How to (and not to) fool your brain to perceive 3D from planar …€¦ · How to (and not to) fool your brain to perceive 3D from planar displays Stefan Seipel 2009-11-13 The perceptual

How to (and not to) fool your brain to perceive 3D from planar displays

Stefan Seipel

2009-11-13

The perceptual basis for stereoscopic displays

IPD

Ver

genc

eD

ista

nce

1θ

2θ

When converging at objects at somecertain distance, a point at different distances in the scene will appear at the retina with some lateral disparity.

Binocular disparity

independent of vergence.

Lateral disparity of more than 10° cause diplopia.

Experiment: Thumb and Window

Retinal Disparity: Viewing in the real visual world

21 θθ −=Disp


Parallax: Viewing on plano-stereoscopic displays

Parallax is lateral displacement of homologous points on the planar display.

Zero Parallax

Converging at a point on a display surface causes homologous points on display to have zero parallax.


Positive Parallax

Converging at a point behind the display surface causes homologous points on display to have positive parallax.This point is said to be in screen space.




Negative Parallax

Converging at a point in front of the display surface causes homologous points on display to have negative parallax.This point is said to be in viewer space.




Converging the eye´s axes upon a real point in 3D space implies verging the eyes towards that point.The neuro-muscular functions to control vergence are also evaluated to assess distance.

The relationship between convergence and accommodation

The point is kept a focus by adjusting the lens (accommodation).

Under normal natural viewing conditions, accommodation and convergence correspond. The correspondence of convergence and accommodation is habitual an can be voluntarily put out of function (crossing the eyes).


Converging the eye's axes upon a virtual point at distance Dc supportsfusion of the parallax image and stereopsis.

Keep the visual structure on-screen at focus, requires accommodation at screen distance Ds.

Usually, accommodation is dominant andfor unaided viewing, we see one planar double-image in focus.

With some training (crossing the eyes) wecan converge at Dc and see on fused 3D Image out of focus.

Convergence and accommodation in plano-stereoscopic displays

DsDc


Converging the eye's axes upon a virtual point at distance Dc supportsfusion of the parallax image and stereopsis.

Keep the visual structure on-screen at focus, requires accommodation at screen distance Ds.

Usually, accommodation is dominant andfor un-aided viewing, we see one planar double-image in focus.

With some training (crossing the eyes) wecan converge at Dc and see on fused 3D Image out of focus.

Stereo-graphic devices (e.g. stereo glasses) greatly support image fusion and stereo-opsisat the cost of suppressed accommodation.

DsDc


Summary:

• Parallax of regions in an image on a stereoscopic display is yielding to retinal disparity, which is one cue for perceiving depth in a scene.

• Parallax and retinal disparity are equivalent.

• The brain can fuse binocular retinal images into one spatial image (stereopsis)

• Stereopsis is limited to lateral disparities up to some certain amount (e.g. 10° Kalawasky[1992]), otherwise diplopia.

• Equivalently, there are limits to display parallax.(1,5° of visual angel Lipton[1991])

• Viewing non-zero parallax images on plano-stereoscopic displays infringes the accommodation/convergence relationship learned in natural viewing.

Practical issues in stereo graphics

Lipton [1991] – Parallax Control

Don’t exceed parallax values of more than 1.5° visual angle (rather than using explicit parallax values on screen).

R

L

1.5°

Viewing distance D

On-screen parallax osp

10,477,865,242,621,961,31osp [cm]

4003002001007550D [cm]

Practical examples for on-screen parallax values:


Virtual spatial depth due to observer distance and limited parallax.

Negative parallax situation:Allowable spatial depth d towards viewer space

IPD

Vie

win

g D

ista

nce

D

1

...

+

=

−=

osp

IPD

Dd

dD

d

IPD

osp

d

osp

Example for IPD = 6,5 cm

0,620,550,450,290,230,17d/D

246,83164,1789,2428,7217,408,38d

10,477,865,242,621,961,31osp [cm]

400,00300,00200,00100,0075,0050,00D [cm]


Virtual spatial depth due to observer distance and limited parallax.

