Evaluation of User-Centric Optical See-Through Head-Mounted DisplayCalibration Using a Leap Motion Controller

Kenneth R Moser∗ J. Edward Swan II†

Mississippi State University

(a) (b) (c)

Figure 1: Examples of manual OST AR calibration procedures. (a) A standard environment-centric calibration performed by aligning on-screenpoints with the center of a fiducial marker in the world. (b) A user-centric calibration performed by aligning on-screen points with the tip of astylus held by the user. (c) A virtual hand overlay generated using Leap Motion tracking information.

ABSTRACT

Advances in optical see-through head-mounted display technologyhave yielded a number of consumer accessible options, such as theGoogle Glass and Epson Moverio BT-200, and have paved the wayfor promising next generation hardware, including the MicrosoftHoloLens and Epson Pro BT-2000. The release of consumer de-vices, though, has also been accompanied by an ever increasing needfor standardized optical see-through display calibration procedureseasily implemented and performed by researchers, developers, andnovice users alike. Automatic calibration techniques offer the possi-bility for ubiquitous environment independent solutions, un-reliantupon user interaction. These processes, however, require the use ofadditional eye tracking hardware and algorithms not natively presentin current display offerings. User dependent approaches, therefore,remain the only viable option for effective calibration of current gen-eration optical see-through hardware. Inclusion of depth sensors andhand tracking cameras, promised in forthcoming consumer models,offer further potential to improve these manual methods and providepractical intuitive calibration options accessible to a wide user base.

In this work, we evaluate the accuracy and precision of manual op-tical see-through head-mounted display calibration performed usinga Leap Motion controller. Both hand and stylus based methods formonocular and stereo procedures are examined, along with severalon-screen reticle designs for improving alignment context duringcalibration. Our study shows, that while enhancing the context ofreticles for hand based alignments does yield improved results, LeapMotion calibrations performed with a stylus offer the most accurateand consistent performance, comparable to that found in previousstudies for environment-centric routines. In addition, we found thatstereo calibration further improved precision in every case. We be-lieve that our findings not only validate the potential of hand andgesture based trackers in facilitating optical see-through calibration

∗e-mail: moserk@acm.org†e-mail: swan@acm.org

methodologies, but also provide a suitable benchmark to help guidefuture efforts in standardizing calibration practices for user friendlyconsumer systems.

Index Terms: H.5.1 [[Information Interfaces and Presentation]:Multimedia Information Systems]: Artificial, augmented, and virtualrealities—; H.5.2 [[Information Interfaces and Presentation]: UserInterfaces]: Ergonomics, Evaluation/methodology, Screen design—

1 INTRODUCTION

The growing availability of consumer level Optical See-Through(OST) Head-Mounted Displays (HMDs) has produced a burgeon-ing market for new and innovative Augmented Reality (AR) ap-plications intended for use by the general populace. This surgein consumer access is accompanied by a rapidly growing need forstandardized calibration procedures offering intuitive and easily im-plemented methodologies for researchers, developers, and noviceusers alike. While past offerings in the consumer domain, for exam-ple the Google Glass and Epson Moverio BT-200, include standardsensory options, such as gyroscopes, accelerometers, and built-incameras; next generation OST devices, including the MicrosoftHoloLens and Epson Moverio Pro BT-2000, promise a wide varietyof additional integrated and on-board sensors. Depth, gesture, andhand tracking cameras, in particular, offer unique potential for notonly novel application and interface designs, but also for the cre-ation of standard calibration practices and methodologies applicableacross devices and markets.

The goal of OST HMD calibration is to properly model the user’sviewpoint through the display screen. Unlike Video See-Through(VST) AR, where the user’s view of the world is provided by meansof an externally mounted camera, OST AR allows virtual content tobe directly overlaid onto the real world from the user’s own naturalperspective. Since the ”camera” in an OST system is the user’s eyeitself, it is not possible to use standard image processing techniquesfor calibrating the viewing frustum. Approximation methods mustinstead be used to estimate the user’s perspective. The accuracyof these methods ultimately determines the registration quality, orcorrectness in location, of virtual content in relation to physicalobjects, such as an overlay registered to a user’s hand, Figure 1 (c).

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Automatic calibration is an increasing possibility for future dis-play systems, with promising results being shown by recently de-veloped approaches, such as Itoh and Klinker’s INteraction-FreeDIsplay CAlibration (INDICA) [9] and Plopski et al.’s CornealImaging Calibration (CIC). These methods utilize additional cam-era hardware and image processing algorithms to directly measurethe location of the user’s eye within the head-mount, allowing dy-namic calibration updates at run-time. While automatic processesfundamentally allow ubiquitous, any time any where, calibration,off the shelf commercial HMD offerings do not natively include thenecessary eye-tracking hardware fundamental to these procedures,making the applicability of INDICA and similar approaches limitedat the current time. As a result, calibration techniques for OST dis-plays have traditionally relied on manual interaction methods, whichestimate the viewing frustum through user feedback.

