A Simple Real-time Eye Tracking and Calibration Approach for

Autostereoscopic 3D Displays

Christian Bailer, Jos´e Henriques, Norbert Schmitz and Didier Stricker

Augmented Vision, German Research Center for Artiﬁcial Intelligence, Trippstadter Strasse 122, Kaiserslautern, Germany

Keywords:

Eye Tracking, Glasses-free Stereoscopic Displays, Calibration.

Abstract:

In this paper a simple eye tracking and calibration approach for glasses-free stereoscopic 3D displays is pre-

sented that requires only one ordinary camera for tracking. The approach is designed for the use with parallax

barrier based screens, but should with(out) limitations also be usable with other autostereoscopic screens.

The robust eye tracking approach can easily be reimplemented and is based on well chosen search areas and

parameters that were determined experimentally. Thanks to efﬁcient eye position prediction delays can be

eliminated that are normally a problem in realtime systems. The calibration approach allows us to calibrate

the eye tracking camera to the 3D screen in a direct and simple way. Direct means that the calibration is

realized pixel-wise and simple means that there is no need for a (complex) camera/screen model in contrast to

many other calibration approaches. There is even no need to determine any camera parameter for calibration.

The accuracy of the eye tracking approach and the eye position prediction is evaluated experimentally.

1 INTRODUCTION

Thanks to technological advances, glasses-based 3D

displays are nowadays nearly as cheap as 2D dis-

plays, while they were still very expensive only a

few years ago. This strongly promotes the distribu-

tion, but not necessary the acceptance, of 3D technol-

ogy. Still 3D glasses are inconvenient to use. One

ﬁrst has to put them on before one can make use of

the 3D effect. Furthermore, the glasses can be un-

comfortable to wear especially for spectacle wearers,

that have to wear two pairs of glasses at once. More-

over, the glasses darken the environment considerably

which is a disadvantage for vision with indoor illumi-

nation. These disadvantages can be avoided by using

glasses free 3D displays. They are still expensive –

but similar to the price drop of glasses based 3D dis-

plays their price might drop signiﬁcantly within the

next few years.

Glasses free 3D displays can basically be divided

into two classes: autostereoscopic displays and vol-

umetric/holographic displays. Volumetric displays

work by displaying the scene from many perspec-

tives at once. This makes it besides the complexity

of the display itself inapplicable for 3D movies, that

were recorded from two perspectives only and hard

for realtime rendering as extremely powerful hard-

ware is necessary to render all perspectives at once.

Autostereoscopic displays on the other hand, only re-

quire two perspectives at a time like glasses based

stereoscopic displays. To work this requires the user

to either stay at a special spot in front of the display

like with the Nintendo 3DS or eye position estimation

(eye tracking) is required to determine at which coor-

dinates in front of the screen the image for an eye is

required.

In this work we present a parallax barrier based

autostereoscopic 3D system with eye tracking. Our

approach allows us to work with only one single cam-

era for eye tracking. Usually eye tracking systems

for 3D screens require either two cameras (Su et al.,

2003; Perlin et al., 2001) or a depth camera (Li et al.,

2012) as they need three dimensional eye positions.

Also many eye tracking systems build on the red eye

effect (Zhu et al., 2002) which requires pulsing in-

frared light that must be synchronized with the track-

ing camera. This requires a more expensive camera

that has to have a good infrared sensibility (especially

in bright rooms) and a higher framerate. Also, the

setup is more complex. It is even more complex if the

red eye effect is required in both cameras of a stereo

camera setup (Perlin et al., 2001). Also such setups

cannot deal well with fast eye movement especially if

there are reﬂections e.g. on glasses.

Our tracking approach can be easily reimple-

mented as essential parts of the approach are based on

123

Bailer C., Henriques J., Schmitz N. and Stricker D..

A Simple Real-Time Eye Tracking and Calibration Approach for Autostereoscopic 3D Displays.

