Extracting
Dynamic Pattern
through
the Processes that Generate
Apparent Motion
and
Apparent Stability
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Contents:
General
Framework
Computational
Level Analysis
Algorithmic/Implementational Level Analysis
Review of Apparent Motion
Phase
Relations between System Dynamics and Representation
Apparent
Motion
Window Size Greater than Basin Length
Window Size Less than Basin Length
Apparent Stability
Extracting Basin Patterns: Window
Size Equal to Basin Length
Extracting Sub-basin Patterns:
Window Size Equal to Sub-Basin Length
Simulating
a Dynamic Universe
Exemplar
1: Interactive interface for extracting basin and sub-basin patterns
Extracting
General Patterns from a Dynamic Universe
Exemplar
2: Interactive interface for extracting general patterns
Exemplar
3: Interactive interface for extracting emergent wave forms in layers
Discussion and Conclusions
Notes
References
General
Framework for Proposing a Mechanism of Pattern Perception
David Marr (1982) in Vision
proposed an approach to
understanding complex systems that remains useful and influential twenty
years later. He was primarily concerned with human vision and the sorts of computations
(processes) any seeing system would need to perform in order to see. He required
descriptions of the workings of the system at three levels: Computational, Representational
and Algorithmic, and Implementational.
The computational level addressed (1) the goal
and function of the computation (the "what and why" in his terms),
and (2) the necessary constraints built into the accomplishment of the goal.
The Algorithmic level addressed the specifics of how input and output would
be represented and what algorithm would transform input to output. The implementational
(hardware) level addressed the details of the physical system (e.g., mammalian
neurology, computer circuitry) that would embody the representations and algorithm
and would accomplish the function of the system.
Marr wrote at time when the linear information
processing framework was predominant. While we do not espouse a linear information
processing framework (input--representational coding--tranformation--perceptual
representation--output), we will begin by outlining the issues involved in the
extracting of dynamic patterns from a dynamic universe using Marr's approach
because of its utility in maintaining conceptual clarity. [Note
1.] In our conclusions, we will recast important issues in a less linear,
more systemic framework.
Computational Level Analysis
What and Why. Human perception must be able
to extract pattern from a dynamic universe. The universe is dynamic for two
rather different reasons. First the universe is changing over time. Some of
these changes are slow, even geological in their pace. Others are fast like
changing heart rate and the blush on a cheek. Second, things move. Things move
relative to an observer and observers move relative to things.
Example. Imagine a scene. Moving down a steep
mountainside carpeted by autumn tinted shrubbery, a herd of tawny deer is obscured
by a thick cover of brown autumn leaves, appearing no more than a collection
of flickering spots moving together at the same downward angle. How is that
we can extract a coherent pattern that marks a herd of deer as distinct from
all the other motion, distinct from the shimmering motion of the leaves in the
wind, distinct from the swaying of tree branches, distinct from the motion of
a flock of small brown birds flitting among trees along a trajectory that intersects
that of the deer, distinct from the motion of the tree trunks which appear to
move with respect to the observer who also is moving? There are many motives
for extracting dynamic pattern in a dynamic context, curiosity being perhaps
the most basic. Whether a being is simply a curious human or bird constructing
knowledge of how the world works, whether a being is a predator or a prey, whatever
the motive, knowing about patterns that are moving has fundamental significance.
The curious bird who detects the motion of the deer herd may learn that the
deer regularly eat leaves of bushes which also carry tasty seeds.
A being needs to be able extract many distinct dynamic patterns
at once. Besides detecting the deer, bird may learn of the the tasty seeds in
other ways--the sudden cessation of the movement of other birds as they land
on the branch of a bush; dark seed pods swaying in the wind. The autumn scene
is a patchwork of disconnected fragments of motion. How are coherent patterns
formed from this dynamic puzzle?
Constraints. What are the constraints we would
like to place on this extraction of dynamic pattern? For various reasons we
would like to be able to extract patterns of motion that are not immediately
adjacent. This may be because the object of interest is actually a collective
like a herd, so that one deer is separated from the others, higher up the mountain
slope and lagging behind. Or it may be because a single coherent object, a deer,
may be masked by something irregular like leaves so that only parts of it show
through. In either case, a useful requirement is that a coherent pattern does
not have to be coherently adjacent on the retinal image.
