HUMAN
FACTORS,
1992,34(5),571-581
Using the Stereokinetic Effect to Convey
Depth: Computationally Efficient
Depth-from-Motion Displays
MARY K. KAISER, I NationalAeronautics
and Space Administration, Ames Research Center,
Moffett Field, California, and DENNIS R. PROFFITT, University of Virginia,
Charlottesville, Virginia
Recent developments in microelectronics have encouraged the use of 3D data
bases to create compelling volumetric renderings of graphical objects. However,
even with the computational capabilities of current-generation graphical systems,
real-time displays of such objects are difficult, particularly when dynamic spatial
transformations are involved. In this paper we discuss a type of visual stimulus
(the stereokinetic effect display) that is computationally far less complex than a
true three-dimensional transformation but yields an equally compelling depth
impression, often perceptually in discriminable from the true spatial transformation. Several possible applications for this technique are discussed (e.g., animating
contour maps and air traffic control displays so as to evoke accurate depth percepts).
INTRODUCTION
Current microprocessor technology has allowed the development of highly sophisticated computer-generated imagery. The improvement in the cost-to-performance ratio
in the past decade is remarkable. Graphical
workstations currently entering the marketplace are designed and priced for the personal user, yet they achieve graphical rendering capabilities superior to visual simulation
systems of the 1960s and early 1970s.
Despite such impressive achievements in
I Requests
for reprints should be sent to Mary K. Kaiser,
NASA-Ames Research Center, Mail Stop 262-3, Moffett
Field, CA 94035-1000.
hardware and software architecture, the performance of graphical systems inevitably
falls short of users' requirements. This is particularly true when graphic systems must
generate imagery in real time or be used in an
environment in which cost, space, or other
constraints limit the sophistication of the systems that can be used. Thus it will always
prove beneficial to provide computational
simplifications that can be introduced while
maintaining the visual effects the system
needs to deliver.
One prominent example of such computational simplifications is fractal rendering, in
which a relatively simple propagation algorithm is used to create scenes of seemingly
complex texture and structure (Mandelbrot,
@ 1992, The Human Factors Society, Inc. All rights reserved.
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HUMAN
1982). Although the fractal image possesses
far more mathematical
regularities
(selfsimilarities) than are found in the natural
scene, the bases of these regularities are
higher-order statistics to which the human
visual system is relatively insensitive.
In this paper we introduce an analogous
simplification
for producing compelling
depth-from-motion displays, utilizing motion
algorithms far less complex than those required to produce the proper motion transformation of a 3D data base. Like fractal rendering, this technique creates a compelling
visual effect that is often perceptually indiscriminable from a veridical transformation,
but it greatly reduces the computational
overhead. We present psychophysical evidence for the effective equivalence of these
two transformations and two demonstrations
showing how this technique can be used to
create compelling depth information in visual displays. The examples are a moving
contour map display and an air traffic control
display.
THE STEREO KINETIC EFFECT
In the 1920s, Italian perceptual scientists
discovered
and studied a class of twodimensional (2D) stimuli that, when rotated
in the picture plane, produce a compelling
impression of depth (Musatti, 1975). A typical
display, consisting of an eccentric arrangement of nested circles, is shown in Figure 1.
When this stimulus is rotated observers report a compelling percept of a cone (or, alter-
Figure 1. Two frames (0 and 90 deg) of a traditional
SKE display.
FACTORS
natively, a tunnel). This phenomenon was
termed the stereokinetic effect (SKE) because
a solid, three-dimensional (3D) percept was
evoked by motion. (Interestingly, common
usage of the word stereo implies two spatially
separated samples, as in stereoscopic displays or stereophonic sound. However, this is
a corruption of the original meaning and reflects our assumption concerning how threedimensional impressions are formed-i.e.,
via the binocular fusion of two spatially disparate images.) This phenomenon was of scientific interest because the transformations
that occur in the stimuli do not correspond to
any realizable 3D geometry, though a compelling impression of a volumetric object results. However, the phenomenon was not
studied systematically and served primarily
as a demonstration.
