Optimization of an Autostereoscopic Display for a Driving Simulator

Eva Eggeling

, Dieter W. Fellner

2,3

, Andreas Halm

and Torsten Ullrich

Fraunhofer Austria Research GmbH, Inffeldgasse 16c, Graz, Austria

Institute of Computer Graphics and Knowledge Visualization, TU Graz, Graz, Austria

GRIS, TU Darmstadt & Fraunhofer IGD, Darmstadt, Germany

Keywords:

Raster Display Devices, Virtual Reality, Global Optimization.

Abstract:

In this paper, we present an algorithm to optimize a 3D stereoscopic display based on parallax barriers for

a driving simulator. The main purpose of the simulator is to enable user studies in reproducible laboratory

conditions to test and evaluate driving assistance systems. The main idea of our optimization approach is to

determine by numerical analysis the best pattern for an autostereoscopic display with the best image separation

for each eye, integrated into a virtual reality environment.

Our implementation uses a differential evolution algorithm, which is a parallel, direct search method based

on evolution strategies, because it converges fast and is inherently parallel. This allows an execution on a

network of computers. The resulting algorithm allows optimizing the display and its corresponding pattern,

such that a single user in the simulator environment sees a stereoscopic image without being supported by

special eye-wear.

1 INTRODUCTION

The concept of a 3D display has a long and varied

history stretching back to the 3D stereo photographs

made in the late 19th century through 3D movies in

the 1950’s, holography in the 1960’s and 1970’s and

the 3D computer graphics and virtual reality of today

– as summarized by PHILIP BENZIE et al. in “A Sur-

vey of 3DTV Displays” (Benzie et al., 2007).

Taking all the options into account to realize a

3D-display (Lancelle, 2011), our customer chose a

parallax-barrier-based autostereoscopic display due

to its cost-efﬁciency. The ﬁeld of application is a driv-

ing simulator, which shall be used to test and evalu-

ate driving assistance systems in user studies in re-

producible laboratory conditions; i.e. the main user

in this specialized virtual reality (VR) environment is

a driver in a typical driving position. This setting of-

fers the possibility to adopt the VR visualization with

extensive assumptions.

Therefore, we focus on the parallax barriers and

present a way to optimize it. Using numerical analy-

sis in combination with geometric modeling, we show

that it is possible to determine the best setup conﬁgu-

ration for a parallax barrier and to predict its quality,

in terms of separable pixel, even during the simula-

tor’s planning phase. This optimization approach is

beneﬁcial not only for autostereoscopic displays but

for optimized VR-environments in general.

2 RELATED WORK

2.1 3D Displays & Parallax Barrier

A graphical display is termed autostereoscopic when

all of the work of stereo separation is done by the dis-

play (Eichenlaub, 1998), so that the observer does not

need to wear special eye-wear.

Nowadays, a wide range of autostereoscopic dis-

play technologies exists. While technologies like

holographic displays can still be considered experi-

mental, other technologies, like variations of parallax

barriers or lenticular lenses which have been utilized

by several consumer TVs as well as the Nintendo 3DS

handheld console, are already quite common (Benzie

et al., 2007).

These binocular display types are quite simple to

produce but have a number of limitations. The most

important one is, that they are limited to one user

whose position needs to be ﬁxed or is at least lim-

ited to a few viewing spots. For the parallax barrier

method a ﬁne vertical grating or lenticular lens ar-

318

Eggeling E., Fellner D., Halm A. and Ullrich T..

Optimization of an Autostereoscopic Display for a Driving Simulator.

DOI: 10.5220/0004290203180326

In Proceedings of the International Conference on Computer Graphics Theory and Applications and International Conference on Information

Visualization Theory and Applications (GRAPP-2013), pages 318-326

ISBN: 978-989-8565-46-4

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: An autostereoscopic display can be realized us-

ing a parallax barrier. The barrier is located between the

eyes (visualized in blue and red) and the pixel array of the

display. It blocks certain pixels for each eye, which results

in the eyes seeing only disjoint pixel columns (at least in

an optimal setting). If the display is fed with correct image

data, the users sees a stereo image.

ray is placed in front of a display screen. If the ob-

server’s eyes remain ﬁxed at a particular location in

space, then one eye can see only the even display pix-

els through the grating or lens array, and the other eye

can see only the odd display pixels (see Figure 1).