Common manual calibration techniques, such as Tuceryan etal.’s [29] Single Point Active Alignment Method (SPAAM), requireusers to move about their environment and visually align on-screenpoints to real world target locations, as demonstrated in Figure 1(a), with the fiducial marker indicating a known world location. Pro-viding that an adequate number of screen to world correspondencepairs are obtained, an estimation of the perspective projection, usedto model the user’s viewpoint, can be obtained. Traditionally, targetpoints taken from the world are static locations or fiducial markerswhose locations are measured off-line or actively tracked withinthe user’s environment. Unfortunately, the use of external objectsor patterns for alignments inherently imposes dependency on theenvironment restricting users to specific locations or forcing them toconstruct and maintain portable targets and fiducials. Nevertheless,environment agnostic calibration may be feasible through utilizationof body tracking technologies, allowing the replacement of envi-ronment dependent target points with the user’s own fingers andhands.

The Leap Motion controller is one commercially available solu-tion for providing low cost hand and stylus tracking. Differing fromthe Microsoft Kinect and Asus Xtion, which are primarily wholebody motion trackers, the Leap Motion affords close proximity ges-ture and hand detection for natural user interaction and interfacesin both VR and AR applications. Unpredictable tracking accuracy,particularly for occluded or oblique hand orientations, imposes somelimitation on the utility of the technology. However, small size, formfactor, and software versatility make the Leap Motion ideally suitedfor integration into consumer HMD offerings. The ability to performSPAAM-like manual calibration using hand and finger alignments,as seen in Figure 1 (b), liberates the user from environment de-pendent target constraints and achieves a user-centric methodology,easily integrated into most OST AR systems, easing the burden onnot only users, but also application developers alike.

In this work, we present the results of an investigation into theefficacy of the Leap Motion controller as a means for facilitatinghand and stylus alignment based calibration of an OST HMD sys-tem. In contrast to a previous cursory demonstration [11], our studyadditionally includes an examination of accuracy and precision dif-ferences between monocular and stereo calibration variants. We alsoexplore several reticle designs and the effect of alignment contexton hand calibration results. Our analysis employs standard objectivemeasures and metrics, including reprojection error and extrinsic eyelocation estimates, to compare not only the performance of eachcondition, but also the viability of OST calibration with Leap Mo-tion in general. We provide a final discussion of our results andtheir benefit to standardizing calibration practices, and close withrecommendations and remarks to guide future work.

2 BACKGROUND AND RELATED WORK

Previous studies evaluating or presenting improved calibration tech-niques primarily focus on accuracy and time reduction measures.

While these metrics are fundamental to comparisons of efficiencyand robustness between methods, considerably less attention hasbeen attributed to reducing the restrictions that calibration proce-dures impose on users and system developers.

2.1 Environment-Centric CalibrationInitial modalities for determining a user’s perspective through anOST HMD required rigid head fixation, [4, 5, 14], while users manu-ally adjusted the location of on-screen reticles to align with specifictarget points in the environment. Even though these bore-sightingapproaches offer a hardware independent calibration solution, in-hibition of user movement makes this methodology both tediousand impractical for consumer use. Tuceryan and Navab’s SPAAMprocedure [29] relaxes this restriction allowing far greater freedomof movement, while users perform screen to world alignments. Aminimum of 6 alignments is required to solve for the 11 free pa-rameters, plus a scale factor, of the 3× 4 projection matrix usedto describe the viewing frustum created by the user’s eye and thedisplay. Subsequent developments by Genc et al. [6] extend SPAAMto stereo OST HMDs, allowing simultaneous calibration of boththe left and right eye views. Stereo SPAAM alignments utilize3D virtual points by exploiting stereoscopic depth cues producedby binocular displays. The usability gains of SPAAM calibration,though, is counter balanced by the introduction of misalignmenterror caused by movement, or sway, of the user’s body and headduring the procedure.

Tang [27] revealed that misalignment error could be ameliorated,to an extent, by increasing the variation of screen to world align-ments in depth. Axholt et al. [1] further indicates that Tang’s DepthSPAAM achieves more stable results with 20–25 alignments welldistributed to cover a larger region of the environment. However,related studies, [3, 15], show that error contributions from user mis-alignment are highly dependent on display type, user stance, andinput methods. Alternative two phase calibration methods providevarious means for not only reducing user interaction, but also envi-ronmental constraints as well.

Easy SPAAM [7, 17] optimizes previous calibration results byadjusting the projection matrix to an updated location of the user’seye triangulated through standard user driven 2D-3D alignments.This approach, while still bounded by the accuracy of the existingcalibration data, significantly reduces the number of screen to worldcorrespondences required and also isolates the impact of furtheralignment error to the new extrinsic, eye location, measures. Owenet al.’s [20] Display Relative Calibration (DRC) removes the de-pendency on previous calibration results by fully decoupling theeye’s perspective into intrinsic, display dependent, and extrinsic,user specific, components, and implements two separate proceduresfor independent measure of each. The first phase, conducted off-line,directly computes display specific parameters through image pro-cessing and computer vision techniques. The second phase, similarto that of Easy SPAAM, still utilizes a small number of screen-worldalignments for triangulating the extrinsic location of the user’s eyerelative to the display screen. Innovative, recently proposed, twostep calibration methods seek to improve the second phase of theDRC approach and completely eliminate user interaction, creating auser-centric, environment independent, process as a consequence.