Recently Proffitt and colleagues (Caudek
and Proffitt, in press; Proffitt, Rock, Hecht,
and Schubert, 1992) provided comparisons of
the motion information carried in SKE displays with that contained in geometrically
correct structure-from-motion
displays (i.e.,
motion parallax and the rigid object rotations). Those analyses showed that SKE displays contain a subset of the motion components that are present when observing
motion parallax and object rotations.
Stereokinetic Effect versus Kinetic
Depth Effect
The kinetic depth effect (KDE) refers to the
perception of depth that occurs when observing a 2D projection of an object rotating
about some axis other than a line of sight. The
motions present in this situation can be decomposed into two transformations, only one
of which is present in SKE displays. For exposition, we will discuss this distinction in
terms of the SKE cone. Figure 2a shows three
projected contours on a shallow, rigid cone.
The symmetry axis of the cone is rotating
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STEREO KINETIC DISPLAYS
October
1992-573
KDE
a)
SKE
b)
Figure 2. Three frames of (a) a KDE display, depicting - SO, 0, and + SO deg rotations
about the y axis, and (b) the corresponding frames of an SKE display. Note that the
transformations in (a) consist of both between-contour and within-contour motions,
whereas only between-contour motions occur in (b).
back and forth (oscillating) around the y axis
by about 50 deg on either side of the depicted
ative to the picture plane. This change in the
line of sight. (We define the picture plane vertical as being the y axis, the horizontal as being the x axis, and the depicted line of sight as
being the z axis.) Two transformations are
produced by this oscillation. First, individual
contours move relative to each other. If we
imagine a line connecting the centroids of the
projected contours, then the length and
signed orientation of this line (the tip of the
cone's left/right orientation relative to the
centroid of the base) changes as the cone oscillates. These changes in the relative position and orientation of object contours will be
called between-contour motions. Second,
there is a change in the shape of each projected contour that is attributable to changes
in its observer-relative slant. Notice that the
cone's contours vary in their aspect ratio in a
manner that is proportional to their slant rel-
same contour that is attributable to the contours' changing slant relative to the project
plane will be called within-contour motions.
Rigid object rotations always present both
of these motions. SKE displays present only
the between-contour motions, such as those
shown in Figure 2b. The contours move relative to each other just as in the rigid object
rotation depicted in Figure 1; however, the
contours themselves never deform. In this
case, they remain circular. As we discuss
later, this SKE display is geometrically inconsistent with the rotation of any rigid object (except one with infinite depth), yet people perceive this display as moving in the
same manner as the rigid objects shown in
Figure 1 and as having a specific tip-to-base
depth.
Here is a more general way to define the
distance between any pair of points on the
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HUMAN
two transformations: Consider an object (e.g.,
a cone pointed toward an observer) in which
the z axis corresponds to the principal axis of
the object. If the cone has contours painted on
it with the lines parallel to its base, the points
on a single contour will not differ in the z
value but will be separated in the x,y plane.
Oscillating the cone about the x, y, or both
axes produces motions between contours that
are attributable
to their separation
in z
depth. It also produces within-contour motions that are attributable
FACTORS
b
a)
to the changing
slant of the contour's x,y planes. SKE displays present only the former motions (relative motions between points separated in z)
but no changes for points with equivalent z
values. Thus there are two motions: those
produced by differences in z depth and those
produced by changes in x,y slant. KDE displays manifest both, whereas SKE displays
manifest only the former. In essence, SKE exploits those transformations related to object
depth while ignoring those that are incidental to changes in observer-relative slant.
SKE versus Perceiving Depth in
Motion Parallax
Motion parallax occurs when a viewer
moves past stationary objects (or when objects translate by a stationary observer on
some path other than the line of sight, as
shown in Figure 3a). This creates a gradient
of angular velocities in the optical flow-field,
which specifies relative depth. (If a point on
an object is tracked, then the image velocities
increase with the distance from that point;
however, we assume no such tracking.) As depicted in Figure 3b, a motion parallax velocity flow-field can be decomposed into two
components, following an analysis similar to
the decomposition of the KDE transformations into observer-relative
and objectrelative transformations.