The limitation to a single user is not a problem in

this scenario since it is limited to one user (the driver)

anyway. The other major drawback of this approach,

namely the fact that the observer must remain in a

ﬁxed position, can be lifted by virtually adjusting the

pixel columns such that the separation remains intact,

as presented in (Sandin et al., 2001; Peterka et al.,

2007). For this to work, some kind of user tracking is

needed which also limits the amount of possible users.

Since the user’s possible positions are very lim-

ited in this scenario, there is no need to adjust for

user movement other than head rotation. Especially,

there is no need to adjust for large distance variations,

for example, using a dynamic parallax barrier (Perlin

et al., 2000).

Most consumer products containing autostereo-

scopic displays, however, just combine parallax bar-

riers with lenticular lenses, which does not put any

constraints on the number of possible users at a time.

This approach is relatively restricted concerning the

possible viewing position(s).

The one remaining drawback of this technique is

that the resolution drops down to a half for just a sin-

gle user. In the presented scenario, this is not a critical

point since the available resolution is quite high.

2.2 Numerical Analysis

An optimization problem can be represented in the

following way: For a function f mapping elements

from a set A to the real numbers, an element x

∈A is

sought-after, such that

∀x ∈ A : f (x

) ≤ f (x). (1)

Such a formulation is called a minimization problem

and the element x

is called a global minimum. De-

pending on the ﬁeld of application, f is called an ob-

jective function, cost function, or energy function. A

feasible solution that minimizes the objective function

is called the optimal solution.

Typically, A is some subset of the Euclidean space

, often speciﬁed by a set of constraints (equalities

or inequalities) that the elements of A have to fulﬁll.

Generally, a function f may have several local min-

ima, where a local minimum x

satisﬁes the expres-

sion f (x

) ≤ f (x) for all x ∈ A in a neighborhood of

. In other words, in some region around x

all func-

tion values are greater than or equal to the value at x

The occurrence of multiple extrema makes problem

solving in (nonlinear) optimization very hard. Usu-

ally, the global (best) minimizer is difﬁcult to identify

because in most cases our knowledge of the objective

functional is only local and global information are not

available. Since there is no easy algebraic character-

ization of global optimality, global optimization is a

difﬁcult area,especially in higher dimensions.

Further explanations on global optimization can

be found in “Numerical Methods” (Boehm and

Prautzsch, 1993), “Numerical Optimization” (No-

cedal and Wright, 1999), “Introduction to Applied

Optimization” (Diwekar, 2003), “Compact Numer-

ical Methods for Computers: Linear Algebra and

Function Minimisation” (Nash, 1990), as well as in

“Numerische Methoden der Analysis” (english: Nu-

merical Methods of Analysis) (H

ollig et al., 2010).

Besides these introductions and overviews some

books emphasize practical aspects – e.g. “Practical

Optimization” (Gill et al., 1982), “Practical Methods

of Optimization” (Fletcher, 2000), and “Global Op-

timization: Software, Test Problems, and Applica-

tions” (Pinter, 2002).

All optimization algorithms can be classiﬁed in

gradient-based methods, which use the objective

function’s derivatives, and non-gradient-based meth-

ods, which do not rely on derivatives. As most gradi-

ent based methods optimize locally, they most likely

ﬁnd local minima of a nonlinear function but not its

global minimum. To ﬁnd a global minimum local

optimization algorithms can be combined with ge-

netic algorithms (Janikow and Michalewicz, 1990),

(Michalewicz, 1995), (Michalewicz and Schoenauer,

1996) which have good global search characteris-

tics (Okamoto et al., 1998). These combinatorial

methods – such as simulated annealing (Ingber, 1993)

– improve the search strategy through the introduction

of two tricks. The ﬁrst is the so-called “Metropolis

algorithm” (Metropolis et al., 1953), in which some

iterations that do not lower the objective function are

accepted in order to “explore” more of the possible

space of solutions. The second trick limits these ex-

OptimizationofanAutostereoscopicDisplayforaDrivingSimulator

319

plorations, if the cost function declines only slowly.