A second design constraint is that there be a way of distinguishing
dynamic patterns; there needs to be, in effect, a way of highlighting one dynamic
pattern and then shifting to another dynamic pattern and highlighting it, or,
even better, a way of having multiple highlights each pointing at different
dynamic patterns in the same scene.
What is the function of the human neurology that produces
Apparent Motion? Another way of stating the computational level issues
is to ask what is the function of the human neurology that enables the perceptual
experiences we call apparent motion. Surely evolution did not teleologically
aim for enabling movies, video, and computer animation? What use is the neurology
that Thomas Edison took advantage of when he invented movies?
Top
Algorithmic and Implementational
Level Analysis
We are proposing that a central mechanism for extracting pattern
from dynamic scenes is the mechanism that allows the phenomenon of apparent
motion. The ability to see movies and videos presupposes the existence of some
algorithm and neural basis for that ability. It is not our intention to explain
or specify neural bases nor the algorithms that enable apparent motion phenomena.
Rather, given that such bases must exist, we propose to use them as a mechanism
that explains many phenomena in pattern perception, particularly the perception
of dynamics. Perhaps our findings will reflect back in a useful way upon frameworks
about apparent motion.
Top
A Review of the Apparent Motion
Suppose that Figures 1 a through d represent
frames from a movie. These frames are shown in rapid succession. The dark
rectangle (top row) and bottom rectangle (bottom row) will appear to move
across the frame from left to right. Timing is important in this effect; when
the frames are shown at around 25 frames per second (fps) the effect is maximal.
The motion, of course, can be seen to be going backwards
(here represented by right to left).
Background prerequisites. For this discussion,
it is important to understand the concepts related to basins in a dynamic system.
The logico-mathematical basis of the concept is covered in E42:
A Description of a Discrete Dynamic System. Critically, toward the end of
that web page, is information about how basins are represented visually as a
Historical Trace in the E42 interface. As a contrast to how
they are found on this web page, an analytic method for finding basins is presented
in TAO Tool.
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Phase Relations
between System Dynamics
and Representation:
Apparent Motion and Apparent Stability
Example. Suppose that we have a simple two-node
dynamic system (Figure 3) that has basin length L=4. For the system taken as
a whole, the pattern of black and white squares repeats every four iterations.
The historical trace represents the periodic cycles of basins rolled out onto
the horizontal axis. In Figure 3, the iteration numbers along the horizontal
axis are alternated shade and white is sets of four iterations to emphasize
that the basin is four iterations long. The pattern seen in the historical trace
for iterations 1 through 4 is identical to that for iterations 4 through 8 and
for iterations 9 through 12 and iterations 13 through 16.
Basins and Sub-basins. Notice that it is node
1 that defines the basin length of 4, since its pattern only repeats every fourth
iteration. In contrast, node 2 repeats its pattern every two iterations, and
so we define the pattern of node 2 in the historical trace as constituting a
sub-basin of length SubL=2. If people focus their attention exclusively on node
2, they will experience a pattern that repeats itself every two iterations.
If they focus on the whole system (nodes 1 and 2 taken together) they will notice
a pattern that only repeats every four iterations.
| Node 1 |
 |
| Node 2 |
| Iteration # ==> |
Figure 3. Historical trace
of sixteen iterations of a simple two-node system that has basin length
L=4. The repetition of the basin pattern (length 4) is emphasized by alternating
shading in the Iteration # row.
Note: {This is an impossible Boolean System made up to illustrate Apparent Motion ideas. It requires (or presumably would have) a third node to have a deterministic flow.} |
Basin patterns are cyclic and there is no necessary starting
point [Note 2]. So we can change our starting point for
perceptual reasons if we want. Perceptual grouping occurs when basin dynamics
are represented as historical traces. So it is relatively easy to perceive a
small checkerboard pyramid as it repeats across the linear historical trace:
See iterations 4, 5, 6 or 8, 9, 10, or 12, 13, 14 in Figure 3. Thus we could
have started the basin pattern with iterations 4, 5, 6, 7 to emphasize this
pyramid.