2.2 User-Centric CalibrationItoh and Klinker [9] enhance the on-line component of the DRCmethodology, by automating the measurements needed to estimateuser eye location. Their INDICA technique employs image process-ing methods, similar to Swirski’s iris detection [26] and Nitschke’slocalization algorithm [18], to estimate the 3D position of the user’seye relative to miniature cameras mounted within the HMD. Plop-ski et al.’s Corneal-Imaging Calibration [21] parallels this approachby using feature detection algorithms to identify the orientation

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of known patterns reflected onto the user’s cornea by the displayscreen. Comparing the distortion of the reflected features to a sim-plified model of the eye’s structure, yields more accurate 3D local-ization estimates compared to direct iris detection. Both techniques,though, fully remove the need for user interaction and provide a com-pletely autonomous process, ideally suited for consumer devices.Unfortunately, these automatic schemes require additional built-ineye-tracking cameras, and related components, not yet standard incurrent HMD products. Additionally, the high level of expertiseneeded to effectively deploy ad-hoc versions of these systems isbeyond the capability of casual users. Therefore, manual interac-tion methods are still the most viable calibration option for currentconsumer OST HMD offerings.

Alternative techniques, which diverge from the two phase method-ology, but maintain a user-centric approach, employ hand held track-ing markers for alignment based calibration [13, 19]. Moving themarker around the field of view, mimicking the distance variationof Depth SPAAM, yields viable accuracy results and reduces usermovement since the entire procedure may be conducted while seated.Even though this method offers a usable environment agnostic pro-cedure, like other manual calibrations it too ultimately requires thepossession of external alignment targets to proceed. Hand and ges-ture tracking technology, such as the Leap Motion controller, maybe a viable option for replacing hand held markers with the handitself.

2.3 Leap Motion Accuracy and PrecisionThe Leap Motion controller employs modern computer vision al-gorithms to process images from stereo IR cameras, facilitatingnear proximity hand, gesture, and stylus tracking. Research appli-cations for the device center primarily around innovative and novelcomputer interfaces [22, 25, 28, 31] as well as VR interaction ca-pabilities [23, 24]. A number of formal evaluations targeting theaccuracy and precision of Leap Motion tracking [8, 12, 30] haveshown that, while both hand and stylus accuracy quickly diminishat distances greater than 250mm from the device, stylus tracking towithin 0.7mm or less is possible. Measurements for hand trackingshowed much larger fluctuations according to the degree of handand finger orientation and occlusion, as well as hand shape andsize. Despite current tracking inconsistencies, the accessibility andcurrent prominence in VR applications offers a strong foundationfor transitioning use of Leap Motion into OST AR, and exploitingbody tracking for calibration use. Our study provides the first formalevaluation of attainable calibration accuracy in OST AR systemsusing Leap Motion controllers.

3 EXPERIMENT DESIGN

We construct a complete OST AR framework, combining a LeapMotion controller with a commercially available HMD. Since theLeap Motion is able to perform both hand and stylus tracking, weutilize each for performing monocular and stereo SPAAM basedcalibrations of our system. We employ a straight-forward manualprocedure, requiring multiple alignments between on-screen reticlesand either a finger or stylus. While achieving consistent alignmentsto a single point on a stylus is relatively intuitive, the ability of a userto maintain repeated alignments with a single point on a finger tip isfar more inexact. Instead of utilizing an additional physical cap, ring,or other wearable indicator, we incorporate several variations ofon-screen reticle design to provide visual context for aiding the userin properly positioning their finger during calibration alignments.We believe this approach more adequately represents what a viableconsumer oriented calibration mechanism would provide.

3.1 Hardware and SoftwareAn NVIS ST50 binocular OST HMD is used as the primary displayfor our study. The ST50 is capable of producing stereo images

Figure 2: (right) Our HMD and Leap Motion system. (left) A userperforming stylus to screen alignments. The right-handed headrelative coordinate frame, in relation to the Leap Motion, is shown.Positive X extends horizontally to the user’s left, positive Y forward,and positive Z downward to the ground.

Figure 3: Illustrations of the cross (a), box (b), and finger (c) reti-cles used for hand alignments. (d) View through the HMD of thecomplete grid of alignment points for left eye calibration.

with a resolution of 1280×1024, a 40◦ horizontal and 32◦ verticalfield of view, and a manufacturer specified spatial resolution of1.88 arcmn/pxl. A custom 3D printed mount attaches the LeapMotion to the front of the display. Figure 2 shows the completeassembly and orientation of the Leap Motion tracking coordinateframe. The tracking calibration of the Leap Motion controller itselfwas confirmed using the resources included with the Leap Motionsoftware. Integrating the Leap Motion tracking information into ourHMD calibration software is performed using version 2.3.1.31549of the Leap Motion SDK. An Alienware m18 laptop, i7-4700MQ2.4GHz processor with 16 GB RAM running Windows 7 x64, isused to drive the graphics for the display, via HDMI, as well as runall necessary software applications.