The first of these
two components is the common motion of the
whole velocity field. The second of these two
---- ---~
b)
~
Motion
Parallax
~
~
+
~
~
~
~
~
~
~
ObJecl ••el.,I ••
transformations
Observer-relatlvc
transformations
{SKE componenl.
(Common component
01 motion)
Figure 3. (a) A motion parallax event: an object
translates from its initial (abc) to final (a'b'c') position, creating an observer-relative displacement of the
object (Il) which also defines its effective observerrelative rotation, (b) Schematic of the decomposition
of the motion parallax velocity flow-field into its ob·
server-relative and object-relative components. (Note:
Common motion vectors are not drawn proportionately.) As defined by Caudek and Proffitt (in press), an
SKE display of this event would contain only the object-relative transformation.
components is obtained by the subtraction of
this common motion component from the
whole velocity field.
The common component of motion parallax corresponds to changes in the angular displacement of the object relative to the observer (9 in Figure 3a). In motion parallax,
the common motion component thus comprises the observer-relative transformation.
The second component in motion parallax
consists of the differential angular velocities
of the optic flow field, which are determined
by the depth relations within the distal
object.
These motions
are called the
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STEREO KINETIC DISPLAYS
object-relative transfonnation. Consistent with
the previous definition, these object-relative
transformations of a motion parallax velocity
flow field are equivalent to the transformations presented in an SKE display.
Psychophysical
Studies
Both canonical
structure-from-motion
transformations
(KDE displays and motion
parallax) can be characterized as consisting
of two subcomponents: observer-relative and
object-relative
transformations.
SKE displays contain only the object-relative transformations. In a series of psychophysical
studies (Caudek and Proffitt, in press; Proffitt
et ai., 1992) it has been demonstrated that the
perception of depth is essentially equivalent
regardless of whether the observer-relative
transformations are present or absent.
SKE
KDE
1.4
..•............ ..."
1.2
1.0
~
•.'
O.S
.•.•.•.•.•.•. /
}:: ///
____
- - .•
r
~
r
Figure 4. Schematics for the SKE and KDE stimuli
used in Proffitt et al. (1992). The top figures depict the
side views of the virtual 3D cones that project into the
contours at the bottom. The virtual SKE and KDE
objects are identical in the radius of the base (r) and
eccentricity (e). The projections of these objects are
identical except that the KDE contours are foreshortened because of the virtual cone's tilt (0.).
KDE Simulated
-
-.......
0.2
0.0
0.0
KDE Judged
SKE Judged
i
0.2
0.4
0.6
Eccentricity
O.S
1.0
1.2
(e/r)
Figure 5. Mean perceived heights (expressed in terms
diameter of the cone's base) for the SKE and
KDE stimuli in Proffitt et al. (1992) as a function of
stimulus eccentricity (elr).
of the
In a study comparing the subjective height
of SKE and KDE cones (Proffitt et ai., 1992,
Experiment 6), observers were asked to judge
the height of the cone relative to its base.
Stimuli varied on their maximum eccentricity (defined as elr, where r is the radius of the
cone's base, as shown in Figure 4). For the
KDE stimuli, eccentricity was an appropriate
indicant of height, since the tilt of the cone (0:)
was held constant
~
1992-575
October
at 37 degrees. (That is, for
any constant tilt, the height of the cone will
covary with the eccentricity of the stimuli for
KDE displays.) Given the absence of withincontour changes in the SKE stimuli, the eccentricity to height mapping is unrealizable.
For both kinds of stimuli perceived height
was a monotonic function of stimulus eccentricity (Figure 5); subjective height was actually greater for SKE stimuli with comparable
eccentricities. This overestimation seemed to
result from observers' tendency to see the
cone as possessing a height-to-width ratio
close to 1.0, whereas most of the KDE stimuli
reflected lower ratios.