DOI: 10.5220/0005309101230129

In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), pages 123-129

ISBN: 978-989-758-091-8

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: The (doted) rays from the left-most and right-most

end of the screen are limiting the optimal viewing areas for

both eyes. Green: Area where the image for the left eye

is visible. Red: Area for the image of the right eye. The

lines passing through the corners of the rhombuses meet at

the middle of the screen. If the tracking camera is placed

here there is no advantage anymore in determining the eye

depth. See text for more details.

established algorithms with publicly available source-

code. Search areas (e.g. Figure 5) are chosen to work

well for all tested persons plus some extra margin,

while being strict enough to exclude outliers. The sys-

tem can work under different lighting conditions (we

tested it with sunlight as well as infrared light). A ma-

jor beneﬁt of the proposed setup is that the calibration

approach is pixel-wise and thus does not require the

determination of camera and screen parameters. De-

termining such parameters can be complicated espe-

cially if even two cameras must be calibrated to each

other (Andiel et al., 2002).

The paper is structured as follows: In Section 2

we give an overview over our 3D system including

the camera for tracking and the 3D screen. In Sec-

tion 3 we are describing our approach of calibrating

the tracking camera to the 3D screen. In Section 4

we describe the actual eye tracking system in detail.

The eye tracking system includes eye tracking as well

as eye detection elements. While we differ between

the tracking and detection parts in Section 4 the term

“eye tracking” is in other sections only used to refer

to our whole eye tracking system. Finally, we eval-

uate and conclude our approach in Section 5 and 6,

respectively.

2 THE 3D SYSTEM

In this section we describe our 3D system. The sys-

tem consists of the following hardware parts: The 3D

screen, the camera for eye tracking, a PC (Xeon E3

@3.4Ghz) running our software and infrared LEDS

for optional night vision. The software consist of

the eye tracking and calibration system. Our track-

ing camera is a common camera which operates at a

resolution of 1216 x 866 pixels at 50 frames per sec-

Moved barrier:

Unmoved barrier:

Eye

distance

Figure 2: The stripes illustrate the colors on the dashed line

in Figure 1. The width of a stripe is roughly the eye distance

of a human. First row: original screen image. Second row:

images for eyes are swapped. This creates different 3D ar-

eas. In theory every point is covered by these two states. In

practice it will not work in the transit area if the eyes are not

exactly in the depth of the dashed line in Figure 1. This can

be solved by a movable barrier, which gives us in our case

4 different states.

ond. Our 3D screen is based on the parallax barrier

principle (see Fig. 2 in (Neil, 2005)) with multiple

viewing zones (see Figure 1 and Fig. 3/4 in (Neil,

2005)). The barrier of our screen can be moved, so

that we cannot only swap the image for the left and

the right eye but have in common four possible states

(Figure 2). For details on the technology concerning

movable barriers see e.g. (Isono et al., 1993; Yi et al.,

2008). The camera is placed at the intersection point

of the rhombuses (Figure 1). Thereby we do not have

to consider the depth (z value) for calibration and eye

tracking as we can determine the best possible screen

setting directly from pure 2D eye positions. Please

note that although the intersection point in Figure 1

is in the center of the screen we can move the cam-

era freely alongside the parallax barrier stripes (the

dimension not visible in the ﬁgure). This allows us to

place it on top of the screen. If the camera position-

ing opposed to the barrier is not accurate the size of

the rhombuses is reduced slightly. In practice, a rough

central placement is sufﬁcient.

3 CALIBRATION

The goal of our calibration approach is to calibrate

(assign) the pixel positions in the camera used for eye

tracking directly to the appropriate states of the 3D

screen. Assigning pixels directly allows us to cal-

ibrate the system without knowing all the relevant

camera and screen parameters. This is a big advan-

tage as the relevant screen parameters might even be

vendor or model speciﬁc. To do so, we put the screen

2 meters away parallel to a wall (as this is the optimal

distance of operation, dashed line in Figure 1). Then

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124

Figure 3: Left: One of the two input images with noise and image artifacts. Right: The resulting stripe pattern.

we render a black image for one eye and a white im-

age for the other eye. In a dark room this creates a

pattern like the one that can be seen in Figure 3 left.

