)Right tibia 418(30) 439(35) 445(37) 447(37) 451(36)Upgraded Kinect sensorLeft humerus 268(20) 241(10) 240 . .
6) 243 . .
4) 244 . . ig. 1. The coordinate system of the Kinect sensor. The endpoints of the specificbone are identified as S and E. The angles θ and φ define the orientation of thebone in space, whereas the angle ω pertains to the Kinect view of the bone; whenKinect views the bone at right angle, ω = 0 ◦ . The (focal point of the) camera of thesensor appears in the figure as point K. .8 0.85 0.9 0.95 1220230240250260270280290300310320 | cos ω | L ( mm ) Left humerus | cos ω | L ( mm ) Right humerus
Fig. 2. The profile histogram of the humeral-bone length (separately for the left-and right-side bones) in | cos ω | bins; the data has been captured with the originalKinect sensor. In walking motion, the swinging of the right arm of the subject usedin our data acquisition, is very small. .8 0.85 0.9 0.95 1220230240250260270280290300310320 | cos ω | L ( mm ) Left humerus | cos ω | L ( mm ) Right humerus
Fig. 3. The profile histogram of the humeral-bone length (separately for the left-and right-side bones) in | cos ω | bins; the data has been captured with the upgradedKinect sensor. In walking motion, the swinging of the right arm of the subject usedin our data acquisition, is very small. | cos ω | L ( mm ) Left ulna | cos ω | L ( mm ) Right ulna
Fig. 4. The profile histogram of the ulnar-bone length (separately for the left- andright-side bones) in | cos ω | bins; the data has been captured with the original Kinectsensor. In walking motion, the swinging of the right arm of the subject used in ourdata acquisition, is very small. | cos ω | L ( mm ) Left ulna | cos ω | L ( mm ) Right ulna
Fig. 5. The profile histogram of the ulnar-bone length (separately for the left- andright-side bones) in | cos ω | bins; the data has been captured with the upgradedKinect sensor. In walking motion, the swinging of the right arm of the subject usedin our data acquisition, is very small. .75 0.8 0.85 0.9 0.95 1400420440460480500520540560 | cos ω | L ( mm ) Left femur | cos ω | L ( mm ) Right femur
Fig. 6. The profile histogram of the femoral-bone length (separately for the left-and right-side bones) in | cos ω | bins; the data has been captured with the originalKinect sensor. .75 0.8 0.85 0.9 0.95 1360380400420440460480 | cos ω | L ( mm ) Left femur | cos ω | L ( mm ) Right femur
Fig. 7. The profile histogram of the femoral-bone length (separately for the left-and right-side bones) in | cos ω | bins; the data has been captured with the upgradedKinect sensor.bins; the data has been captured with the upgradedKinect sensor.
Fig. 7. The profile histogram of the femoral-bone length (separately for the left-and right-side bones) in | cos ω | bins; the data has been captured with the upgradedKinect sensor.bins; the data has been captured with the upgradedKinect sensor. .4 0.6 0.8 1360380400420440460480500 | cos ω | L ( mm ) Left tibia | cos ω | L ( mm ) Right tibia
Fig. 8. The profile histogram of the tibial-bone length (separately for the left- andright-side bones) in | cos ω | bins; the data has been captured with the original Kinectsensor. .4 0.6 0.8 1360380400420440460480 | cos ω | L ( mm ) Left tibia | cos ω | L ( mm ) Right tibia
Fig. 9. The profile histogram of the tibial-bone length (separately for the left- andright-side bones) in | cos ω | bins; the data has been captured with the upgradedKinect sensor.bins; the data has been captured with the upgradedKinect sensor.