Our implementation uses such an algorithm: dif-

ferential evolution (Storn and Price, 1997). It is a par-

allel, direct search method based on ideas of evolution

strategies. It uses n vectors x

i,k

(i = 1,...,n) as a pop-

ulation for each generation k. The members of a new

generation k + 1 are generated by a permutation and a

cross-over process. For each vector x

i,k

a trial vector

∆ = x

α,k

+ F ·(x

β,k

−x

γ,k

) (2)

is generated with a constant F ∈ R, F > 0, and ran-

domly chosen α,β,γ ∈ {1,...,n}\{i}, which do not

equal each other α 6= β 6= γ 6= α.

To increase the diversity of the parameter vectors,

a cross-over process mixes x

i,k

with ∆. The result-

ing vector y consists of a sequence of elements of

i,k

, whereas other elements are copied from ∆. If

the new vector y yields a smaller objective function

value than x

i,k

, then x

i,k+1

is replaced by y otherwise

the old value x

i,k

is retained.

The differential evolution method for minimizing

continuous space functions can also handle discrete

problems by embedding the discrete parameter do-

main in a continuous domain. It converges quite fast

and is inherently parallel, which allows an execution

on a network of computers.

3 ALGORITHMIC OVERVIEW

The main idea of our optimization approach is to de-

termine the best pattern for an autostereoscopic dis-

play by numerical analysis; i.e. the pattern (as illus-

trated in Figure 1) has free parameters (line width,

line distance, and line orientation) and is interpreted

as a function. Embedded into a geometric scene the

objective function simply counts the number of pix-

els, which can be seen by both eyes, or which cannot

be seen at all. If this value is minimized, the number

of pixel, which can be seen only by one eye is maxi-

mized. As a consequence, the best image separation

is reached.

3.1 Geometric Description

In detail, the objective function is an algorithmic rou-

tine, whose inner structure is very similar to a ray

tracer. It consists of the components display, pattern,

occluder and eyes, as described below:

Display. The display, respectively its 2D pixel array,

is deﬁned by its four corner points in R

, which

form a planar rectangle, and its horizontal h and

vertical w resolution. These parameters are ﬁxed

and not subject to the optimization.

f (x) =

√

2π

−x

0 4−4

Figure 2: A random variable X has a Gaussian distribution

with mean µ and variance σ

; written X ∼N(µ,σ

), if it has

a probability density function f (x) =

√

2π

−(x−µ)

/(2·σ

)

This plot shows the standard normal distribution N(0,1).

Based on this display deﬁnition a sequence of pix-

els

P = {p

,...,p

h×w

} (3)

in 3D is generated.

Pattern. The parallax barrier is deﬁned by seven pa-

rameters. Four of them are points in 3D space,

which form a planar rectangle, and three values

describe the pattern itself (the line width l

, the

distance between two consecutive lines l

mea-

sured between medial axes, and their deviation

from a vertical alignment l

). These three vari-

ables

) (4)

are subject to the optimization.

Occluder. The geometric description also contains

occluders – simple triangles, which are used to de-

scribe, e.g., the car’s geometry in Section 5.

Eyes. The eyes are speciﬁed by a center point, a look-

at-direction and an up-direction, which deﬁne a

local coordinate system. Together with the eye-to-

eye distance the position of the left and the right

eye are calculated.

Similar to light sampling approaches, in ray trac-

ing we sample the eyes in order to describe area

lights by point lights. Ten parameters describe the

average eye movement; i.e. the center position

(in all, three coordinate axes) as well as the look-

at-direction (respectively its angular components

of spherical coordinates) are weighted and spread

according to stochastically independent Gaussian

distributions speciﬁed by mean and variance for

each coordinate component (see Figure 2). Based

on this description a stochastic sampling is per-

formed, which results in a list of eye positions

E = {(e

)

,(e

)

,...,(e

)

}. (5)

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3.2 Objective Function

Depending on the free parameters (l

), a ge-

ometric scene is created, which results in a classiﬁ-

cation of pixels (for this particular setting) as shown

in Figure 3: each pixel is seen by both eyes (illus-

trated in white), by one eye only (red or blue), or by

no eye (black). The objective function simply counts

the number of pixels, which can be seen by both eyes,

or which cannot be seen at all.