3.2 Alignment MethodsCalibration of our system, by a user, is performed by aligning asequential series of on-screen reticles to either the index finger tipon the user’s right hand or to the end of a hand held stylus. Aspreviously noted, we incorporate several reticle designs to provide avisual indication of finger orientation during alignment. However,only a single reticle type is employed for stylus alignments, sincethe tip in this case is more well defined.

Hand Alignments: Tracking data from the Leap Motion is ableto provide the position and orientation of numerous points alongthe hands and arms, as long as they are within the field of view ofthe device. We reduce the alignment complexity of hand calibrationby using only the position information for the tip of the right indexfinger. A more thorough specification for the location of this point,relative to the finger bones, is provided within the Leap Motion’saccompanying documentation. We employ three on-screen reticle

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(a) (b) (c) (d)Figure 4: Stylus and hand alignments for each reticle design, as seen through the HMD. (a) Cross reticle alignment. (b) Box reticle alignment.(c) Finger reticle alignment. (d) Stylus alignment.

designs to provide varying degrees of context to aid in finger po-sitioning during calibration alignments. Perfect alignment occurswhen the center of the right index finger tip coincides with the targetpoint specified for each reticle.

Cross A simple cross-hair, Figure 3 (a), comprised of a hori-zontal and vertical line, is displayed with the target point located atthe center of the intersection point. The on-screen dimensions of thecross are 64×64 pixels with line thickness of 3 pixels. The ubiq-uitous application of cross-hairs for targeting and aiming purposesmakes this a natural design for alignment procedures. Figure 4 (a)illustrates an alignment between a hand and cross reticle as seenthrough our HMD system.

Box The design of the box reticle, Figure 3 (b), is intendedto provide a pseudo cap for the user’s finger. The box reticle iscreated from a 3 sided rectangle displayed with an ’X’ placed onthe upper edge intersecting the target alignment point. The on-screen dimensions of the box are 128× 128 pixels with line and’X’ thickness of 10 and 5 pixels respectively. The structure of thebox design is such that a user would naturally center their fingerwithin the outlined region, improving the likely hood of consistentalignment to the finger tip. Figure 4 (b) illustrates an alignmentbetween a hand and box reticle as seen through our HMD system.

Finger The finger reticle, Figure 3 (c), provides an anatomicalfinger outline onto which the user’s real finger is aligned. The targetpoint for this reticle is located at the center tip of the outline’s upperedge. The on-screen dimensions of the finger is 128× 384 pixelswith average outline thickness of 20 pixels. The finger reticle isintended to provide the most position context of all three designs.The center portion of the reticle is not filled in order to allow theuser a clear view of their finger throughout alignment. While it ispossible to provide a completely solid design, the brightness of thedisplay often inhibits the ability to clearly distinguish the location ofreal objects behind AR content. Figure 4 (c) illustrates an alignmentbetween a hand and finger reticle as seen through our HMD system.

Stylus Alignments: A stylus, or tool as it is referred to in the LeapMotion documentation, is treated as a simplified cylinder object witha length, diameter, and tip located at the center point of the cylinder’send. The tip position and pointing direction of any cylindricalobject of appropriate length and diameter, as specified within theLeap Motion documentation, is automatically tracked by the LeapMotion as long as an appropriate amount of the object is visiblewithin the Leap Motion’s field of view. Our stylus object is createdfrom a 5mm diameter wooden dowel rod, approximately 20cm inlength, held to allow the majority of the length to extend beyond theuser’s hand. The cross reticle, as described previously, is used forstylus calibrations, and perfect alignment occurs when the centerof the cross coincides with the center of the stylus tip. Figure 4 (d)illustrates a stylus alignment as seen through our HMD system.

3.3 Calibration ProcedureWe utilize a standard alignment based SPAAM procedure to calibrateour OST AR system. As recommended in Axholt et al. [1], a total

of 25 alignments is used to generate the final calibration results. Thedistribution of on-screen alignment points is arranged to producea 5×5 grid, as shown in Figure 3 (d), providing an approximatelyeven coverage of on-screen area. In order to facilitate binocularcalibration of both eyes simultaneously, the on-screen location of allreticles is shifted differently for each eye so that the fused left andright binocular reticle image will be perceived stereoscopically indepth by the user, between 200–400cm, or within arms reach. Eventhough the placement of on-screen reticles differs between left andright eyes, we do not change the patterns between monocular andstereo calibrations, or across calibration sets. Therefore, a consistentpattern is always shown to the left eye regardless of condition, andlikewise a consistent sequence of locations is maintained for theright eye alignments regardless of condition. Both hand and styluscalibration conditions proceed in an identical manner.

A single on-screen reticle is rendered to the display screen. Theuser then moves their right index finger or stylus tip until it alignsas closely as possible to the target point of the reticle, as previ-ously described. Once a sufficiently accurate alignment has beenachieved, a button press, on either a keyboard or wireless controlleractivates recording of positional data acquired by the Leap Motion.Throughout the recording process, the color of the on-screen reticleis changed from green to yellow providing visual confirmation to theuser that measurement has begun and to indicate that the alignmentshould be maintained until recording has ceased. The 3D finger orstylus tip location, relative to the Leap Motion coordinate frame, ismeasured every 100ms for 1sec resulting in 10 data points per align-ment. The median X, Y, and Z position value from the 10 recordingpoints is used as the final measure. This location estimate, alongwith the X, Y, screen pixel location of the reticle’s target point, issaved, and the complete set of 25 world and screen correspondencepairs is combined to produce the calibration result.