The pattern is too dark to be directly recordable by our

camera. However, we can create the image by taking

several images and averaging their brightness values

to obtain the image I

. Then we invert the screen illu-

mination and take another averaged image I

. Invert-

ing the screen illumination means that we render a

white image for the eye where we originally rendered

a black image and vice versa. Then we compare I

to I

. If a pixel is brighter in I

than in I

we set this

pixel to 1 in a new binary image I

. Otherwise we

set the pixel to 0. If we apply a median ﬁlter on I

to remove single outliers we get the image visible in

Figure 3 on the right side. As can be seen the stripes

are nearly detected perfectly although the original im-

ages are noisy and contain artifacts. I

could now be

used to ﬁnd camera parameters that lead to the deter-

mined pattern. However, this is unnecessary as it is

more accurate and less effort to use I

directly instead

of approximating it with a model. In total we create

4 images I

for the 4 states in Figure 2 which we call

...I

. The ﬁrst two are for the unmoved barrier and

the last two for the moved barrier. Practically we do

not save I

and I

as they are just the inverse of I

and

, respectively.

To determine the correct state for given eye posi-

tions from the eye tracker we ﬁrst calculate the eye

center position by averaging both eye positions. This

makes sense as there is no advantage in treating them

independently. In the unlikely case where our eye

tracker (described below) only provides the position

of one eye we take the head center (also provided by

our eye tracker) for the x and the eye position as the

y coordinate of the eye center position. To determine

how well the eye center position ﬁts to a state s we

determine the distance of the eye center pixel to the

next white to black transit in the corresponding image

. The state where the transit is the closest from the

eye center pixel is the state that is chosen.

Note that our direct calibration approach is also

suited for displays with freely moving stripes evenif it

only provides two viewing spots at a time (See (Neil,

2005) Fig. 4b) ) . We do not have to record a calibra-

tion pattern for every possible position or state as we

can simply interpolate in between positions/states by

the distances of the eye center position to the white

black transit in the two best ﬁtting calibration pat-

terns.

4 THE EYE TRACKING SYSTEM

In this section we present our eye tracking system,

which is outlined in Figure 4. In the ﬁrst frame we

perform eye detection to ﬁnd the positions of the two

eyes. If an eye is detected it is tracked in the next

frame(s), but at the same time we also try to redetect

it.

This helps to get a more accurate position if the

detection and tracking do not lead to the exactly same

position. Furthermore, redetection helps us to update

the appearance model of the tracker – however, we are

not only considering the newly detected position for

model update but also the previous one in our fusion

approach. Thanks to redetection we can also still ﬁnd

the eye in frames where either tracking or detection

fails. In the subsequent part of this section we will

describe the individual parts of our approach in more

detail. We also describe our prediction approach that

predicts eye positions to eliminate delays.

4.1 Eye Detection

To be able to perform robust and fast eye detection

ASimpleReal-TimeEyeTrackingandCalibrationApproachforAutostereoscopic3DDisplays

125

Figure 4: The eye tracking pipeline. “Eye=” means that the

eye position is set from the stated value. “no eye” means

that there is no eye detected in the frame.

we ﬁrst use face detection to detect face candidates.

Face detection is performed on a scaled-down image

to speed up detection. Scaling down the image usu-

ally does not drop the detection rate much as faces

are much larger than eyes but clearly speeds up detec-

tion. Autostereoscopic displays usually have a limited

working distance. Thus, we are searching the face

only for face sizes that correspond to a distance in the

range of operation ± 20%.

After one or multiple face candidates are found

the eyes are searched in deﬁned areas inside each face

candidate (see Figure 5). If only one eye candidate

is found inside the search area of each eye it is kept.

Otherwise all of them are discarded. As this happens

only seldom with our well chosen search areas we do

not want to risk to choose the wrong one.

For eye and face detection we use Haar fea-

ture based cascade classiﬁers (Viola and Jones,

2001; Lienhart and Maydt, 2002). More precisely

we are using the following pretrained classiﬁers

that are publicly available in the OpenCV library

“haarcascade

frontalface alt.xml” for face detection

and “haarcascade

mcs lefteye.xml” and “haarcas-

cade mcs righteye.xml” for the detection of left and

right eye, respectively. The search size for eyes we

set to be between 0.2 and 0.4 times the face size for

the width and 2/3 of this value for the height.

In our tests we could not ﬁnd a case where we

found both eyes for false positive face candidates.

available at: www.opencv.org

0.5F

0.32F 0.32F0.36F

0.38F

Figure 5: The search areas for the left eye (blue) and the

right eye (dashed red) inside the area of a detected face. Val-

ues were determined carefully through experiments. Note

that eyes are determined as areas i.e. the center of an eye

position cannot be in the whole search area.

