Motion Stereopsis (Binocular
Depth-from-Motion, BDFM)
[
as a counterpart, the conventional stereopsis is
Disparity Stereopsis (Binocular Depth-from-Disparity, BDFD) ]
Ai-Hou Wang, MD. PhD.
(Some images in this
article require red-blue glasses. Right eye blue lens, left eye red lens.)
This article partly
originates from the 1999 Arthur Jampolsky fellows'
meeting
Since Sir Charles
Wheatstone (1802–1887), https://en.wikipedia.org/wiki/Charles_Wheatstone,
invented the stereoscope (see figure), stereoscopic vision has been attributed
to the disparity between the images seen by the two eyes - the left and right
eyes are like two cameras or video cameras, and the images seen are slightly
dissimilar. The brain can convert these slightly dissimilar parts into depth
perception. This depth perception derived from disparity is called stereoscopic
vision or stereopsis.
Conversely,
simulating the images seen by both eyes, placing two slightly dissimilar images
(see figure) on Wheatstone's stereoscope for the left and right eyes can also
allow the brain to transform into depth perception. As shown in the figure, the
cube and double circles are simulations of real three-dimensional objects.
Some people look at
the images cross-eyed – the image for the right eye is placed on the left, and
the image for the left eye is placed on the right. This makes it easier to
merge the images from both eyes, easier to see a three-dimensional image with
depth perception.
In the image, the
blue square appears slightly to the left in the right eye's view and slightly
to the right in the left eye's view. Stereoscopic vision in the brain
translates this disparity into the blue square appearing to float above the
yellow background.
In 1960, Bela Julesz at Bell Labs invented and created a random-dot
stereogram (RDS) based on the same principle (see figure). The hidden shaped
within random-dot stereograms cannot be seen with either eye alone; they are
only visible after the texture of random dots are fused by both eyes. The
principle behind creating random-dot stereograms is the same as that of contour
stereograms – the square in the right eye is slightly shifted to the left, and
the square in the left eye is slightly shifted to the right. This remains
utilizing the "disparity" between the images seen by both eyes to
create depth perception.
Some people find it
easier to see the floating square by crossing their eyes – placing the image
for the right eye on the left side, and the image for the left eye on the right
side.
This article
introduces another binocular mechanism for depth perception besides disparity –
Motion stereopsis, or Binocular Depth-from-Motion, BDFM.
When we observe an
object moving in different directions in space, it will create different
combinations of two motion vectors on the retinas of both eyes (see figure).
Conversely, different combinations of two motion vectors on the retinas of both
eyes contain sufficient information to calculate and to perceive its direction
of motion in depth. This is motion stereopsis. It needs to be tested separately
from the stereopsis coming from binocular disparity that we are familiar with.
Motion in the left-right directions results in identical-magnitude,
same-direction motion vectors on the retinas of both eyes (Figures 1 and 7);
motion in the front-back directions results in opposite-direction,
identical-magnitude motion vectors on the retinas of both eyes (Figures 4 and
10) (see figure).
Disparity stereopsis
is a static depth perception (Depth-from-Disparity) arising from the
dissimilarity in retinal images of the two eyes; while motion stereopsis is
dynamic, arising from the difference in motion vectors of the two eyes' retinal
images (Depth-from-Motion). In Wheatstone's era, perhaps due to the lack of
dynamic displays of modern computer, another mechanism
of binocular depth perception, other than disparity, arising from motion
perception was not recognized.
Static stereopsis is
the depth perception generated by the disparity between the two semi-stereo
images of the left and right eye. Dynamic stereopsis is not simply a dynamic
version of disparity stereopsis; some papers refer to it as "dynamic
stereopsis", which is inappropriate, failing to grasp the key to the
physiological mechanism of motion stereopsis. Motion stereopsis is the depth
perception generated by the difference in "motion perception" between
the two eyes.
ayama of Harvard
University's Department of Psychology argued that motion perception should be
studied and discussed independently of form (contour) perception. Similarly,
"motion stereopsis" should also be discussed separately from
"disparity stereopsis," as a parallel topic. This article describes
testing disparity stereopsis and motion stereopsis using a random-dot dynamic
stereogram, allowing for separate testing of depth perception derived from
disparity cues and depth perception derived from motion cues.