One concern with comparisons of SKE
with KDE is that the information differentiating the two stimuli (i.e., the withincontour changes) is subtle. For the cone stimuli, these observer-relative transformations
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576-0ctoher
HUMAN
1992
are instantiated in the elliptical foreshortening of the concentric circles. The degree of
foreshortening is a cosine function of the tilt
of the cone (a in Figure 4). For the tilt shown
(37 deg), the foreshortening is about 20% (i.e.,
the x axis of the ellipse is 20% shorter than
the y axis). For tilt angles of less than 15 deg,
however, the observer-relative
transformations are near or below· threshold.
However, transformation salience cannot
explain why observers fail to attend to observer-relative
transformations
in motion
parallax displays. As can be seen in Figure 3,
as an object translates relative to an observer,
it undergoes an effective observer-relative rotation that is equivalent to its angular displacement (6). As with rigid rotations, the
distance between points band c will be foreshortened as a cosine function of this angle;
however, in motion parallax, the angle of effective rotation need not be computed from
observer-relative foreshortening because it is
given robustly by the extent of the common
motion component, e.
Despite the increased salience of the observer-relative transformation in motion parallax as compared with KDE displays, only
the object-relative transformations (the SKE
component) appear to playa significant role
in the formation of depth impressions. In a
series of studies, Caudek and Proffitt (in
press) compared the depth perceived in geometrically veridical motion parallax displays
with that induced by SKE displays (i.e., with
the observer-relative motion component removed). When observers were asked to judge
the depth-to-width ratio of simulated objects,
their ratings were virtually identical for the
motion parallax and SKE displays (see Figure 6).
These findings hold at least two consequences for spatial display design. The first is
that, contrary to ideal competence models of
vision (e.g., Koenderink,
1986; Longuet-
FACTORS
1.5
:c
'0
i
.t:
1.0
a.
CD
e
I
- =1
---0--
.t:
a.
CD
0
...
0.5
CD
>-
1i
;;
"0.0
0.0
0.5
Simulated
1.0
Depth
(Depth
1.5
I
Width)
Figure 6. Mean perceived depth (expressed as a
depth-to-width ratio) as a function of simulated depth
for motion parallax (MP) and stereokinetic (SKE)
stimuli in Caudek and Proffitt's Experiment 2 (1991).
Higgins and Prazdny, 1980; Ullman, 1979),
human observers may not be able to use all of
the available information needed to recover
the three-dimensional structure of distal objects from projective transformations.
(In
fact, Caudek and Proffitt's reanalysis [in
press] of seven psychophysical studies of motion parallax indicates that the monocular
depth-from-motion system makes use of only
object-relative transformations,
the magnitudes of which are combined with assumptive heuristics.) The second, more positive,
consequence is that the stimulus information
that does evoke depth impressions is geometrically simpler than the full set of transformations and, thus, is easier to instantiate on
graphical display systems.
We now present two examples of spatial
displays utilizing SKE depth cues. The first
is a moving map display in which the elevation contours undergo the SKE transformation. The second is an ATC display, wherein
object-relative motions are created for the
aircraft icons (and associated altitude ladders) to produce a visual impression of altitude separation.
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October 1992-577
STEREO KINETIC DISPLAYS
STEREO KINETIC
DISPLAY APPLICATIONS
Given that object relative transformations
in isolation are sufficient to evoke compelling
impressions of depth, we now consider ways
to exploit this perceptual tendency in spatial
displays. The most logical candidates are
those systems requiring real-time motion but
in which constraints of cost, size, or reliability preclude the use of 3D geometry engines.
Two examples we have developed are moving
contour maps and air traffic displays.
Moving Contour Maps
Contour maps are used in nap-of-the-earth
navigation, whereby the flight crew correlates terrain features viewed outside the cockpit with the features depicted on the map to
achieve and maintain geographical orientation (Hart and Battiste, 1991). Although most
flights currently use paper maps, electronic
map displays are being developed and field
tested. Terrain elevation is traditionally depicted by contour lines, with each line repre-
3D transformation (and usually executed via
a geometry engine for real-time applications),
our SKE display requires only that the magnitude of the motion in the image plane be
scaled according to a coefficient reflective of
the contour's depth (z axis value).