In detail, the objective function is

f (l

) =

∑

p∈P

∑

)∈E



isVisible

occ∪pattern(l

)

,p) XNOR

isVisible

occ∪pattern(l

)

,p)



(6)

where occ ∪ pattern(l

) is a list of geometric

occluders, which comprehends static occluders occ,

such as a car’s geometry, and dynamic occluders, i.e.

the parallax barrier pattern deﬁned by (l

As the objective function iterates over all pixels

and calculates a “small” result – one whose size does

not depend on the input data set and therefore is con-

stant – it is implemented using the estimation tech-

nique presented in “Linear Algorithms in Sublinear

Time” (Ullrich and Fellner, 2011). This technique re-

duces the needed time for a display optimization to a

few minutes each.

The optimization routine has been tested for two

settings: a simple desktop environment with a single

display and the simulator environment with 24 dis-

plays. As the optimization process is the same for

both environments, we only describe the desktop en-

vironment in detail. For the simulator environment

only the differences are outlined.

Figure 3: In a parallax barrier setting all pixels can be clas-

siﬁed according to their visibility. Pixel can either be seen

by both eyes (visualized in white), by one eye only (red or

blue), or by no eye (black). Depending on the eyes’, the

display’s and the barrier’s position in 3D a characteristic

pattern comes into existence. As an ideal pattern does not

contain any black or white pixels, the optimization routine

optimizes the pattern for stochastically sampled eye posi-

tions and minimizes the sum of black and white pixels.

4 DESKTOP SETTING

4.1 Geometric Measurement

In order to arrange the display and the parallax bar-

rier properly, the metrics of the monitor is needed –

especially the distance between the pixel array inside

the LCD and the outer surface of the glass panel. As

this value is normally not documented by the manu-

facturer and as we do not want to void the hardware-

guarantee terms, we used a 3D laser scanner to mea-

sure the desired distance. Figure 4 shows the scan-

ning process. With a Post-it note on the glass pane,

the scanner returns a triangular mesh of the Post-it as

well as a few more triangles from inside the monitor.

Figure 4: A laser scanner can be used to measure the dis-

tance between the outer surface of the glass pane and the

pixel array inside without having to open the display and

violating the hardware guarantee terms.

The result of the scanning process is visualized in

Figure 5. It shows the Post-it’s geometry (in yellow)

and a plane ﬁtted to it (in blue). The ﬁtted plane is

used as a reference for the outer surface of the glass

pane. The “few more triangles” also found in the data

set correspond to the inner pixel array. Another plane,

ﬁtted exclusively to these triangles, is also shown in

Figure 5 (in red). The distance between these planes

reveals a distance between the outer surface and the

Figure 5: The scan towards the inside of a display (see

Figure 4) reveals geometric measurements normally not

documented by manufacturers; e.g. the distance between

the outer surface (on which a sticky note has been placed,

shown in yellow and approximated by the blue plane) and

the inner pixel array (approximated by the red plane).

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0.0mm

2.5mm

5.0mm

7.5mm

10.0mm

0.0mm

2.5mm

5.0mm

7.5mm

+20.0°

-20.0°

-10.0°

0.0°

+10.0°

100.0%

0.0%

25.0%

50.0%

75.0%

line width line distance line orientation non-separable

pixels

Figure 6: All evaluations of the objective function are plotted in parallel coordinates – a common way of visualizing multi-

variate data. Each objective function call is represented by a polyline, connecting its input parameters (“line width” on ﬁrst

axis, “line distance” on second axis, and “line orientation” on third axis) with its function value (“non-separable pixels” on

last axis). In order to emphasize the minimization result, the polylines are hue color-coded and sorted from back (worst pa-

rameter) to front (best parameter). While the best “width” and “distance” parameters can be identiﬁed easily, the “orientation”

parameter has only limited inﬂuence on the objective function. This leads to a wide interval of good values along the “line

orientation” axis.

inner pixel array of 5.1mm for the iMac shown in Fig-

ure 4. The other geometric values (display position in

3D, user position in 3D) have been measured easily.

Furthermore, user’s eyes’ movement approximated by

a normal distribution has been estimated roughly.