Representing Sets of Successive Iterations Simultaneously
in a Single Window
Printing several iterations at once in a window (frame).
Generally, we conceptualize the historical trace as outputting the state (black
or white) of each node on each iteration at the moment that that iteration occurs.
What if we change how we represent the historical trace on the screen? What
if we let the system run for X iterations and then print the
set of X iterations at once in a window? Next we would let the system run for
X more iterations and output those X new iterations on the screen right
over the output of the previous X iterations. And so on. The representation
will now become a window showing the pattern generated by X iterations. This
pattern is over-written as soon as the next X iterations of the system are complete.
Such a window will in effect be like a frame on movie film:
It will show one pattern (of length X iterations) then the next pattern of X
iterations then the next pattern of X iterations, and so on. Differences in
the positions (relative to the window as frame of reference) of various elements
of a pattern on successive windows will generate apparent motion (and apparent
stability) effects. Let's examine how that happens.
Top
Apparent
Motion:
The phase relations between the length of the Window (X)
and the length of the Basin (L)
Apparent Motion: Window Size Greater than Basin Length.
To be concrete, what happens in the Figure 3 example when Window Size = 5 iterations?
Notice that this Window Size is greater than the basin length of the system,
which is four iterations. In other words, we wait five iterations and then print
the resulting historical trace pattern for all five iterations at once in a
window. The first time we draw this frame on the screen it will show the first
five iterations (1 through 5). The next time this window is painted it will
show the next five iterations (6 through 10). And so on. Figure 4, below, shows
windows of size 5 (marked by hatched boundaries) imposed on the flow the system.
The viewer would see only one window: That window would be have its content
(outlined by hatched areas in Figure 4) changed repeatedly. If these windows
replace each other successively at the correct rate, the viewer will experience
apparent motion.
Backwards Movement. Notice that the basin
pattern appears to be moving backwards relative to the window taken as a frame
of reference. This movement is easier to see if you pick out some distinctive
pattern such as the checker-board pyramid found on iterations 4, 5, 6 (and again
on iterations 8, 9, 10 and on iterations 12, 13, 14). This pyramid moves backward
relative to the frame of the window in successive windows. This is generally
true, when window size is greater than basin length, the basin pattern will
(apparently) move backwards (right to left).
| Node 1 |
 |
| Node 2 |
| Iteration # ==> |
Figure 4. A window of size
5 iterations imposed on sixteen iterations of the the historical trace of
a simple two-node system that has basin length L=4. The basin patterns (length
= 4) are emphasized by alternating shading in the Iteration # row.
Note: {This is an impossible Boolean System made up to illustrate Apparent Motion ideas. It requires (or presumably would have) a third node to have a deterministic flow.} |
Apparent Motion: Window Size Less than Basin Length.
What if we present the output of the system in a window that shows only 3 iterations?
The first time we draw this frame on the screen it will only show the first
three iterations (1 through 3). Then next time this window is painted it will
show the next three iterations (2 through 4), and so on. Figure 5 shows this
succession of windows. Notice that in this case the basin pattern appears to
move forward (left to right). Again, looking at the pyramid shaped pattern makes
the movement easier to discern. This forward movement of the basin pattern for
window sizes less than basin length is quite general.
| Node 1 |
 |
| Node 2 |
| Iteration # ==> |
Figure 5.
A window of size 3 imposed on the historical trace of sixteen
iterations of a simple two-node system that has basin length L=4. The basin
patterns (length = 4) are emphasized by alternating shading in the Iteration
# row.
Note: {This is an impossible Boolean System made up to illustrate Apparent Motion ideas. It requires (or presumably would have) a third node to have a deterministic flow.} |
Top
Apparent
Stability:
Extracting Basin Patterns by adjusting the phase relations between
Window Size and both Basin Length and Sub-basin Length
Apparent Stability: Window Size Equal to Basin Length.