Thus, we can robustly reject false positives by reject-

ing faces where we cannot ﬁnd both eyes. If we ﬁnd

one eye we will reject the detected eye if we either

detect another face with two eyes or if the tracked po-

sition contradicts with the detection. In case of two

persons in the image we prefer the currently tracked

person for a display like ours that supports 3D only

for one person.

4.2 Eye Tracking

Eye tracking is performed by template matching.

Template matching is fast and according to our tests

in our case also more robust and accurate than many

more advanced tracking methods. We found that one

reason for this is the small size (in pixels) of our tem-

plates, which leads to poorer results with many fea-

ture based tracking methods. We also think that the

appearance of eyes of having one central blob is ad-

vantageous for template trackers in case of appear-

ance change. In frames where the eye is detected the

eye template is created or updated from the image de-

tail at the eye position. In frames where there is no de-

tection it is not updated to avoid drifting. For robust-

ness and speed, templates are only matched to a local

image area where the eye is expected. The center of

this area is at the eye position at the last frame plus the

movement between the two last frames if available.

If the matching score of the best position deceeds a

threshold tracking fails without a valid position and

the template is deleted.

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As template matching function we are using Nor-

malized Cross Correlation, which is robust to illumi-

nation changes. In OpenCV this can be easily utilized

by using the “matchTemplate” function. To better be

able to deal with appearance changes template match-

ing is performed with a slightly Gaussian blurred tem-

plate and image. Thanks to the blur, pixels do not

have to ﬁt perfectly and it rather improves matching

accuracy than reducing it.

4.3 Information Fusion

Pixel-wise template matching is usually more accu-

rate in position than object detectors that are based on

coarse image features like Haar or HOG. We cannot

directly beneﬁt from the higher accuracy as the tem-

plate is based on the detection. However, the tracker

allows us to shift the detected eye position from one

frame to the next. The shifted detection can then be

directly compared to the detection in the next frame.

This allows us to average the detected eye positions

of the detector in different frames. Formally the eye

position at a frame n, P

is calculated as:

= S

+ T

(1)

where T

is the tracked position at frame n and S

the

shift correction calculated as:

= round

∑

i=n−k+1

(2)

= D

− T

(3)

n+i

= S

n+i−1

− S

n+i

(4)

is the detected eye position and k the number of

considered previous frames. A template with center

is used as new tracking template. In case that track-

ing fails the considered frames k must be reset to one.

We deﬁne K= k

max

4.4 Dealing with Reﬂections on Glasses

Reﬂections on glasses caused e.g. by sunlight or in-

frared illumination for tracking in the dark can dis-

tract our tracking and detection methods. The dis-

traction can be reduced signiﬁcantly by lowering the

brightness value at brightness peaks caused by the re-

ﬂections. To do so we determine for each pixel the

average brightness of its local surrounding (We use

the eye template size as the size of the local surround-

ing. See Section 5 for its size). If a pixel exceeds 3

times the average brightness or has the maximal rep-

resentable brightness value it is considered to be part

of the reﬂection and is set to the average brightness of

the local surrounding. By using integral images this

approach can be implemented with very low runtime

cost.

4.5 Temporal Prediction

A problem with realtime eye tracking for 3D displays

is that there is a temporal delay i.e. the eye position is

already outdated when calculated. Humans can rec-

ognize even a very short delay well. To prevent the

delay we predict the eye position for a time where

we do not yet have an image from the eye tracking

camera. We test and compare two types of prediction,

simple speed based prediction:

(1)

n+i

= P

+ i(P

− P

n−1

) (5)

and acceleration based prediction:

(2)

n+i

= P

+ i(P

− P

n−1

) + 0.5i

− 2P

n−1

+ P

n−2

)

(6)

Our system has a delay of around 55 ms. 10 ms be-

cause the average eye position is in the middle of the

exposure. The software delay from starting receiving

a new image from the camera until a new state is send

is around 25 ms (As steps for different frames can be

performed in parallel we can still process more than

50 frames a second). We assume on average 15 ms

delay for the time to the next display refresh plus the

displays reaction time. Furthermore, we calculate 5

ms as extra delay e.g. for the time the graphics card

actually needs to transmit an image. If makes no dif-

ference if the single eye positions are predicted before

eye center calculation or if the eye center position is

predicted directly.