Informal examinations indicate that the
depth percept created by the SKE transformation persists for some time after the motion has ceased. Thus, we created a display
that iteratively presents a short, cardioidal
depth-inducing
translation
followed by a
static interval. Depth perception viewing this
display is stable and natural. Further, the
depth-inducing translations do not interfere
with the perception of the common translational motion created when the user scans the
viewpoint to different areas of the map. A
pair of images from this simplified contour
map is shown in Figure 8.
Air Traffic Control Display
In routing and queuing air traffic, controllers need to recover the 3D spatial relationships among aircraft. Currently employed
in elevation (typi-
plan-view displays make such recoveries a
cally 50 to 150 feet) and bolder lines
indicating larger increments (usually five
times the smaller increment). Interpreting
this elevation information is not intuitive; naive observers looking at a contour map get no
immediate
impression
of elevation (i.e.,
depth, because the map is a plan view).
In our moving contour map display, contours were programmed to translate in the
picture plane in both the x and y directions by
a magnitude proportional to their altitude.
Like the contours on the SKE cone stimuli,
the map contours translate relative to one another but do not change shape. This vastly
reduces the computational complexity of the
motion transformations, as can be seen by examining the C code shown in Figure 7. Unlike
the matrix multiplication required for true
highly cognitive task; altitudes must be derived from alphanumeric information contained in the data blocks associated with each
aircraft. A number of alternative display formats utilizing perspective cues for altitude
have been developed and assessed (Burnett
and Barfield, 1991; Ellis, McGreevy, and
Hitchcock, 1987), although no such display
augmentation is expected in the air controller
display suite currently under development
(Burnett and Barfield, 1991).
The air traffic control display we developed
utilizes a graphical cue for altitude (i.e., an
altitude ladder, in which the two sides indicate current and future position and the
rungs represent units of altitude) but adds an
SKE depth-motion augmentation. In our display, depth-inducing motions are produced
senting some increment
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578-0ctober
1992
HUMAN
FACTORS
r
demo version of ske-topographical map display "J
#include <stdio.h>
#include <pixrecVpixrect_hs.h>
#define NULLPR (struct pixrect ") NULL
#define MAXLEV 32 r number of contour surfaces (parallel planes) "J
struct pixrect "PR:B:OVR[MAXLEV);
main()
(
r
r
r
int i;
;nt ske,obs;
int xobs,yobs;
int xSke,yske;
int xO,yO,x1,y1,elev:
PR=pr _open("Jdev'fb");
cmap();
for (i=O;i<MAXLEV;i++)
OVR[i]=mem_create(512,512,1);
r create 512x512 overlays, 1 bit deep "'
B=mem_create(256,256,1);
r display buffer is 256x256 "'
read map elevation data from stdin "'
while (5==scanf("%d
%d %d %d %d",&xO,&yO,&x1,&y1,&elev))
if ((elev<MAXLEV)&&(elev>=O))
pr_vector(OVR[elev],xO,yO,x1,y1,PIX_SET,O);
r draw each vector in the overlay appropriate to its elevation "'
clear graph ics buffer "'
pr_rop(PR,O,O,1152,900,PIX_CLR,NULLPR,O,0):
draw 512x512 reference map (below main display) "'
for (elev=O;elev<MAXLEV;elev++)
pr_rop(PR,O,256,512,512,PIX_SRCIPIX_DST,OVR[elev],0,0);
ske=O; r index ske phase "'
obs=O; r index position of observer "'
while(1)
(
xske=yske=ske<2?ske·1 :3-ske; r diagonal oscillation ske (arbitrary) "'
xobs=obs<256?obs:512-obs;
yobs=12B;
r horizontal translation of viewer (arbitrary) "'
r
clear buffer "'
puop{B, 0, 0,256,256, P IX_ CLR, N U LLPR, 0,0);
r construct the display (this is the important part)
for each elevation (elev), superimpose the part of the appropriate overlay (OVR[elev])
indexed by the observer's position (xobs,yobs) to the temporary buffer (B), offset one
increment (xske,yske) for each level of elevation "J
for (elev=O;elev<MAXLEV;elev++)
puop( B, 0, 0 ,256,256, P IX_ S RC IP IX_DST, OVR[ e lev], xobs· xske" e lev, yobs ·ys ke" e lev);
r
copy buffer to screen "'
pr _rop( PR, 0, 0,256,256, P IX_ S RG, B,O,0);
obs=(obs+4)%512;
ske=(ske+ 1)%4;
I
cmap()
I
unsigned char red[2],grn[2),blu[2];
red[O]=g rn[O]=blu[O] =0;
red[1 ]=grn[1 ]=blu[1 ]=255;
pr_putcolo rmap( PR, 0, 2, red, grn, bl u);
Figure 7. Computer code (C language) used to generate simple contour map display.