Figure 6, below, shows a window of size 4 imposed on the pattern of a basin
that has length 4. Notice that the window corresponds to the basin pattern and
so each repaint of the window shows the same pattern. To the viewer, even though
the system is dynamically generating iterations and the window is being repainted
rapidly, the pattern that appears in the window will appear static. The view
through the window is constant even though that view is both dynamically generated
and actively repainted every few milliseconds. We call this "apparent
stability" because the system is actually ongoing and dynamic
and regenerating itself many times per second. Its apparent stability is as
much an illusion as apparent motion is considered to be in the classical perception
demonstrations.
This freezing of the overall basin structure is epistemologically
significant. In this specific example, if the viewer has controls that allow
an adjustment in window size, and is actively adjusting window size, the viewer
can immediately detect the whole basin pattern when the view through the window
becomes stable. The dynamic basin pattern emerges as a stable "thing."
Our more provocative proposal is that there is some neural analogue of that
adjustment. We are using Window Size as an explicit variable that adjusts phase
relations between system dynamics and representation. We do not think neurology
has such windows. But neurology may have processes for adjusting the phase relations
between the dynamics encoded on the the retinal image and the representation
of pattern in experience. So, to recast the second sentence of this paragraph
we propose that there is a neural mechanism that allows for the adjustment of
phase relations between image and representation. To learn how powerful such
a mechanism would be, let us continue the discussion.
| Node 1 |
 |
| Node 2 |
| Iteration # ==> |
Figure 6. A window of size
4 imposed on the historical trace of sixteen iterations of a simple two-node
system that has basin length L=4. The basin patterns (length = 4) are emphasized
by alternating shading in the Iteration # row.
Note: {This is an impossible Boolean System made up to illustrate Apparent Motion ideas. It requires (or presumably would have) a third node to have a deterministic flow.} |
This freezing of the ongoing dynamics will happen for integer
multiples of basin length. That is, if the window size is 1, 2, 3, ... times
as long as the basin length, the dynamics of the basin pattern will become apparently
stable. Top
Top
Apparent
Stability (of subsets): Extracting
Sub-basin Patterns
Apparent Stability: Window Size Equal to Sub-Basin
Length. Figure 7, below, shows a window of size 2 imposed upon the
basin pattern represented as a historical trace. Notice that if we consider
node 2 (second row) in isolation, the pattern for node 2 is identical in each
window. This means that the second row (node 2) of the pattern will be static
as the windows are repeatedly repainted to the screen. In fact, the second row
is being generated by the dynamic system and painted to the screen many times
a second (at least 20 to 25 times a second). Its "staticness" is an
illusion due to the fact that the window size is exactly equal to the the length
of the sub-basin.
Notice, in contrast, that if we consider node 1 (first row)
in isolation, it alternates between two patterns in successive windows of size
2. In the first window it has the left cell ON (black) and the right cell OFF
(white); in the second window, both cells are OFF. These two patterns alternate
across subsequent windows. The experience of the viewer will be of a flashing
black node in the left-most cell of the top row (node 1).
This contrast between what is perceived for the nodes 1 and
2 is important epistemologically. Potential sub-basins within a larger system
can be extracted manipulating window size. When one node (or set of nodes) in
the system freezes and other nodes remain dynamic, the frozen nodes are exhibiting
a sub-basin. Sub-basins can only be of lengths that are integer divisors (without
remainder) of a system's basin length.
| Node 1 |
 |
| Node 2 |
| Iteration # ==> |
Figure 7. A window of size
2 imposed on the historical trace of sixteen iterations of a simple two-node
system that has basin length L=4. The basin patterns (length = 4) are emphasized
by alternating shading in the Iteration # row.
Note: {This is an impossible Boolean System made up to illustrate Apparent Motion ideas. It requires (or presumably would have) a third node to have a deterministic flow.} |
Finding sub-basins, where they exist, within the basin structure
of a system is non-trivial. Analytic techniques are possible, but they are rather
awkward and complex, and they simply provide a list nodes that have such and
such length sub-basins. This is amazingly uninformative, especially in terms
of direct experience with the behavior of a system. It would be like, using
our example, a list of leaves that are moving and their coordinates in space,
as distinct from a list of tawny deer fur patches and their coordinates in space.