Monocular calibration sets always proceed by first calibratingthe left eye followed by the right without interruption. Stereo cali-bration sets, of course, produce both left and right results together.Additionally, the user is instructed to perform all hand alignments inan identical manner, by keeping their palm flat and facing towardthe display screen with all five fingers as evenly spaced as possible.We impose this requirement to maintain a hand tracking quality asconsistent as possible across conditions. All stylus alignments arealso performed with the user holding the stylus in their right hand.No further restrictions were placed on the alignment procedure.

4 ANALYSIS OF RESULTS

We recorded alignment data from repeated calibrations by a singleexpert user. Our primary objective is to verify the efficacy of theLeap Motion controller itself, for calibrating OST displays, and notthe inherent usability or intuitiveness of our design. In this regard,repeated measures from an expert user, knowledgeable with theprocedure as similarly employed by [9, 10], provide more stableresults, void of subjective affects. The ordering of reticle conditions,along with monocular and stereo presentation, was randomly per-muted across all conditions. Our expert completed 20 monocularand 20 stereo calibrations for each of the three hand and single stylus

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(h)Figure 5: Estimated user eye locations relative to the Leap Motion coordinate frame. (a) Cross reticle, (b) Box reticle, (c) Finger reticle, and (d)Stylus calibration 3D position estimates. 2D eye position plots showing only X and Y estimate locations for (e) Cross reticle, (f) Box reticle,(g) Finger reticle, and (h) Stylus calibrations. In all plots, the center of the Leap Motion is at location (0, 0, 0), with monocular calibrationestimates displayed in blue, stereo calibration estimates plotted in red, and green circles used to denote an area of plausible eye points.

alignment methods, resulting in 20×4×2 = 160 calibrations total.Each calibration session lasted between 30 and 40 minutes, with theentire data collection task requiring an estimated 12 hours, spreadover a period of two weeks. In order to decrease the amount ofdiscomfort experienced by our expert, we limited the amount of timethat the display was worn to no more than 2 hours in a day. Beforebeginning the data collection task, we carefully aligned the OSTHMD optics for the user’s interpupillary distance, 62mm. However,the user did not perform any additional optical alignments beforeeach calibration session; instead the user simply placed the HMDupon their head and began calibrating. Although this means that theuser’s eyes were not always aligned with the optical centers of theHMD’s monocles, we felt that this represented a more realistic usepattern for HMD calibration.

We utilize three primary metrics for determining the accuracyof calibration results for each condition. First, the estimated eyelocation of the user relative to the Leap Motion coordinate frame isobtained by decomposing the extrinsic component from the SPAAMcalibration results. This is a standard evaluation metric for OSTHMD calibration, [2, 10, 16]. Our second metric is reprojection er-ror, calculated as the difference between the ground truth on-screenposition of each reticle, used during calibration, and the screen coor-dinate that results from back projecting the corresponding finger orstylus 3D tip position using the calibration result for that alignmentset. We additionally examine binocular disparity values, taken asthe difference between the left and right eye location estimates foreach monocular and stereo calibration, along each axis relative tothe Leap Motion coordinate frame.

We tested dependent measures with repeated-measures analysisof variance (ANOVA). We used calibration session (1–20) as therandom variable, in order to remove session-to-session variance thatmay have resulted from the slightly changing alignment betweenthe user’s eyes and the OST HMD optics. For each ANOVA test,if Mauchly’s test indicated non-sphericity, we adjusted the p-value

according to the Huynh-Feldt ε value; in such cases we report εalong with the ANOVA F-test.

4.1 Eye Location EstimatesFigure 5 provides the estimated eye locations obtained from themonocular and stereo calibration results of each alignment method.Since the actual ground truth location of the user’s eye, with respectto the Leap Motion, is not directly attainable in our system, a regionof plausible locations, based on measurements of the physical displayscreen and the user’s interpupillary distance (IPD) of 62mm, ispresented within each plot. The 3D eye positions, relative to theLeap Motion coordinate frame, are provided in Figure 5 (a) through(d) for the Cross, Box, Finger, and Stylus alignment method resultsrespectively. Likewise, a top-down view, showing only the positionsrelative to the Leap Motion’s X and Y axis, are plotted for eachalignment condition in Figure 5 (e) through (h).

Visual inspection of both 3D and 2D eye location estimates showthat the stylus alignment method produced the most accurate extrin-sic results, in relation to plausible ground truth eye positions. Thehighest level of precision, for both monocular and stereo calibrations,likewise occurs for stylus alignments. Nearly all values for stylusalignments fall within plausible locations. Similar to the findings ofAxholt [1] and Moser et al. [16], the primary errors occur along thedepth dimension (the Y axis). The three hand alignment methodsproduce noticeably less uniform results.