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October 1992-579
STEREO KINETIC DISPLAYS
a.
b.
0 cycles, b = 0.5 cycles) of the contour map display. The
arrows indicate the magnitude of the contour movement during the SKE motion cycle
(no common translation is shown in this figure).
Figure 8. Two frames (a
=
with the following options. The operator can
move the mouse, thereby causing the planes'
icons to move by magnitudes proportional to
their altitudes. Simply moving the mouse to a
new stationary position reveals the ladder
structure; the ladder's base remains fixed,
whereas its top translates. Pressing the left
mouse button at any time causes the display
to return to a 20 plan-view configuration.
Once the mouse has been moved and the 30
structure has been revealed, the operator can
press the right mouse button and the ladders'
tops will revolve around their bases by a
magnitude equivalent to that set by the initial move of the mouse. The ladders do not
change their orientation
relative to the
ground. Thus the operator has control over
the magnitude of the rotations as well as
whether or not a motion occurs. Having this
direct control over the icons' motions makes
the depth-inducing motions easier to interpret. In addition, the ability to stop motion
(and toggle to a 20 plan view) reduces the
likelihood that the perspective and/or motion
features will interfere with the extraction of
information best gleaned from the plan view
(e.g., aircraft identifier).
This multiple-format capability allows the
operator to use the mode most suited to the
current task. Whereas the SKE-motion mode
would likely be distracting and even disruptive for normative air control activity (much
of which occurs in the temporal rather than
the spatial domain), this mode is particularly
useful for examining the airspace for altitude
conflict situations (see Figure 9).
CONCLUSIONS
SKE motion displays consist of certain picture-plane translations among object features
and contours; thus displays that utilize only
this component can achieve compelling
depth impressions at a much lower computational cost than would be incurred with full
30 object rotations. By producing appropriate translations between object features and
contours, these SKE-based displays can provide the same level of depth compellingness
and specification as do the far more complex,
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580-0ctober
HUMAN
1992
..
a.
,
b.
FACTORS
full 3D graphical data base displays. Capitalizing on this perceptual "cheat," display designers can create real-time volumetric displays even with low-end graphical systems.
Such a capability is especially useful when
the system must be highly portable (e.g., a
moving-map display for cockpits) or is just
one of several display modes in a multifunction operator station (e.g., air traffic control
terminal). By identifying the limits of human
sensitivities to depth-from-motion information, we can better specify how to make spatial displays computationally efficient while
retaining their perceptual effectiveness.
Further research is required to determine
how SKE motion tools can be optimally integrated into display designs. Two examples of
these design issues are defining proper modulation frequencies for the SKE motion (the
frequencies used in the studies we have described were deemed by the designers to be
effective in the 0.5-1.0 Hz range) and minimizing display clutter when SKE "structures" are added to complex displays. Fortunately for the latter concern, SKE motion
appears to be one of the most economical
means to effectively convey depth in a display.
ACKNOWLEDGMENTS
c.
This work was supported by NASAAmes Research Center, Moffett Field, California, Grant No. NCA2-468to Dennis Proffitt. We thank Walter Johnson and Vern Battiste
for their helpful comments on an earlier version of this
paper.
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(with aircraft data blocks removed); (b) the enhanced
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STEREO KINETIC DISPLAYS
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Downloaded from hfs.sagepub.com at PENNSYLVANIA STATE UNIV on September 11, 2016
Downloaded from hfs.sagepub.com at PENNSYLVANIA STATE UNIV on September 11, 2016