Something more direct, something like visual organization of dynamic pattern
gives a more immediate, and for most purposes, more useful representation.
We are now ready to introduce a dynamic interface which makes
the detection of basin and sub-basin structures immediately present in perception.
These two (basin and sub-basin phase relations) are not the
only, or even the most important set of phase relations. But they are where
we will start. After we understand them, we will go on to the extraction
of patterns in general.
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Simulating
a Dynamic Universe
River Rapids. As another
example think about the flow of a swiftly falling rapids on a river. A river
runner (boater or kayaker) standing on the bank looking at the rapids will see
standing waves (large and small), holes (generally to be avoided) and small
sub-rivers where the river's overall current snakes across the surface and hints
at ways through. The boater's success in the rapids depends critically on extracting
dynamic patterns and sub-patterns from what at first may seem to be the chaos
of the thundering fall of water. This pattern extraction becomes even more complex
once the river runner puts in and is sucked into the rapids. The boater will
be moving in relation to river's patterns. How are coherent patterns perceived?
E42: Simulating A Dynamic Universe. River
rapids or wind blown autumn leaves and herds of deer represent the sort of thing
that is of central interest; still, they are difficult to capture in a way that
can be widely shared among many people. So we will use output from an N, K Boolean
system to simulate a dynamic universe from which we will extract various patterns
and sub-patterns.
Top
Finding Basins and Sub-basins Visually
 |
| Figure 8.
Four highlighted repetitions of a basin of length L=18 in a historical trace
of the dynamics of a small system. The system's nodes are the vertical axis
and the iterations (time) are the horizontal axis. |
Finding Basins:
Using Apparent Motion & Stability
In a moment we will examine Exemplar 1, which is an interactive
simulation that allows the reader to play with variables affecting how apparent
motion can extract patterns from dynamics. As a start, we will quickly examine
some static snapshots of the dynamics you will see and point at some important
characteristics.
Figure 8 shows four repetitions of the basin of length L=18
iterations from the Exemplar 1 dynamic system. In Figure 8, the four basins
are made distinct by alternating the background shading.
In terms of our discussion above, a window size that is any
multiple of 18 (18, 36, 54, 72, ...) will give apparent stability to representation
the dynamics of the system in the window. When the dynamics appear to be static,
it is easier to examine the pattern of the basin.
Top
 |
| Figure 9: Sub-basins of length 2.
All nodes (rows) have been dimmed out except those rows that have sub-basins
of SubL=2. For the overall basin, the length L=18. The system's nodes are
the vertical axis and the iterations (time) are the horizontal axis. |
Finding Sub-basins:
Length SubL=2
In Figure 9 we have dimmed out all rows corresponding to all
nodes except those nodes which generate sub-basins of length 2
iterations. Notice that the brighter, white-background, nodes all have a period
of 2 iterations.
Top
 |
| Figure 10: Sub-basins of length 3.
All nodes (rows) have been dimmed out except those rows that have sub-basins
of SubL=3. For the overall basin, the length L=18. The system's nodes are
the vertical axis and the iterations (time) are the horizontal axis. |
Finding Sub-basins:
Length SubL=3
In Figure 9 we have dimmed out all rows corresponding to all
nodes except those nodes that generate sub-basins of length 3
iterations. Notice that the brighter, white-background, nodes all have a period
of 2 iterations.
You can use Figures 8, 9 and 10 static references for your
experiments with extracting patterns using the interactive interface.
Exemplar 1: Finding Basins
and Sub-basins
Now we are ready to leave static images and interact dynamically
to explore how apparent motion/stability allow us to extract patterns from complex
systems.
Exemplar 1: Finding
Basins and Sub-Basins using Apparent Motion Click on the link to view
interactive simulation (requires Java plug in).