Positive parallax situation:Allowable spatial depth d into screen space

IPD

Vie

win

g D

ista

nce

D

==

+=

− 1

...

osp

IPD

Dd

dD

d

IPD

osp d

osp

Example for IPD = 6,5 cm

75,977,794,150,670,430,25d/D

18612,491714,79829,4567,4732,4712,61d

6,425,765,242,621,961,31osp [cm]

245,00220,00200,00100,0075,0050,00D [cm]

IPDV

erge

nce

Dis

tanc

eD

1θ

2θ

21 θθ −=Disp


Virtual spatial depth due to observer distance and limited disparity.

According to Kalawsky image fusion collapses at 10° disparity,

d( )

⎟⎠⎞

⎜⎝⎛

⋅=∧

⎟⎠⎞

⎜⎝⎛ +⋅

−=

⎟⎠⎞

⎜⎝⎛

⋅=∧⎟

⎠⎞

⎜⎝⎛ +=

−

−

−

D

IPDDisp

IPDDd

D

IPDDisp

dD

IPD

2tan

2tan2

...

2tan

2tan

2

1

1

αα

αα

0,920,890,840,730,670,58d/D

366,03266,98168,7272,9950,2528,81d [cm]

0,010,010,020,030,040,06α [rad]

400,00300,00200,00100,0075,0050,00D [cm]


Worth mentioning:

Values for maximum allowable disparity in the literature are expressed in different terms (angular disparity, on-screen parallax etc…)

These values apply sometimes only as a rule of thumb.(Lipton’s appear to work for many VR applications)

Values do not generally apply for all viewing conditions

Once you know the basics, composing stereoscopic images is an art, not a science. (Lenny Lipton,1991)


Does my desktop 3D application also work in the VR theatre?

Many visualization applications are parameterized to work in stereo on desktop systems.

Example:

17” screen approx. 34 cm wide.Application creates maximum parallax of 2 cm, which is comfortable when viewed from approx. 70-80 cm distance.

You bring your application to the computer in the VR theatre, without altering viewing parameters.The stereo-picture is now blown up to 3 meters horizontal size i.e. 850%.

Maximum parallax on the projection screen is now 17,14 cm.

According to Lipton’s recommendation for parallax of max. 1.5°, the observer should be seated at least 6,6 meters from the screen!

Note: Viewing parameters for stereo-viewing do NOT scale linearly!!!

A general problem in computer graphics

Traditional camera viewing metaphor not suitable for VR and stereo 3D!

Traditionally the field of computer graphics has adopted the metaphor of a synthetic camera

Projection math is then

based on central perspective projections

adapted to parameters such as horizontal and vertical field of view

… even worse: focal length and aspect ratio

This is manifested in industry standard APIs (e.g. OpenGL/GLUT, ”gluPerspective”)


What is wrong with a camera model?

1. The scale level in recording/synthesizing an image is not related to the spatialrelations between observer and display at presentation.

This is usually not a problem in monoscopic graphics, but in stereo it is!

(parallax and convergence issues, discussed before)

Example: Hyper-stereo and excessive parallax when photographing a frog from 30 cm distance with a IPD of 6 cm and display on a 4m x 3m screen.

What focal length is applicable for visualizing atoms and molecules?



2. Binocular viewing of (projected) plano-stereoscopic displays requires off-axis projected images

typical setup for camera based

stereo

Non co-planar projection planes Same display plane for both images

Left eye Right eye



3. A central model with central perspective projection assumes theviewer to be located in front of the center of the image

Non co-planar projection planes Same display plane for both images

”Correct” viewing position”Incorrect” viewing position

What can we do about it?

Presentation of 3D objects on planar 2D displays requires generallyan arbitrary relationship between the projection (=presentation) planeand the center of projection (=observer's eye).

This viewing metaphor is called ”Window-on-world”, short WoW.

A WoW implies generally an off-axis projection

The result of off-axis projection is an anamorphic image which ,viewed from the CoP, appears geometrically undistorted.

Anamorphic images are not only compelling in computer graphics…

http://users.skynet.be/J.Beever/

Works of the famous artist Julian Beever

This is the center of projection

Works of the famous artist Julian Beever

http://users.skynet.be/J.Beever/

Here is what you see from the center of projection

How can I accomplish good off-axis projections?