Nakayama K. Biological image motion processing: a review. Vision Res. 1985;25(5):625-60.
An important point to note is that motion perception is a sensory (afference) rather than a motor
(efference) event. Motion
vs. Motor can very often be confusing.
Search YouTube for "Motion Stereopsis"
for 10-minute explanatory videos
on motion stereopsis.
https://www.youtube.com/watch?v=j9PaE92JBKk&t=5s (Chinese)
https://www.youtube.com/watch?v=aEoxO_RdGhE&t=17s (English)
Origin
Dr. Ji-Hau Jan, my deceased colleague, was adept
at computer programming. He designed a computer version of NTU RDS (National
Taiwan University, Random Dot Stereograms) for Dr. Luke Lin and Health
Promotion Administration, Ministry of Health and Welfare for vision screening
of preschool and school children.
The title page of
this program exhibited a stereogram with a square changing its depth
repeatedly. The disparity varied from 1 to 31 and then 31 to 1 pixel(s) (see
figure). This created a dynamic stereogram, similar to
an animated motion picture, showing a floating square whose depth oscillated
continuously between two depths.
This dynamic title
page inadvertently touches upon another topic in the visual study of random dot
patterns – the random-dot kinematogram (RDK) or the
random-dot cinematogram (RDC). An RDK refers to that
either left eye or right eye views this title page to be a dynamic random dot
pattern. No square is visible at any single moment. However, when the animation
starts playing, a square is seen moving leftward and rightward. RDK is a
monocular visual phenomenon, a topic related to temporal form perception.
A person without
stereopsis watching this dynamic title page found that he could perceive the
depth. Contrary to RDS where being able to see the hidden shape serves as
evidence of stereopsis, the square is not hidden in the RDK. Being able to see
the square in RDK does not prove that the subject has depth perception.
However, reporting Emmert's Law does indicate depth perception. Emmert’s Law
says that when the square appears to float and get closer to you, the square
appears smaller. In the real world, when a fixed-size square moves closer to
you, the retinal image gets larger, but you interpret the square as fixed-size.
The square in the RDK has fixed-size; when it floats and gets closer, its
retinal image does not get bigger, so you conversely perceive it as getting
smaller. Experiencing Emmert's Law, this person without stereopsis should
genuinely be experiencing depth perception.
If the RDK on the
title page is paused, it becomes a single, static RDS. Persons with normal
stereopsis will see the forward and backward moving square suddenly stop,
remaining suspended in midair; while persons without stereopsis will find the
square disappears to be invisible.
This implies that, in
addition to disparity cue, motion cue can also generate depth perception.
We employed
4-alternative-forced-choice (4-AFC) paradigm, displaying four moving squares on
the screen. One square moves forward and backward in
depth, while the other three move left and right on a plane. Subjects are
required to find the square that is moving in depth (see figure).
Based on the
principle of motion stereopsis, for the square moving in depth, the squares
viewed by right and left eye move in opposite direction, while for those
squares moving on a plane, the squares viewed by right and left eye move along
the same direction (see figure).
We create dynamic
stereograms with random dot patterns. Please notice only the 3D square jumping
in depth, of which
the squares viewed by
right and left eye move in opposite direction.
From disparity cue,
at time 1, it’s a 3D square coming in front; at time 2, it’s a 3D square
recessed back.
Viewing with the
right eye, it’s an RDK with motion cue; viewing with the left eye, it’s also an
RDK with motion cue, yet moving in opposite direction.
When viewing with
both eyes, you see a square moving back and forth in depth. The depth
perception comes from both disparity and motion cues (see figure).