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Extracting
General Emergent Patterns
Up to this point we have extracted patterns that are tied to
specific basin and sub-basin structures of nodes. We have found either basins
for the whole system of nodes or sub-basins in a subset of nodes. We can find
patterns that are more general than those. Therefore, we will now turn to examples
where phase relations underlying apparent motion/stability will highlight patterns
that are neither basins nor sub-basins.
 |
| Figure 11. Historical Trace from second
exemplar. Figure shows two cycles of a basin of length L=50. There are no
sub-basins in the standard sense. A rich set of complex patterns, some stable,
others dynamic, emerge from adjusting the phase relations between representation
(in the form of a window) and the system's dynamics. |
Exemplar #2: Extracting
General Patterns Click on the link to Exemplar 2 and complete the
experiments suggested there.
Exemplar #3: Extracting
Layers of Emergent Waves Click to link to Exemplar 3
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Discussion
and Conclusions
We live in world of complex dynamic patterns whose perception
is fundamentally tied to motion. Even that which appears stable is stable only
relative to motion.
Physiological Nystagmus. [Note
3 ] Visually static objects in everyday life require the constant movement
of our eyes (physiological nystagmus) in order to be seen. Physiological nystagmus
is produced by tremors in the eye muscles. These tremors prevent the light from
stable objects from falling on the same retinal cells from moment to moment.
They do that by shifting the eye less than one degree of visual angle (which
is about the distance between two foveal cones) around 10 times a second. Experiments
with stabilized images (see Palmer, 1999, p. 521ff) indicate that if an image
moves synchronously with these tremors, the perception of that image disappears
after a few seconds. Bateson (1979, pp. 90, 91) uses nystagmus as a fundamental
example in arguing that difference is the basis of mental process. A static
relation between a static object and a static eye would produce no differences
and therefore no knowledge; this is in full concordance with the stabilized
image results. The perception disappears under such circumstances. Nystagmus
assures that the eye receives a continuous flow of differences from environmentally
static objects.
Enacting a World, Enacting a Mind. We are
proposing that the universe be conceived of as a web of dynamic relations some
of which set up a field of dynamic relations on the neural receptors of the
retina. This, however, is not a passive receiving, as the word "receptors"
taken in its strongest sense might connote. A living being has eye muscles that
actively twitch the eyes (nystagmus) so as to create motion relative to the
context in which it is enmeshed. Add to this other actions (e.g., saccades and
micro-saccades, to say nothing of a being's movement through the world). All
these movements, taken in relation to a dynamic (moving) universe, co-create
the retinal image. That is, the image is not simply received from the world
by the eye; the eye (i.e., the being) is an active partner in creating the retinal
image. The model we prefer is of dynamically active eyes AND a dynamically active
nervous system enacting a receptive field on the retina in relation to dynamic
relations ongoing in the universe. Varela, Thompson and Rosch (1993, p. 9) put
it this way: "We propose the term enactive to
emphasize the growing conviction that cognition is ... the enactment of a world
and a mind on the basis of ... actions that a being in the world performs."
What is proposed here is a more general and macro hypothesis
than those relating to physiological nystagmus, saccades, and micro-saccades,
though those phenomena form a basis for the structure of the model. The proposal
includes not just the co-creation of the retinal image but also what happens
after the retinal image is enacted. The proposal is that after
the retinal image is co-created there is a mechanism that can adjust phase relations
between the dynamics of the retinal image and a later processing, including
a person's experience. That is, we are proposing that a fundamental mechanism
of pattern perception is the ability to create and adjust phase relations. Nystagmus
is simply an early example of this process, an example that influences the retinal
image itself. And we are proposing that the neural mechanisms that adjust these
phase relations produce (as an artifact as it were) those phenomena so-called
Apparent Motion.
But the mechanism of nystagmus introduces a puzzle. To keep
sending signals neurons must be repeatedly stimulated; to gain this repeated
stimulation, nystagmus moves the light-senstive neurons back and forth (for
example) across the edge of stable object in the environment. As we mentioned,
that is one basis for proposing that difference is a fundamental of sensation
and therefore knowledge. The puzzle is that we don't see the edge of objects
trembling back and forth as two adjacent neurons are stimulated. Static objects
appear just that--static. How can they appear static when their perception requires
that they move relative to retinal nerves? Our answer here is a model in which
the phase relations between differing flows of neural activity is adjusted so
as to appear stable in much the same way as happened in Applet that could freeze
sub-basins and basins of a dynamic system. We propose that that which is actually
dynamically created moment by moment has "apparent stability"
in that sense. We propose that the sort of Boolean model used as a basis of
those demonstrations is a useful way of thinking about such apparent stability
in phase relatiosn; indeed, right now, it is the only we model know of to think
rigorously and to communicate explicitly and clearly about how an adjustment
of phase relations might produce apparent stability in the perception of form.