A metrically correct Window-on-world projection requires

a) the relation between window and observer position to be modeled at the same level of scale (same WCS)

b) requires a parameterization of an appropriate off-axis projection matrix

c) zooming of objects in the scene is accomplished through manipulation of object parameters rather than viewing parameters

A) and b) usually require that you implement the projection pipeline into your Vis-App yourself to be sure that the job gets done right.

How to parameterize an off-axis projection matrix?

nearfar

nearfarD

nearfar

nearfarC

bottomtop

bottomtopB

leftright

leftrightA

−⋅⋅

−=

−+

−=

−+

=

−+

=

2

glFrustum(left,right,bottom,top,near,far);

Using built-in OpenGL frustum function

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−

−⋅

−⋅

=

0100

000

02

0

002

C

Bbottomtop

near

Aleftright

near

P

(observer at origin, facing along –z, near defines projection plane)

left

righttop

bottom

near

Parameterize glFrustum for arbitrary WoW


window position

width

height

up-vector

side-vector

viewer position

A window on world arbitrarily identified by:

Window position: wp

Orientation vectors (roll/tilt): sv, up

Width and height: w, h

And an arbitrary observer position: vp



wp

w

h

up

sv

vp

A window on world arbitrarily identified by:

Window position: wpOrientation vectors (roll/tilt): sv, upWidth and height: w, hAnd an arbitrary observer position: vp

This WindowOnWorld is part of a central perspective projection along

(cp-vp)

Which is frustrated at

left, right, top, and bottom

cp

left

top

bottom

right



wp

w

h

up

sv

vp

Calculating glFrustum parameters from WoW parameters:

cp

left

top

bottom

right

upsvwn ×= 0,10.1 =∧= upsv

wpvpvv −=

vv

wn

D

wnvvD •=

wnDvpcp ⋅−=



wp

w

h

up

sv

vp


cp

left

top

bottom

right


wpvpvv −=

vv

wn

D

wnvvD •=

wnDvpcp ⋅−=bl tr

cpupsvwptr

cpupsvwpbl

−⋅+⋅+=−⋅−⋅−=

5.05.0

5.05.0



wp

w

h

up

sv


cp

left

top

bottom

right


wpvpvv −= wn

wnvvD •=

wnDvpcp ⋅−=bl tr

uptrtop

svtrright

uplbbottom

svlbleft

•=•=•=

•=


Adjusting frustum parameters for clipping plane

viewer position

left

top

bottom’

right

cp

D

bottomright’

top’

left’

cd

glFrustum assumes clipping plane To co-incide with plane of projection

D

cdDtoppto

D

cdDrighttrigh

D

cdDbottommbotto

D

cdDlefttlef

−⋅=′

−⋅=′

−⋅=′

−⋅=′

cdDnearHence −=:


Pre-multiplying modelview matrix

viewer position

left

top

bottom’

right

cp

D

bottomright’

top’

left’

cd

glFrustum assumes further:vp is at origin (cp-vp) pointing toward -z

1

1000

−

⎥⎦

⎤⎢⎣

⎡=

vpwnupsvPM

Translating vp to O and frame alignmentBe pre-loading model-view matrix PM

glMatrixMode(GL_PROJECTION);glLoadIdentity(),glFrustum(left’,right’,bottom’,top’,near,far);

glMatrixMode(GL_MODELVIEW);glLoadIdentity();glMultMatrixd(PM);

Putting it together

In-proper interaction between 3Dcontent and screen surround destroys illusion:

Virtual 3D object intersects withscreen borders.

Contradictious 3D cues

Stereo-disparity says:“object is in front of screen”

Object occlusion by surround says:“object is behind the screen”

Sabotaging a good 3D illusion

Giving to much freedom to the user when interacting…

Sabotaging a good 3D illusion

…can cause hyper-parallax and diplopia

Example of dynamic perspective conditions ?