If the squares at
time 1 and time 2 are different random dot patterns – at time 1, it’s a 3D
square coming in front from disparity cue; at time 2, it’s a 3D square recessed
back, also from disparity cue.
Viewing with the
right eye, it is a random-dot correlogram (RDC) at time-domain (or temporal
RDC); viewing with the left eye, it is also a temporal RDC. There is no left-right movement of
square in either eye.
When viewing with
both eyes, a square appears to jump back and forth in depth, which is entirely
from disparity cue, and there is no motion cue (see figure).
See RDCorrelogram for the explanation of random-dot
correlogram (RDC).
If the
squares in the left and right eyes have different random dot patterns – at time
1, it is a spatial RDC; at time 2, it is also a spatial RDC. Pause the dynamic
random-dot pattern at time 1 or time 2 shows no disparity between the
random-dot pattern of the right eye and the left eye, and thus no depth
perception.
Viewing
with the right eye, it’s an RDK; viewing with the left eye only, it’s also an
RDK, with the square moves in the opposite direction to the right eye.
When
viewing with both eyes, a square appears to jump back and forth in depth. This
depth perception is purely from motion cue without disparity cue intervenes
(see figure).
It is summarized in
the following figure,
For stereogram with disparity cue only, the squares
at time 1 and time 2 are different random dot patterns, which constitute
temporal RDC. For stereogram with motion cue only, the squares for the left eye
and right eye are different random dot patterns, which constitute spatial RDC.
In fact, two random-dot patterns may not only be completely identical or completely different. In
between these extreme conditions, two random-dot patterns can be partially
identical. From completely identical to completely different, it can be
modulated gradually.
Any two random-dot patterns with 50% density, when
looking at each pixel's position, consists of 1/4 positions where the pixels in
pattern 1 and pattern 2 are both black; 1/4 positions where the pixels in
pattern 1 and pattern 2 are both white; 1/4 positions where the pixels in
pattern 1 are white while the pixels in pattern 2 are black and 1/4 positions
where the pixels in pattern 1 are black while the pixels in pattern 2 are
white. In other words, at half positions the pixels in pattern 1 and pattern 2
are identical and at another half positions the pixels in pattern 1 and pattern
2 are at opposite polarity.
Conversely, if you change the polarity of half
(50%) pixels in a 50% density random-dot pattern, i.e.
changing black into white and white into black, it becomes a completely
different 50% density random-dot pattern. The logic operation XOR is the exact
operator to change the polarity of pixels. An operator of 50% density will
convert one 50% density random-dot pattern into another completely different
50% density random-dot pattern (see figure).
If the operator is of
20% density, it changes the polarity of 20% pixels of the original random-dot
pattern to convert it into another 50% density random-dot pattern. The new
random-dot pattern is partially different from and partially identical to the original
random-dot pattern. It will keep some ghost image of the original random-dot
pattern (see figure)!
If the operator is of
100% density, it inverts the polarity of all pixels of the original random-dot
pattern and converts it into the negative image of the original random-dot
pattern. The resultant random-dot pattern nevertheless remains to be of 50% density
(see image).
In generating motion stereogram with disparity cue only, the random-dot pattern
of the square at time 1 and time 2 are different. Here, we can apply a temporal
operator (temp) of different densities to modulate the resultant random-dot
pattern from exactly identical to completely
different.
Similarly, in
generating motion stereogram with motion cue only, the random-dot pattern of
the square for the left and right eye are different. We can apply spatial
operators (spat) of different densities to modulate the random-dot pattern from
exactly identical to completely different (see
figure).
If you are interested
in visual science, you can titrate the spatial operator from 0% to 50%. It will
change the disparity cue from all to none.
You can also titrate
the temporal operator from 0% to 50%. It will on the
other hand change the motion cue from all to none.
You may observe how
different people's depth perception relies on different proportions of
disparity cue and motion cue (see figure).