We are proposing that solid environmental edges that nystagmus would transform
into dynamic flows of difference could be re-stabilized by such a mechanism
as the one we are proposing. We are not proposing that Boolean systems are how
the nervous systems work; we are not proposing that Boolean nets are a "replica"
of the nervous system; rather we are proposing that Boolean systems are an idealized
and much reduced model that allows us to think about what the operating characteristics
of the nervous system might be.
That is, nystagmus creates a periodic motion in the retinal
image at a rate of about 10 frames (in our terms) per second. Therefore the
fact that objects are seen as stable is not explainable by nystagmus itself
since it is creating change not stability. Nystagmus by its nature assures that
a stable object is transformed into a dynamic object and thus that some other
mechanism is required to produce "apparent stability."
Two biological puzzles: This is a working
document, so we shall repeat another time: A biological puzzle is provoked by
the fact that a neuron needs repeated input to produce repeated output and we
know that stable objects disappear if they stimulate the same neuron (or sets
of neurons) across time. The solution to this puzzle is to produce the required
dynamics by eye tremors that produce periodic (probably cycle length = 2) inputs
from environmentally stable objects to a neuron. This solution produces a new
puzzle: Stable objects are perceived as stable not as trembling (perhaps alternating
signals from one cone and an adjacent cone). We propose that a phase relation
model can solve this second puzzle. We also use the nystagmus example as a way
of motivating the model, as a way of persuading the reader that it makes sense
that a phase relation mechansim could be an early, built-in perceptual function.
But the nystagmus example is is a minor example of apparent
stability, macro patterns are also extracted from the retinal image and are
of more interest to us. Let's discuss those cases.
In our Java applets we have given explicit control to users
so that they can change the phase relations between the dynamics of a simulated
universe and its representation on the screen. We are proposing that in an analogous
way phase relation adjustments might occur between the retinal image and experienced
representation. We found that adjusting such phase relations produced striking
examples of the extraction of patterns. There were a least three different kinds
of such pattern extractions--basins, sub-basins, and emergent, dynamic patterns
encapsulated in time.
We propose that the neural system has a mechanism that performs
adjustments of phase relations as a fundamental process for pattern perception.
We do not propose that the neural system has spatially defined
"windows" whose size can be adjusted. Rather we propose (that since
what our "windows" did was adjust phase relations) that the neural
system has mechanism that can and do adjust phase relations so that patterns
that could exist on the retinal image actually do come to exist. What do we
mean by that? We mean that if we take a static image, see Figure 11, from Exemplar
2, we cannot discern the images we CAN perceive by dynamically adjusting phase
relations (e.g., window size = 75, 77, 83). Those patterns emerge through the
action of adjusting phase relations. In a similar way, we propose that a retinal
pattern of simulation, supposing we could photograph it, would not show the
patterns that a person experiences. Rather, the patterns that a person perceives
are, in part at least, due to processes that shift phase relations between retinal
image and experienced representation in way a similar to the way that our window
size adjustments changed phase relations. [Note 4]
Marr's Computational Level Analysis Revisited.
Why does human (and perhaps other) neurology enable the "illusion"
of apparent motion? Did evolution teleologically aim for movies and video games?
Obviously (to us) not. We propose that the illusion of apparent motion is possible
because it is based on neural mechanisms which routinely adjust the kind of
phase relations that exist in apparent motion experiments and that are the basis
of a broad (yet unspecified) range of dynamic pattern perception phenomena.
What and Why. In David Marr's terms, we want
to specify the what and why of our proposed pattern perception mechanism. As
we stated above, a being needs to be able extract many distinct dynamic patterns
at once. Some of these are spatially coherent, others are spread out spatially.