5 EVALUATION

In this section we evaluate the accuracy of our eye

tracking approach. For our tests we use a scale down

factor of 2.5 for face detection. The template size

for eye tracking we set to 0.2F × 0.15F, the template

search area to 0.33F × 0.25F and σ of the template

blur to 0.02F, with F being the detected face size.

Tracking fails if the template matching error for the

best position deceeds 0.8.

Our evaluation results can be seen in Table 1. We

evaluated our tracking approach with 8 different per-

sons and told them to move in different ways. Then

we roughly categorized the different recordings ac-

cording to their movement speed and accelerations.

For “still” only slight movement and no big position

change is allowed. However, people are not artiﬁ-

cially trying to avoid movement completely. Slow

ASimpleReal-TimeEyeTrackingandCalibrationApproachforAutostereoscopic3DDisplays

127

Table 1: Our evaluation results. We evaluated the location error for direct tracking and prediction of 3 frames (60ms). On the

right we show the number of frames that exceed an error threshold. K is set to 2 for these threshold tests. Person 3,7 and 8 are

wearing glasses. Please note that the overall average is strongly inﬂuenced by the few fast movement experiments, as there

are great errors with fast movement. We show the overall average for completeness, but practically relevant is the average that

excludes the unnaturally fast movement. The bold numbers show the best value of a K. See text for more details.

Average location error in pixel % frames with pixel error

Direct (P

) Speed Pred. P

(1)

n+3

Acc. Pred. P

(2)

n+3

Speed Pred. P

(1)

n+3

(2)

n+3

Per-

son

Speed K=1 K=2 K=3 K=1 K=2 K=3 K=1 K=2 K=3 ≥

≥

1 still 1.26 1.26 1.14 2.68 1.60 1.25 6.43 2.54 1.83 0.0 0.0 0.0 0.0

3 still 2.53 2.47 2.67 3.67 2.66 2.51 7.97 4.05 3.17 0.0 0.0 0.0 0.0

5 still 0.33 0.28 0.28 1.53 1.17 1.03 5.24 1.74 1.94 0.0 0.0 0.0 0.0

1 slow 0.75 0.67 0.82 2.57 2.25 2.34 6.23 4.31 4.80 0.0 0.0 0.0 2.1

2 slow 1.84 2.10 1.83 3.60 3.03 2.75 7.74 4.52 4.86 0.0 0.0 0.0 3.0

3 slow 1.94 1.78 2.02 2.84 2.80 2.80 6.36 4.91 4.37 0.0 0.0 0.0 2.2

4 slow 0.97 0.73 0.81 2.78 1.57 1.94 7.65 3.76 4.12 0.0 0.0 0.0 0.0

5 slow 0.65 0.59 0.59 2.88 2.42 2.52 6.46 5.13 4.38 0.0 0.0 0.0 0.0

6 slow 1.09 1.14 1.13 2.42 2.03 1.76 5.09 3.58 2.84 0.0 0.0 0.0 0.0

2 middle 1.63 1.89 1.72 6.44 5.60 5.69 9.47 6.61 6.62 0.0 0.0 0.0 4.5

3 middle 1.64 1.42 1.69 7.12 6.44 6.26 11.27 7.94 7.26 0.0 0.0 1.6 9.8

4 middle 0.80 0.64 0.70 3.29 2.56 2.43 6.59 3.83 3.38 0.0 0.0 0.0 0.0

5 middle 0.92 0.88 0.85 3.91 3.65 3.58 7.48 6.45 5.20 0.0 0.0 0.0 8.6

6 middle 0.99 1.09 0.99 4.29 4.01 3.71 6.70 5.31 4.89 0.0 0.0 0.0 5.7

7 middle 1.39 1.31 1.34 5.18 4.46 4.13 10.16 6.94 5.92 0.0 0.0 0.0 3.6

8 still - fast 1.11 0.89 1.19 4.30 4.00 3.99 6.76 4.78 4.78 0.0 1.3 5.1 3.8

1 fast 0.90 0.75 0.97 5.03 4.61 5.53 8.25 7.39 7.80 0.0 5.5 15.0 11.0

2 fast 2.47 3.94 5.08 21.67 20.29 20.62 16.12 13.26

12.85

14.3 35.7 50.0 21.4

4 fast 1.38 1.35 1.76 11.91 11.79 11.35 9.08 10.12 8.93 0.0 4.2 25.0 12.5

7 very fast 9.09 9.33 11.22 32.12 33.12 33.99 64.54 63.07 67.21 23.5 41.2 52.9 64.7