For simplicity in the
clinical work, we tested only (1) depth from full disparity and full motion
cues (Spat=0%, Temp=0%), (2) depth from full disparity cue with zero motion cue
(Spat=0%, Temp=50%) and (3) depth from full motion cue with zero disparity cue
(Spat=50%, Temp=0%).
If both disparity and
motion cues are removed by using 50% spatial operator and 50% temporal
operator, it will surely be impossible to get any depth perception.
Motion
stereopsis is a dynamic binocular visual function. Clinically, dynamic tests
are rare, perhaps due to technological limitations. Currently, binocular visual
function tests mainly fusion and static stereopsis. About their mechanism,
motor fusion can be interpreted as Vergence-from-Disparity, and stereopsis as
Depth-from-Disparity. Both are binocular consequences to the static environment
objects.
We
live in a dynamic world. The retinal images are mostly in motion. The depth
perception coming from comparison of the motion vectors of the retinal images
of two eyes might be used even more frequently. Surprisingly, we don’t have
corresponding clinical examinations for that!
Kitaoji and
Toyama called this mechanism ‘motion stereopsis’. I prefer to name it as
‘Binocular Depth-from-Motion, BDFM’ according more exactly to its physiological
mechanism. At the same time I would interpret the
conventional stereopsis as ‘Binocular Depth-from-Disparity’ or ‘Disparity
stereopsis’.
Regan provided a
thorough description of ‘the depth perception from object motion’ and ‘the
spatial motion of an object’. That is Depth-from-Motion and Motion-in-Depth
respectively.
Regan D. Depth from
motion and motion-in-depth. In: Cronly-Dillon JR, ed.
Vision and visual dysfunction, Vol. 9. Houndmills:
Macmillan. - Regan D, ed. Binocular vision. Chapter 8. 1991;137-169.
The study of spatial
motion is twofold – 1. ‘looming’ or ‘optic flow’ describes and locates the
movement of ourselves in space, 2. depth-from-motion describes the movement of
objects in space.
The spatial movement
of objects produces different combinations of motion vectors on the two
retinas, and conversely, from these different combinations of vectors, we have
sufficient information to calculate and infer the direction of movement of the
object in space.
Note that the
terminology ‘motion’ in depth-from-motion refers to the image motion on the
retina. It’s a sensory perception rather than motor event. While the ‘motion’
in motion-in-depth refers to the movement of the object in space.
The image motion on
the retina of a single eye also evokes certain perceptions of distance and
depth. That’s why I emphasize ‘Binocular’ Depth-from-Motion as the study object
of this article.
Motion stereopsis or BDFM of strabismic patients
We have tested 54 patients with small-angle strabismus, some
post-operatively and some did not receive any surgery.
These subjects failed the 35
min-of-arc static random-dot stereopsis test (NTU RDS
35min) yet passed the motion stereopsis test. They passed the RDS test with
both disparity and motion cues, passed the RDS test with motion cue only, but
failed the RDS test with disparity cue only (see figure).
This demonstrates that
their depth perception comes from motion cue. They cannot pass this stereopsis
test with disparity cue only, which is consistent with their inability to pass
static random-dot stereograms, such as TNO stereopsis test.
Individuals who fail
conventional stereopsis tests lack the binocular disparity mechanism of
stereopsis. In daily life, motion cues serves as their
binocular mechanism for judging distance. Many strabismic patients who fail
conventional stereopsis tests report that they still perceive depth and
distance when watching 3D movies.
Another example is Pulfrich pendulum – viewing a pendulum with one eye through
a neutral density filter will produce Pulfrich
phenomenon. The pendulum moving in a single plane appears to rotate along an
elliptical trajectory, moving closer to and farther from the observer (see figure).