Some are unmoving and stable, others are spatially disconnected flows of movement
(like hints of a current though a rapidly flowing river mostly obscured but
appearing here and there in the visual field of the kayaker). How do we form
coherent patterns from these fragmented dynamics on the retina?
Computational Constraints. We began this web
page with some broad constraints for a mechanism for the extraction of dynamic
pattern. For various reasons we would like our proposed mechanism to be able
to extract patterns of motion that are not spatially adjacent. We would also
like to be able to shift between different patterns of motion. In our example,
these spatially separated patterns of motion may be a collective like a herd
or a single coherent object, say a deer, that is masked by something irregular
like leaves. In short a useful requirement is that a coherent pattern does not
have to be coherently adjacent on the retinal image. The experiments with the
window size mechanism demonstrate the power of phase relation adjustments in
extracting patterns with these general constraints.
A second design constraint we mentioned at the outset is that
there be a way of distinguishing dynamic patterns, that there be a way of highlighting
one dynamic pattern and then shifting to another dynamic pattern and highlighting
it, or, even better, a way of having multiple highlights each pointing at different
dynamic patterns in the same scene. Again, the experiments with adjusting phase
relations through window size demonstrate the power of a putative neural mechanism
that could make analogous adjustments of phase relations.
Marr's Algorithmic Level of Analysis: E42
and Boolean networks in general.
Summary
Finding the patterns (basins, sub basins, and general
pattern) in the world around us is nontrivial and important. We have shown that
adjusting phase relations between a visual representation and the dynamics of
a system is a way to extract many different patterns within the system's dynamics.
We propose that the apparent motion phenomenon presupposes that neurology has
a way of of adjusting phase relations between the dynamics of the retinal image
and the final representation as experienced. Since that mechanism is in place,
we propose it as a candidate for the extraction of complex patterns from complex
systems.
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Notes
Note 1. Our approach is to frame perception as co-created by
the perceiver and what is perceived. Knowledge is neither here (in the perceiver)
nor there (in the object). Knowledge is the relationship between processes in
the universe and processes within a subset of the universe (the perceiver).
It's neither in one nor the other but rather in the relationship between the
two.
Often the information processing approach is characterized
as linear: the world to be a stable entity which supplies input to the perceiving
system and the perceiving system then extracts features of the world. The flow
of the arrows of influence are in one direction. In contrast, the co-created
view assumes that in general there is a feedback loop from the perceiver to
the world: the world supplies input which is transformed by a system and output
in a way that transforms the world which then supplies more input. In this case,
the arrows of influence are in both directions. See for example the issues raised
by Varela, Thompson, and Rosch (1993,p. 9, p. 134ff). See also, our comments
in the Discussion and Conclusions section of this page.
Note 2. The starting points that define the sets of iterations
{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12} and {13, 14, 15, 16} in Figure 3
are arbitrary. We could just as well have started the cycle on iteration 3 generating
a set of iterations defining a basin = {3, 4, 5, 6}. The TAO
Tool establishes an arbitrary standard for starting a basin (a standard
that is not used in Figure 3).
Note 3. "Physiological nystagmus is a high-frequency oscillation
of the eye (tremor) that serves to continuously shift the image on the retina,
thus calling fresh retinal receptors into operation. If an image is artificially
fixed on the retina it disappears, but physiological nystagmus causes every
point of the retinal image to move approximately the distance between two adjacent
foveal cones in 0.1 seconds. Physiological nystagmus actually occurs during
a fixation period, is involuntary and generally moves the eye less than 1°."
Reference: (http://www.diku.dk/~panic/eyegaze/node16.html)
Note 4. Within this Framework the Physical Analysis of Stimuli
Must Fail. Take your experience with the static image in Figure 11 and compare
it with your experience extracting patterns, dynamic and stable, from Exemplar
2, L=50. The sort of dynamic patterns that emerge are not to be found in a static
physical image (see Figure 11), rather these patterns are the emergent results
of shifting phase relations among various dynamics.
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References
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