…technically speaking we get a whole lot of trouble

Requirements to visualization of 3D features

Eye’s positions needed(tracking)

Multiple individualized views

Dynamic rendering even for static content

Stereo cues (optionally)

This is what we can achieve…

Dynamic viewing conditions Individual content

Pettersson, Spak and Seipel, 2005 : “Collaborative 3D Visualizations of Geo-Spatial Informationfor Command and Control”, proceedings of Sigrad 2004

b) Collaborating in complex tasks

Experimental procedure:20 persons in 10 Dyads5 trial stimuli + 2 x 15 stimuli Blocks of 15 stimuli is randomized

Views of the actual experimental task – a 3D and logical/combinatorial task

Integral view (first person view) Partitioned view for user A

c) Understanding time and geography

Works submitted to Information Visualization Journal and Journal of Applied Perception

Series of experiments investigating the space-time cube:

The space-time cube uses elevation over ground to depict time

2D trajectory of moving targets 3D trajectory of moving targets

Summary: Cues for 3D image generation?

Correct stereo is only one of many spatial cuesCorrect parallax (software)Projector adjustment (hardware)Scaling conditions (sw + hw)Interference with surround

Utilize shadows, shading

Exploit motion parallax Object rotation creates strong optic flow

Keep noise or small spatial features/structures in e.g. 3D imagesobjects with lack of spatial freq. ? -> use textures

Try to use dynamic perspective conditions

3D Display Categories

True Volumetric Displays

Stereographic Displays(2 projected planar views)

Single Display Plane Multiplexed

Dual Display Immediate Mode

Temporal MUX Spatial MUX Chromatic MUX+

Spectral MUX

Polarization MUX

Time Multiplexed Stereo Image Pair

V-Sync at 60 Hz

Addidional V-Sync at 120 Hz(enforced with sync. doubler)

open

clos

e

clos

e

open

Active Shutter Glasses(LCD-Shutters)

Temporal Multiplexing and “Ghosting”

0%

100%

0%

100%

Shutter Opacity Left Eye

Shutter Opacity Right Eye

Pixel Intensity (Phosphor)

Open RightClose Left



Close RightOpen Left

Close RightOpen Left

Two Pixels are Drawn On-Screen:Purple Pixel for the Right EyeGreen Pixel for the Left Eye120Hz screen refresh rate

t

t

t8.3 ms

Left eye sees purple pixel due to after-glowingRight eye sees green pixel due to shutter response

Color Encoded Stereo Image Pair

Chromatic Multiplexing - Anaglyph Technique

Images curtsey: http://axon.physik.uni-bremen.de/research/stereo/color_anaglyph/index.html#ana

Encoding:

A stereo image pair is combined into one so called anaglyph.

The left eyes view is encoded with the red colour component.

The right eye view is encoded with the complementary colour i.e. greenAnd blue colour components.

Decoding:

The left eye uses a red colour filterthat passes through dominant red components.

The right eye uses a cyan colour filterthat passes through dominant blueAnd green components.

Chromatic Multiplexing - Anaglyph Technique

Conventional filter materialsare used to separate the colorspectra of a stereogram.

Image splitting by chromaticseparation.

spectrum of the red filter

spectrum of the cyan filter

Spatial Multiplexing

VR-3100

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

L RR L

LRLRLRLR

L R L R L R L R

The stereo image pair is presented on alternatingpixels, pixel columns, or scan-lines.

Optical arrangements are used to block-outthe the wrong image for the corresponding eye.

Effective resolution is reduced.

Spectral Filtering – Infitec Technology

More info at: http://www.infitec.net/infitec.pdf

Narrow band spectral filters allow differentsub-bands of the tri-stimulus spectra.

Advantage: Filter based optical multiplexingwhich provides ”natural color” stereo imageseparation.

Left eyeSpectral filter

Right eyeSpectral filter

Related literature and references

Additional reading for this lecture:http://www.cs.unc.edu/Research/stc/FAQs/Stereo/stereo-handbook.pdf

Research community in stereoscopic/3D displayshttp://www.stereoscopic.org/2009/program.html

Documents

How to (and not to) fool your brain to perceive 3D from planar …€¦ · How to (and not to) fool your brain to perceive 3D from planar displays Stefan Seipel 2009-11-13 The perceptual