A more quantitative measure of precision is the amount of vari-ance, or spread, in location estimates relative to the centroid valueof each related group. We obtain this value by calculating theEuclidean distance from each 3D eye estimate location to the cor-responding median position for all estimates relative to each eyeand alignment method grouping. Distance values for each align-ment method group are provided in Figure 6. Mean and standarddeviation values for the group median distances, with both left andright eye values combined, are provided in Table 1. We performed

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Figure 6: Distances between estimated eye positions and the medianlocation value for monocular (blue) and stereo (red) calibrations foreach alignment method. Mean and ±1 SEM bars are shown for thevalues within each condition group.

ANOVA analysis to identify significant differences between thefour alignment method conditions in relation to both monocularand stereo calibration results. ANOVA results indicate significantdifferences between alignment methods for monocular calibrations(F(3,57) = 13.3, p < 0.001). A post-hoc Tukey-Kramer honest sig-nificant difference test confirms that the cross alignment methodmedian group distances are significantly higher compared to theremaining three methods at p < 0.001. No further significancebetween groups is found. ANOVA results for stereo calibrations,similarly indicate significant differences between alignment methods(F(3,57) = 4.7, p= 0.01,ε = 0.68), with post-hoc analysis confirm-ing that the cross alignment method median group distances, forstereo calibration, are significantly higher than the finger and stylusdistances at p < 0.001. No further significance between groups isfound.

We also directly compare the monocular and stereo results withineach alignment method, combining values for left and right eyefor each condition. We find that cross distances significantly differbetween mono and stereo calibration (F(1,19) = 7.7, p = 0.01).Distances to the group median for the finger alignment methodalso differ significantly between monocular and stereo calibrations(F(1,19) = 15.6, p < 0.001). Mono and stereo calibrations forthe box and stylus methods do not significantly differ (F(1,19) =2.4, p = 0.14 and F(1,19) = 1.8, p = 0.20, respectively).

4.2 Reprojection ErrorFigure 7 provides a visualization to illustrate the reprojection erroramounts in stereo calibrations performed using the cross and stylusalignment methods. Direction vectors, drawn in red, represent thedifference in screen position, pixels, between the back projectedcoordinate of each alignment point and the ground truth reticlelocation used during calibration, drawn in blue. Figure 8 provides thecomplete set of reprojection error values for both mono and stereocalibrations within each of the four alignment methods. Additionally,mean and standard deviation values for the error in each condition,with both left and right eye groupings combined, are provided inTable 1.

Visual inspection of the reprojection error values of Figure 8clearly shows a noticeably lower occurrence of error in styluscalibration results compared to the three finger alignment meth-ods. Repeated measures ANOVA for monocular calibration re-sults indicates a significant difference across alignment method(F(3,117) = 41.0, p < 0.001,ε = 0.68). Post-hoc analysis con-firms that reprojection error values for both the cross and stylusalignment method are significantly different from all other meth-

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(d)Figure 7: Reprojection error plots for stereo calibrations using theCross reticle, (a) and (b), and Stylus, (c) and (d). Blue circlesindicate ground truth reticle location during alignment. Red linesindicate direction and magnitude of reprojection error in pixels.

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Figure 8: Reprojection error for monocular (blue) and stereo (red)calibrations of each alignment method. Mean and ±1 SEM bars areshown for the values within each condition group.

ods (p < 0.001). No further significance between groups werefound. ANOVA for stereo calibration results, similarly, indicatesa significant difference between alignment method reprojection er-ror (F(3,117) = 45.8, p < 0.001,ε = 0.54), with post-hoc resultsshowing that the cross and stylus alignment methods’ reprojectionerror values differ significantly from all other methods (p < 0.001).

We perform additional ANOVA analysis to directly compare re-projection error results between mono and stereo calibrations ofeach alignment method. No significant difference is found be-tween mono and stereo reprojection error for cross calibrations(F(1,39) = 2.1, p = 0.15), though a significant difference in repro-jection error, between mono and stereo calibrations, does occur forthe box alignment method (F(1,39) = 8.7, p = 0.005), as well asfor the finger and stylus methods (F(1,39) = 30.6, p < 0.001 andF(1,39) = 9.4, p = 0.004, respectively).

4.3 Binocular X, Y, Z DisparityOur final evaluation metric is the difference between the separate X,Y, and Z components of the paired left–right eye location estimates(Figure 5) from mono and stereo calibrations. These three binocular

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(c)Figure 9: Differences between left and right eye location estimates for monocular (blue) and stereo (red) calibration pairs. Difference betweenX (a) positions represents interpupillary distance (IPD). The green line indicates the measured IPD, 62mm, of the expert user. Y (b) positiondifferences indicate forward and backward offsets and Z (c) vertical offsets between left and right eye estimates in relation to the Leap Motioncoordinate frame. Mean and ±1 SEM bars are shown for the values within each condition group.

disparity values, for eye pairs within each condition, are provided inFigure 9 (a), (b), and (c), respectively. The difference in X locationbetween eyes provides a measure of interpupillary distance (IPD).The real IPD for the expert user is measured to be approximately62mm, also indicated in Figure 9 (a). The physical differences inthe Y, depth, and Z, vertical, offsets between the expert user’s eyesare not directly measured, but are reasonably expected to be ap-proximately 0mm. Examination of the binocular differences alongall three directions clearly shows that stereo calibrations result inmore accurate disparity, or offset, values compared to monocularcalibration results. Table 1 provides the mean and standard devia-tion for disparities in each direction for all four alignment methodconditions.