6◦ ≤ middle 1.24 1.20 1.24 3.72 3.14 3.04 7.35 4.77 4.40 0.0 0.1 0.4 2.7

6◦ all 1.68 1.73 1.94 6.51 6.00 6.00 10.78 8.51 8.36 1.9 4.4 7.5 7.6

and middle corresponds to usual movement in front

of the screen if the user wants to change his position

or if he wants to test the 3D effect while moving. Fast

and very fast are unnatural fast movements with very

strong accelerations, that should only happen if one

wants to ﬁnd the limits of our system. Thus, we show

fast movement only as completion as it is usually ir-

relevant for the practical application.

Figure 6: Circles: two inaccurate detections, one form the

current frame and one shifted from the last frame. Doted

circle: Average position of the two circles. Cross: ground

truth. Only in the right example the doted circle is closer to

the ground truth than the average distance of the two normal

circles to the ground truth. As the position variations of the

eye detector is mostly like on the left (one sided error) there

is no big beneﬁt for our information fusion approach in av-

erage pixel location error. However, the doted circle is less

noisy in position than the original circles which supports

prediction (see text).

The determined pixel error is the error of the eye

center position (the average of both eye potions) com-

pared to labeled ground truth, as the accuracy of the

eye center position and not the accuracy of single eyes

is relevant for our approach. As can be seen in Ta-

ble 1 the pixel location error without prediction is for

natural movement on average only 1.2 pixels (K=1),

which are roughly 0.8 mm. Here, we cannot beneﬁt

much from information fusion on average location er-

ror.

Figure 6 shows a likely reason for it. However, if

we use prediction the more stable and less noisy posi-

tion is a real beneﬁt and leads to clearly smaller pixel

location errors especially for acceleration based pre-

diction. Up to K=3 the average location error drops.

For bigger K the shift error of several shifts in a row

(errors are summing up) exceeds the beneﬁt. Without

prediction K=2 is already the limit. Although, accel-

eration based prediction beneﬁts more from informa-

tion fusion it cannot compete with simple speed based

prediction in accuracy. Thus, we practically use speed

based prediction with K=3.

In our tests the measured stripe size was around

But in the number of sequences where K=2 and K=3 is

better than K=1 the difference is signiﬁcant when excluding

fast movement speed.

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128

96 pixels. Thus, we can allow in the best case 48

in the average case 36 and in the worst case 24 pix-

els location error to be still in a correct screen state.

In Table 1 we also measure the percentage of frames

where the pixel error exceeds a limit (K=3 is used).

In practice it is recommendable to stay below the the-

oretical values. Thus, we also tested for 18 pixels. As

can be seen, even 18 pixels are no problem with speed

based prediction for up to middle movement speed,

while the limit is exceeded several times in differ-

ent sequences with acceleration based prediction. In

contrast, for fast movement speed, acceleration based

prediction is often superior (also in accuracy). Practi-

cally, the user can (due to limit exceedances) see some

ﬂicker for fast movement, mainly when he abruptly

starts or stops moving.

6 CONCLUSION

In this paper we presented an accurate calibration ap-

proach for or autostereoscopic 3D displays that does

not require the knowledge of camera and screen pa-

rameters and is thus very universal and simple to

apply. Furthermore, we presented an easily imple-

mentable but robust eye tracking system. In our eval-

uation we demonstrated its effectiveness. We showed

that it mostly even works for very high movement

speeds. Thanks to the temporal prediction and the

information fusion that improves the prediction accu-

racy even a reaction delay of 60 ms is no real prob-

lem in our realtime autostereoscopic system. In fu-

ture work we plan to expand our system to more com-

plex autostereoscopic displays that can directly adapt

to the users distance to the screen. We, for example,

can determine the interocular distance with our eye

tracker to calculate the rough viewing distance and

calibration could e.g. be performed for two or more

distances and in-between distances could be interpo-

lated.

ACKNOWLEDGEMENT

This work has been partially funded by the BMBF

project Density.

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