The Pulfrich phenomenon is generally explained with static
disparity mechanisms, stating that the neutral density filter over one eye
causes neural conduction delay. This delay in time creates disparity between
the two eyes, thus generating depth perception. In fact, binocular motion
perception mechanisms also participate in this process, which can be
demonstrated using random-dot correlograms (RDC),
removing the mechanism of disparity.
Among 54 patients, 9
had early-onset strabismus, as their optokinetic nystagmus (OKN) showed naso-temporal asymmetry and/or coexistent latent nystagmus.
Although early surgical intervention for infantile esotropia often fails to
restore their disparity stereopsis, motion stereopsis can be restored when the
strabismus is corrected to certain smaller angle. Consequently, early surgery
for infantile esotropia, beyond the cosmesis, also has functional benefits of
binocular vision and the ability to enjoy 3D movies.
Motion Stereopsis or
BDFM in subjects with normal stereopsis
We have tested subjects
with normal disparity stereopsis. They often find that the stereograms with
motion cue only are harder to read than those with disparity cue only. Yet with
practice, most can pass the motion stereopsis test with motion cue only.
There’re nevertheless two persons who remained not
being able to pass, no matter how hard they had practiced!
We interpret
as that people with normal stereopsis seem accustomed to using disparity
mechanisms to judge distance, putting aside the motion mechanism, although the
motion mechanism does exist in their brains.
Neurophysiology of
Binocular Depth-from-Motion (BDFM)
In everyday life,
objects with motion-in-depth, such as a mosquito in flight, their images on two
eyes typically have two characteristics – changing disparity and changing
motion vectors. Cumming and Parker investigated two possible binocular
mechanisms for detecting moving objects in depth. One is to detect changes of
motion vectors between the two eyes (depth-from-motion); the other is to detect
changes of image disparities over time (depth-from-disparity) (see figure).
Cumming BG, Parker
AJ. Binocular mechanisms for detecting motion-in-depth.
They believe it is
the second mechanism, arguing that there is no evidence to support the human
body's ability to detect the difference between motion vectors of the two eyes.
Our clinical observations, however, tend to support the first mechanism, at least
in patients with strabismus. Because strabismus patients lack the ability to
detect disparity, they obviously cannot calculate the change of disparity over
time.
The
stereopsis examination we conduct in the
strabismus/amblyopia clinic can be simplified into three steps:
Step
1: 300 seconds-of-arc random dot stereogram (NTU RDS 300 sec-of-arc)
(The
visual screening of students is also based on NTU RDS 300 sec-of-arc as the
criterion for passing/failing.)
If
this test is passed, it is accepted as normal stereopsis. If not pass, we
proceed to the next step
Step
2: 35 minutes-of-arc (=2100 seconds-of-arc) random dot stereogram (NTU RDS 35
min-of-arc) (2100 sec-of-arc)
If
this test is passed, it is accepted as subnormal stereopsis. Patients with
esophoria and anisometropia often fall into this category. Their stereopsis is
not perfect yet is not entirely absent.
We
explain to the parents that being able to pass the coarse random dot stereopsis
test is already a fairly good binocular vision
function. If still not pass, we proceed to the next
step
Step 3: Motion stereopsis test
If
this test is passed, we will explain to the parents that although they cannot
read static stereograms on the books, they will be able to watch dynamic 3D
movies (motion pictures / animations).
If they fail again, we explain
to the parents that not having stereopsis does not cause much inconvenience in
daily life. Monocular cue also gives spatial perception and distance judgment.
The computer section of
Universal Eye Center has made a cross-platform program of stereopsis
examination for public use, which includes both disparity and motion
stereopsis.
https://www.eyedoctor.com.tw/Stereopsis/
By the
way, you may also be interested in the stereopsis
SCREENING program we made:
https://www.eyedoctor.com.tw/Stereopsis_Screening/
Professor
Takashi Fujikado (ふじかど たかし)
of the Department of Medical Research, Graduate School of Medicine, Osaka
University, is also interested in motion stereopsis. He once gave a lecture at
a pediatric ophthalmology/strabismus conference in mainland China. The topic is
"Can people without stereopsis watch 3D movies?". The subject must be
the same as the main theme of this article - motion stereopsis!