Repeated measures ANOVA for the monocular calibration IPDvalues (X axis), in Figure 9 (a), indicate a significant differencebetween alignment conditions (F(3,57) = 5.4, p = 0.01,ε = 0.56).Post-hoc results reveal that the stylus values are statistically differentfrom both the cross and finger values (p = 0.004). Stereo calibrationvalues similarly indicate a significant difference between alignmentmethods (F(3,57) = 7.4, p< 0.001) , with post-hoc results showingthat stylus values differ significantly from cross and finger values(p < 0.001). No further significant differences are found betweengroups. Additional ANOVA analyses, comparing the stereo andmono values within each alignment method, reveal that only fingercalibration results show a significant difference between mono andstereo IPD values (F(1,19) = 5.8, p = 0.03). No significant differ-ences were found between mono and stereo IPD values for the cross,box, or stylus alignment method.

ANOVA across alignment conditions for binocular disparityalong the Y axis, Figure 9 (b), shows a significant difference be-tween monocular calibrations (F(3,57) = 8.0, p = 0.003,ε = 0.52),with post-hoc results confirming significant differences betweenthe cross alignment method and both the box and stylus conditions(p < 0.001). Stereo calibrations also show a significant differencebetween calibration conditions (F(3,57) = 3.1, p= 0.04), with post-hoc results confirming significant differences between the cross andstylus alignment method values (p = 0.03). No further significantdifferences are found between groups. Additional ANOVA analy-ses reveal that mono and stereo values significantly differ withineach calibration condition: cross (F(1,19) = 12.9, p = 0.002), box(F(1,19) = 10.5, p = 0.004), finger (F(1,19) = 17.9, p < 0.001),and stylus (F(1,19) = 8.3, p = 0.009).

Similar statistical results are found for binocular disparity val-ues along the Z axis, Figure 9 (c), with mono calibrations showinga significant effect from alignment condition (F(3,57) = 4.2, p =0.02,ε = 0.76), and stereo calibrations showing a trend towards

being significantly affected by alignment condition (F(3,57) =3.5, p = 0.06,ε = 0.43). Post-hoc results for both cases confirma significant difference between cross and stylus groups for mono(p = 0.012) and stereo calibrations (p = 0.023). No further signifi-cant differences are found between groups. Additional ANOVA anal-yses reveal that mono and stereo values significantly differ withineach calibration condition: cross (F(1,19) = 12.7, p = 0.002), box(F(1,19) = 24.1, p < 0.001), finger (F(1,19) = 22.1, p < 0.001),and stylus (F(1,19) = 17.5, p = 0.001).

5 DISCUSSION

We begin our discussion with a review of the eye location errormetric, starting with comparison between monocular and stereocalibration results. While our statistical analysis only showed sig-nificant differences between mono and stereo sets for the cross andfinger alignment calibrations, the mean values from Table 1 showthat stereo results produced consistently smaller distance to groupmedian values, indicating that stereo calibration yields a consistentlyhigher level of precision, over all. This can also be, somewhat, vi-sually seen by the tighter clustering of eye points in both the 3Dand 2D plots of Figure 5. A clear distinction, though, between notonly the precision, but also the accuracy, can be seen across align-ment method. Calibrations performed with the stylus alignmentmethod produce lower distances to group medians and the highestlevel of accuracy in comparison to plausible eye locations. In fact,the Leap Motion stylus based calibrations yield far greater extrinsicestimates compared to both the finger alignments employed in ourstudy and also compared to extrinsic values found in nearly all previ-ous studies evaluating SPAAM procedures for environment-centricalignments, [1, 2, 10, 16]. We believe that significantly more accu-rate extrinsic values for stylus alignments is directly related to thetracking ability of the Leap Motion and the easily discernable tip ofthe stylus itself.

As previously noted, the accuracy of hand tracking, by the LeapMotion, is highly dependent on the orientation, position, and oc-clusion level of the fingers, palm, and hand features. This inherentsystematic variability naturally leads to less consistent measures inall three of our finger based alignment methods. Conversely, the highprecision in stylus tracking by the Leap Motion inherently yieldsmore reliable results. Additionally, the presence of actual misalign-ment error between the target points of the on-screen reticles and theuser’s finger tip further increases the potential for inaccuracies andhigh variability in calibration results. We attempted to address theconcerns about the ability of a user to perform repeated alignmentsto the exact finger tip, by employing the three reticle designs. Our re-sults do show that the improved positioning context afforded by the

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Table 1: Mean and standard deviation for each error metric, with both left and right eye values combined, separated by alignment method.