4.2 Parallax Barrier Optimization

Having set the geometric input parameters, the opti-

mization routine determined the best solution within

the parameter domain

[0.1mm,0.1mm,−20

◦

] −[10.0mm, 10.0mm, +20

◦

];

(7)

i.e. the minimum line width and distance is 0.1mm,

the maximum line width and distance is 10.0mm,

and the line orientation may vary between −20

◦

and

+20

◦

. All evaluations of the objective function are

plotted in Figure 6 using parallel coordinates (Insel-

berg, 2009). Each objective function call is plotted as

a polyline, connecting its parameters with its function

value (axes from left to right: input parameters “line

width”, “line distance”, “line orientation”, and result-

ing “non-separable pixels”). In order to emphasize the

minimization result, the polylines are hue color-coded

and sorted from back (worst parameter) to front (best

parameter). Furthermore, the optimal result



1.1828mm 2.3651mm 19.7

◦



(8)

is highlighted.

This parameter setting results in a conﬁguration,

in which 5.7288% of all pixels cannot be seen by one

eye only. Although the objective function has no reg-

ulation terms to ensure the balance between the num-

ber of pixels seen by the left eye in comparison to the

number of pixels seen by the right eye, the optimal

result is balanced.

In order to analyze the importance of the “line

orientation” parameter additional function evalua-

tions have been added. Especially the parameter set

(

1.1828mm 2.3651mm 0

◦

) has been tested and

returned a slightly higher and therefore non-optimal

value of 6.7946% non-separable pixels. Nevertheless,

the “line orientation” parameter is not very important:

conﬁgurations similar good as the optimal one can be

found along the complete “line orientation” axis in

Figure 6.

The resulting pattern of the globally optimal con-

ﬁguration is shown in Figure 7 (in 1:1 original size).

In order to avoid local minima, the result has been

checked using the “Probability of Globality” tech-

nique (Eggeling et al., 2013).

Figure 7: For the desktop setting described in Section 4,

the optimal parallax barrier has lines, which are 1.1828mm

thick. The lines have a distance of 2.3651mm to each other

(measured from medial axis to medial axis) and are rotated

by 19.7

◦

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322

5 SIMULATOR SETTING

5.1 Geometric Arrangement

The major goal of the manual arrangement procedure

was to block the driver’s view as good as possible;

i.e. from the driving position it should not be possible

to see the real environment. Only the virtual envi-

ronment, that is shown on displays, should be visible.

The most important part of the view is the windscreen,

while the side windows play only a minor role. There-

fore, 20 of the available 24 monitors are aligned in

front of the car, while two monitors are reserved for

each side.

For the process of optimizing the layout the mod-

eling and ray tracing software blender (Blain, 2012)

has been used. A model of the car was centered in

the scene, surrounded by a cylinder. A perspective

camera was put between the eye positions and was set

up to create a 180

◦

horizontal, 90

◦

vertical panoramic

image (the eyes’ position, respectively their distribu-

tion within a car, is a standardized ergonomics value,

which covers 95% of the adult population). This way

the rendered image contains the maximum view frus-

tum that the user can see. At the approximated left

eye position a blue point light was positioned, at the

right eye position a red point light. The ray tracer has

been conﬁgured so that the car model casts shadows,

but does not block the view. The same conﬁguration

applies to the models of the monitors. The resulting

image is thereby only a panoramic view on the sur-

rounding cylinder, only lighted blue or red where the

left or right eye can see past the monitors, respec-

tively (see Figure 8). The white parts in the image

correspond to viewing directions, in which both eyes

cannot see any monitors.

Figure 9 illustrates the maximal view frustum of

the user and the car geometry; a 180

◦

horizontal and

◦

vertical panoramic image with the parts hidden

by the car geometry highlighted in gray. The cam-

Figure 8: Result of the visibility test: Black areas are ei-

ther blocked by the car body or by the monitors. Red and

blue colors mark areas, where one of the eyes can see the

surrounding scene behind the monitors.

Figure 9: The panoramic view of the car body uses the same

camera settings as Figure 8 and thereby allows for easy in-

terpretation of the visibility test.

era settings are exactly the same as in Figure 8, which

shows that the monitor coverage of the windscreen is

very good, and even the coverage of the side windows

are good. The vertical lines near the middle of the im-

age are near the A-pillar of the car, which is the most

difﬁcult part of the car. The smaller, horizontal arti-

facts are unavoidable because of the uneven nature of

the hood. The chosen monitor arrangement is shown

in Figure 10.