Clinical studies at
Nagoya University suggest a relationship between sensory fusion (as assessed by
the Worth-4-dots test) and the presence of motion stereopsis.
Maeda M, Sato M,
Ohmura T, Miyazaki Y, Wang AH, Awaya S. Binocular depth-from-motion in
infantile and late-onset esotropia patients with poor stereopsis. Invest Ophthalmol Vis Sci 1999;40:3031-3036.
Clinical examination
of binocular vision generally considers motor fusion a prerequisite for
traditional stereopsis (disparity stereopsis). Is motion stereopsis also a
prerequisite for disparity stereopsis? Is motion stereopsis a more fundamental
and basic form of binocular vision than disparity stereopsis? Or are they
parallel, independent entities of binocular depth perception? (See figure)
In my clinical
practice, I test disparity random-dot stereopsis first; if it fails, I test
next the motion stereopsis. Many people failed the disparity stereopsis but
could pass the motion stereopsis test.
So, are there people
with normal disparity stereopsis but no motion stereopsis? Laby found that some
people with normal stereopsis lack dynamic stereopsis. He therefore considered
disparity stereopsis and motion stereopsis as two parallel mechanisms.
Laby DM, Kirschen DG. Dynamic stereoacuity: priliminary
results and normative data for a new test for the quantitative measurement of
motion in depth. Binocular Vis & Eye Muscle Surgery. 1995;10:191-200.
We have two patients
with normal stereopsis, who, even after practice, could not pass the motion
stereopsis test with motion cue only. The neural mechanisms relating motion stereopsis and disparity stereopsis require further
study and discussion.
e patient had
residual esotropia of 18Δ – she had 27Δ esotropia and wore 9Δ base-out prism
glasses. Among our series of patients, she is the one with largest deviation
angle who passed the motion stereopsis test. This suggests that the receptive
field of the motion stereopsis neural mechanism is greater than 18Δ.
Infantile esotropia (or Congenital esotropia)
For infantile esotropia, the general
consensus is surgery before the age of two. Despite it is impossible to
regain random dot stereopsis, monofixation with
peripheral fusion and motion stereopsis can be restored.
The disadvantage of early surgery is the higher chance of reoperation.
Doctors who emphasize the early surgery are focused on
the restoration of binocular vision. It is generally believed that the earlier
the surgery, the greater the chance to restore motor fusion. But whether motion
stereopsis necessarily needs such early surgery for restoration, or whether it
can be restored with later surgery, requires further clinical experience to
answer this question.
Some people cite the
motion stereopsis test procedure but change the name to ‘dynamic stereopsis’
which loses the fundamental concept that this stereopsis is based on the
difference of motion perception of two eyes. Motion stereopsis (Binocular
Depth-from-Motion) is another mechanism to generate binocular depth perception,
as opposed to disparity stereopsis (Binocular Depth-from-Disparity).
Static stereopsis is
the depth perception generated from the ‘disparity’ between the two
half-stereograms viewed by left and right eyes. Motion stereopsis is not a
dynamic version of disparity stereopsis; some papers call it ‘dynamic
stereopsis’ which is inappropriate and fails to grasp the key points of the
physiological mechanisms of motion stereopsis. Motion stereopsis is the depth
perception generated from the difference of ‘motion perception’ between the two
eyes.
Motion stereopsis
originates from motion perception, and it is, of course, a dynamic testing
method. However, the term ‘dynamic stereopsis’ has other applications. The
figure below depicts the pattern designed to record the visual evoked potential
(VEP) of stereopsis, consisting of 16 stereograms of hidden checkerboards.