Distance to GroupMedian Eye Location

(mm)

BinocularDisparity Along X

(mm)

BinocularDisparity Along Y

(mm)

BinocularDisparity Along Z

(mm)

Reprojection Error

(pixel)mean std mean std mean std mean std mean std

Cross mono 39.46 25.26 72.52 17.38 95.5 96.82 10.29 10.7 14.54 6.46stereo 22.45 21.56 67.06 5.83 16.96 16.48 1.91 2.37 12.92 3.82

Box mono 22.23 15.32 66.57 6.63 31.58 27.99 4.79 3.46 12.41 3.37stereo 16.97 11.07 64.44 4.08 9.05 11.24 0.97 0.63 10.27 2.94

Finger mono 28.01 20.17 71.26 8.09 58.42 46.67 8.4 7.18 14.21 4.12stereo 14.7 8.66 67.13 2.48 12.58 8.12 0.77 0.68 10.25 1.92

Stylus mono 12.22 9.3 61.48 3.98 16.72 12.62 3.83 3.15 5.54 0.82stereo 8.78 7.54 61.94 3.11 7.02 5.57 0.86 0.43 5.98 0.78

box and finger, positively effect calibration results for both monocu-lar and stereo procedures, though not to a high enough degree to becomparable to the stylus results.

The heightened performance of our stylus calibration, comparedto the results from prior investigative studies, we believe is a productof the environment-centric methodology employed in those systems.The SPAAM procedures commonly employed, and evaluated, almostentirely utilize static locations or markers within the environmentas alignment points. The systemic errors due to measurement inac-curacies of these alignment points is not present in our user-centricapproach. Also, all calibration alignments in these previous workswere performed by standing users, which, as shown by Axholt etal. [3], increases the occurrence and magnitude of misalignmenterror due to postural sway. The Leap Motion calibration allowsalignments to be performed while seated, reducing the tendency ofsway and body motion during the procedure. The reprojection errorand binocular disparity results further validate the viability of LeapMotion procedures for OST HMD calibration.

The low reprojection error seen in stylus calibrations is, no doubt,a product of the more accurate extrinsic eye position estimations,with an attainable reprojection accuracy to within 5–6 pixels (Ta-ble 1), again well within the limits obtained by prior SPAAMevaluation studies. The more contextual box and finger reticlesalso showed improvement in reprojection error when utilized withinstereo alignments, confirming the practicality for intuitive reticle de-signs in finger based OST calibration. The binocular IPD measuresalso support the utility of stylus usage for Leap Motion calibration,yielding estimates very close to the actual ground truth measure.The improvements in disparity values, in every direction, for stereocalibrations is not surprising, though, since the stereo procedureinherently forces the alignment to two screen points coupling theerror across both eyes.

Even though we believe our results conclusively show that accu-rate calibration of an OST AR system is possible using the LeapMotion, our evaluation method could still be improved in a numberof ways. We did not consider any environmental conditions, such aslighting and brightness, that may effect the tracking accuracy of theLeap Motion. Therefore, we are not able to speak to the feasibilityof the method as an outdoor calibration solution. Furthermore, weimposed several restrictions on the finger calibration procedure tomaintain tracking consistency, such as forcing the user to maintainan open, fingers spread, hand pose during calibration. Future stud-ies will be needed to examine the resulting accuracy trends fromcalibrations allowing full freedom of hand movements. Moreover,standardization of reticle designs and alignment processes will even-tually be required in order to maintain uniformity of OST calibrationacross devices, increasing the accessible of the practices to noviceconsumers.

6 CONCLUSION AND FUTURE WORK

In this work, we have examined the use of a Leap Motion in facilitat-ing the calibration of an OST HMD system. We utilized monocularand stereo SPAAM based manual alignment procedures for the cali-bration process, and examined the resulting accuracy and precisionfrom both finger and stylus based methods performed by an expertuser. Our results show that both modalities yield calibration quali-ties well within acceptable levels, as compared to those presented inprior SPAAM evaluation studies. Our findings, additionally, indicatethat hand based calibration accuracy can be improved by using morevisibly contextual reticle designs to aid in finger placement duringthe alignment process. However, our overall analysis indicates thatthe higher tracking accuracy and repeatability of stylus alignmentsmake this the preferred method for OST calibration methods incor-porated using the current version of the Leap Motion. Even thoughthe ultimate goal for user-centric calibration is the removal of depen-dency on physical alignment targets, we believe that the inclusionof a storable stylus, in forthcoming consumer OST devices, is areasonable requirement to facilitate manual calibration techniques.

While our results confirm the utility of the Leap Motion in OSTcalibration, our study did not consider extraneous factors, whichmay impact tracking performance of the device, such as lightingconditions, and degraded internal calibration of the device itself.Future studies will also be required to further refine and identify themost intuitive presentation strategies for on-screen reticles, improv-ing the robustness and usability of manual alignment methods. Thestandardization of OST calibration practices will also benefit futurehardware offerings, making the technology more accessible acrosssystems and markets.

ACKNOWLEDGEMENTS

The authors wish to thank Sujan Anreddy for his assistance. Supportfor this work is provided in part by NSF awards IIS-1320909 andIIS-1018413 to J. E. Swan II, and a NASA Mississippi Space GrantConsortium fellowship to K. Moser.

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