Figure 10: The ﬁnal arrangement of the 24 monitors around

the car: 20 monitors are arranged regularly along the front,

only 2 monitors are at each side window as these are quite

unimportant compared to the front.

Due to the geometry of the side windows, there

has to be some space either on the top of the window

or on its bottom. As it is unlikely that the driver looks

through the top of the side window in the given sce-

nario, an arrangement was chosen which covers most

of its lower parts.

5.2 Parallax Barrier Optimization

The parallax barrier optimization takes the geometric

settings – as described above – into account. The par-

allax barrier itself is placed 10mm in front of each

monitor. Instead of listing all optimization results,

this article focuses on three interesting displays:

• the display placed on the left window near the A-

pillar,

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323

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0.0mm

2.5mm

5.0mm

7.5mm

10.0mm

0.0mm

2.5mm

5.0mm

7.5mm

+20.0°

-20.0°

-10.0°

0.0°

+10.0°

100.0%

0.0%

25.0%

50.0%

75.0%

line width line distance line orientation non-separable

pixels

Figure 11: The optimization of the parallax barrier for the display on the left hand side near the A-pillar (see Figure 10)

reveals the best conﬁguration with an error value of 21.56%.

10.0mm

0.0mm

2.5mm

5.0mm

7.5mm

10.0mm

0.0mm

2.5mm

5.0mm

7.5mm

+20.0°

-20.0°

-10.0°

0.0°

+10.0°

100.0%

0.0%

25.0%

50.0%

75.0%

line width line distance line orientation non-separable

pixels

Figure 12: The important front view has a good pixel separation; i.e. only 8.89% of all pixels cannot be seen by one eye only.

• a display of the front arrangement (2nd column on

the left, 2nd row from below),

• the display placed on the right window near the

A-pillar.

The optimal barrier conﬁgurations for these three dis-

plays are

• (

0.4137mm 0.8287mm 20.0

◦

) for the left

display with an error value of 21.56%,

• (

0.5360mm 1.0806mm −13.4

◦

) for the

middle display with an error value of 8.89%, and

• (

1.0441mm 2.1118mm −6.8

◦

) for the dis-

play on the right with an error value of 27.29%.

The corresponding optimization plots are shown in

Figure 11, Figure 12, and Figure 13 for the left, mid-

dle, and right display respectively.

The results show as expected that with increas-

ing distance between the user position and the dis-

play, the line widths and line distances increase as

well. Concerning the error values, the important dis-

plays in front of the car have a good pixel separation

(8.89%). The side views have rather critical/high val-

ues (21.56% and 27.29%). The ﬁnal visualization

does not necessarily has a bad separation; i.e. for

a ﬁxed, tracked position, the ﬁnal rendering can be

good, although the distributed eye samples (covering

95% of all adults) do not have good, common separa-

tion.

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0.0mm

2.5mm

5.0mm

7.5mm

10.0mm

0.0mm

2.5mm

5.0mm

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-20.0°

-10.0°

0.0°

+10.0°

100.0%

0.0%

25.0%

50.0%

75.0%

line width line distance line orientation non-separable

pixels

Figure 13: The display at the right A-pillar shows similar result than the one at the left A-pillar (see Figure 11).

6 CONCLUSIONS & FUTURE

WORK

Autostereoscopic displays based on parallax barriers

are a cost-efﬁcient alternative to expensive virtual en-

vironments. Nevertheless, a good immersive 3D vi-

sualization requires the optimal interplay of all com-

ponents (user tracking, rendering, visualization, sim-

ulation, etc.).

Within this paper we focus on the parallax barrier

and present a way to optimize it. Using numerical

analysis in combination with geometric modeling, it

is possible

• to determine the best setup conﬁguration for a par-

allax barrier and

• to predict its quality, in terms of separable pixel,

even during the planning phase of the simulator.

This optimization approach is beneﬁcial not only

for autostereoscopic displays but for optimized VR-

environments in general.

Concerning the car simulator, the parallax barrier

optimization is the missing piece to complete the vir-

tual reality pipeline, that consists of the main compo-

nents user tracking and three-pass rendering (for rea-

sons of simplicity and adaptability split up into: left

eye, right eye, and the merged parallax view). Future

work will comprehend the ﬁnal simulator construc-

tion in short terms and its evaluation in mid-terms.

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