Eight stereograms comprise checkerboards with a raised checker at its upper
left corner, and eight stereograms comprise checkerboards with a recessed
checker at its upper left corner. They are played repeatedly, mimicking the
checkerboard reversal patterns used in clinical VEP examinations. However, this
is not a black/white reversal pattern, but a depth reversal pattern. The images
seen by the left eye and right eye individually seem like a snowstorm pattern
after the television ceases broadcasting. When viewed with both eyes, the
checkerboard undergoes depth reversal at a preset frequency. If after signal
analysis the visual evoked potential contains this particular
frequency, it indicates a brain response induced by stereopsis, as there
is no such frequency input from each eye individually.
This figure is what
previous researchers called a dynamic random-dot stereogram. It’s not the
motion stereogram as we discuss in this article. The background and foreground
of each stereogram are all different, and do not contain motion cues. The depth
perception comes from the disparity between the half-stereograms viewed by left
and right eyes, which is different from the motion stereopsis mentioned in this
article – despite both are ‘dynamic’ forms of stereograms.
References
l Kitaoji H, Toyama K. Preservation of position and motion stereopsis in
strabismic subjects. Invest Ophthalmol Vis Sci 1987;28:1260-1267.
l Laby DM, Kirschen DG. Dynamic stereoacuity: priliminary
results and normative data for a new test for the quantitative measurement of
motion in depth. Binocular Vis & Eye Muscle Surgery. 1995;10:191-200.
l Regan D. Depth from
motion and motion-in-depth. In: Cronly-Dillon JR, ed.
Vision and visual dysfunction, Vol. 9. Houndmills:
Macmillan. - Regan D, ed. Binocular vision. Chapter 8. 1991;137-169.
l Nakayama K. Biological image motion processing: a review. Vision
Res. 1985;25(5):625-60.
l Cumming BG, Parker AJ.
Binocular mechanisms for detecting motion-in-depth. Vis Res 1994;34:483-495.
l Maeda M, Sato M,
Ohmura T, Miyazaki Y, Wang AH, Awaya S. Binocular depth-from-motion in
infantile and late-onset esotropia patients with poor stereopsis. Invest Ophthalmol Vis Sci 1999;40:3031-3036.
l Wang AH. Proceedings
of the Jampolsky Festschrift, The Smith-Kettlewell
Eye Research Institute (SKERI), San Francisco, April 2000.
BDFM – Both Motion and Disparity cues
BDFM – Both Motion
and Disparity cues – Right one is jumping in depth
BDFM - Both Motion
and Disparity cues – Upper one is jumping in depth
BDFM - Both Motion
and Disparity cues – Lower one is jumping in depth
BDFM - Both Motion
and Disparity cues – Left one is jumping in depth
BDFM - Disparity cue only
BDFM - Disparity cue
only – Lower one is jumping in depth
BDFM - Disparity cue
only – Right one is jumping in depth
BDFM - Disparity cue
only – Left one is jumping in depth
BDFM - Disparity cue
only – Upper one is jumping in depth
BDFM - Motion cue only
BDFM - Motion cue
only – Left one is jumping in depth
BDFM - Motion cue
only – Upper one is jumping in depth
BDFM - Motion cue
only – Right one is jumping in depth
BDFM - Motion cue
only – Lower one is jumping in depth
Another
thing that is related to motion stereopsis / binocular depth-from-motion is the
Pulfrich pendulum (Pulfrich
effect)
If one
of the eyes is looking through a neutral density filter, or there is optic
neuritis in one eye, the pendulum swinging on a frontal plane without depth
will appear to move along an elliptical orbit (as shown in the figure),
resulting in binocular depth perception in both eyes.
The
general explanation is that the pendulum seen by the eye with light reduction
or optic neuritis creates a delay. At any moment the pendulum seen by this eye
seems to be located at an earlier position than the other eye. And there
appears a disparity of the pendulums seen by the two eyes.
If the
delay is in the left eye, when the pendulum swings to the right, the pendulum
seen by the left eye is more left, and the pendulum seen by the right eye is
more right, resulting in uncrossed disparity, so it feels farther away from us;
When the pendulum swings to the left, the pendulum seen by the left eye is more
to the right, and the pendulum seen by the right eye is more to the left,
resulting in crossed disparity, so it feels closer to us.
The
pendulum thus seems to go along an elliptical trajectory with depth. Viewed
from above, the trajectory rotates in a clockwise (CW) direction. If the delay
is in the right eye, by the same reasoning, it will be seen as going in a
counterclockwise (CCW) direction (see figure).
The
above interpretation is based on a depth perception caused by binocular
‘disparity’ (binocular depth-from-disparity). It is traditionally what we
considered with the vocabulary ‘stereopsis’.
The Pulfrich pendulum also contains motion cues. After the
image of one eye is delayed, at any moment, the pendulum image on two retinas
has different motion vectors. The brain fuses the pendulum images of two eyes,
and its ‘motion-in-depth’ can be calculated from these two motion vectors. This
is motion stereopsis, a depth perception generated by the difference of
binocular motion vectors (binocular depth-from-motion).
Besides
disparity cue, the depth perception of the Pulfrich
pendulum also contains motion cue.
Clinically,
we have found patients without disparity stereopsis, such as those with small-angle esotropia, can still recognize whether the Pulfrich pendulum is rotating clockwise or
counterclockwise. Their depth perception must come from binocular motion cue
(binocular depth-from-motion), because disparity cue (binocular
depth-from-disparity) is absent in their brain.
The
following link is a Pulfrich pendulum test program
(only executable on Windows system, cannot run on Mac or Android).
This
is a program that simulates the Pulfrich pendulum. There
are two pendulums in red and blue colors respectively. Wearing red/blue
goggles, blue lens over right eye and red lens over left eye. Only one pendulum
is seen by each eye.
The
sinewave moving pendulum goes along a 360° cycle in 36 steps, 10° for each
step. There is a time difference between the pendulum of the left eye and the
pendulum of the right eye. The time difference between the two eyes is set by
the program to be 1 step to 15 steps. The less the time difference, the less
the delay between the left and right eyes of the simulated Pulfrich
pendulum, thus the less obvious the depth perception, and it is then less
easier to see it as an elliptical orbit; The more the time difference, the more
the delay between the left and right eyes of the simulated Pulfrich
pendulum, thus the more obvious the depth perception, and it is then easier to
see as an elliptical orbit. If the left eye (red) is delayed, it will be seen
as a clockwise rotation; if the right eye is delayed, it will be seen as a
counterclockwise rotation.
The
left eye delay or right eye delay, i.e. the clockwise or counterclockwise
rotation of the track, is randomly selected by the computer.
The
subject’s work is to determine whether the elliptical track closer to him/her
is moving leftward or rightward. The subject input the
answer by hitting <left> or <right> key on the keyboard. If the
answer is correct, computer gives a crescendo tone,
and if the answer is incorrect, there will be a decrescendo tone.
If you
can't judge the rotation direction and always give wrong answer, you can
increase the delay between the left and right eyes by hitting <+> key,
that will increase the depth of the elliptical track to make it more obvious
and easier to answer. At the beginning of the program, the default delay is 3 steps.
Pressing
the <+> key will increase the delay by 1 step, making the depth judgment
easier; pressing the <-> key will decrease the delay by 1 step, making
depth judgment more difficult. The program sets a minimum delay of 1 step and a
maximum delay up to 15 steps.
The
subjects increase or decrease the delay number by him/herself, to determine the
threshold where they can correctly tell the CW/CCW direction.
By
pressing <Enter> key, you can see the current
delay number in the upper-left corner of the screen. This delay serves as a
threshold of depth judgement of the Pulfrich
pendulum.
To
stop the program, press <Esc> key.
The
title page of the program is shown in the picture
This
is an example of counterclockwise (CCW) rotation.
This
is an example of clockwise (CW) rotation.
