Title: Perception and Attention
1Perception and Attention
Cognitive Neuroscience and Embodied Intelligence
Based on book Cognition, Brain and Consciousness
ed. Bernard J. Baars courses taught by Prof.
Randall O'Reilly, University of Colorado,
and Prof. Wlodzislaw Duch, Uniwersytet Mikolaja
Kopernika and http//wikipedia.org/
http//grey.colorado.edu/CompCogNeuro/index.php/CE
CN_CU_Boulder_OReilly http//grey.colorado.edu/Com
pCogNeuro/index.php/Main_Page
Janusz A. Starzyk
2Image Recognition Problem
- How do receptive fields form?
- Why does the cortex encode oriented bars of
light? - Learning through correlations based on natural
scenes - How do we recognize objects?
- In different locations, sizes, rotations, and
images on the retina - Why does the visual system separate into
where/what pathways?
Spatial invariance is difficult, because
different signs occupy partly the same
receptive fields, and the same signs in different
parts of the retina which are rotated or of a
different size don't activate the same receptive
fields at all.
3Recognition
- Where does invariance come from?
- A 3D image based on 2D projections, what's
remembered is just one 3D representation (Marr
1982). - Syntactic approach form a whole from pieces of a
model.
Variant (Hinton 1981) look for transformations
(displacement, scaling, rotation), conform to the
canonical representation in the memory.
Problem many 2D objects can form different 3D
objects it's difficult to match the objects
because the search space to connect fragments
into a whole is too large do we really remember
3D objects?
4Gradual transformations
- In the brain, rotational invariance is strongly
limited eg. recognizing rotated faces. - Limited invariant object recognition can be
achieved thanks to gradual hierarchical parallel
transformations, increasing invariance and
creating increasingly complex features of
distributed representations.
- Goal not 3D, but to retain enough details to be
able to recognize objects in an invariant manner
after transformation. - Map seeking circuits in visual cognition (D. W.
Arathorn, 2002 )
5Object recognition model
- Model objecrec.proj has many hypercolumns, but
very simple ones. - We allow for regions and transformations between
LGN, V1, V2 and V4/IT. 20 images, but only
vertical/horizontal elements. - The element combinations on the IT level should
react invariably. - Output representation on the symbolic level.
Objects to be recognized, 3 out of 6 possible
segments.
Training on 0-17, test on 18-19. 4 sizes, 5, 7, 9
and 11 pixels.
6Object recognition model properties
- Hypercolumn the same signals, displaced and
partly overlapping. - Elements inside the hypercolumn compete, kWTA,
elements within the layer also compete
inhibition on a greater area. - Complete inhibition max (local, from the whole
layer). - Hypercolumns perform feature extraction across
the whole field of vision gt each hypercolumn can
share the same set of weights.
Objects are represented with the help of edges in
the LGN On/Off layer, each 16x16, wrapped edges
(spherical geometry). V1 has already-learned
representations of vertical and horizontal edges,
4x4 receptive fields in the LGN, there are 8
vertical and horizontal edges for "on" and 8 for
"off", together 16 4x4 units. V2 8x8
hypercolumns, signals from ¼ of the field of
vision, in a 4x4 matrix. V4/IT 10x10, entire
visual field, for such simple objects will
suffice.
7More properties
- Simulations without shared weights for the
hypercolumns give the same results, but they are
significantly more costly the Hebbian mechanism
leads to identical weights for columns with the
same (xi,yi). - Without Hebb, just error correction gives
completely different representations for the
hypercolumns, because it doesn't detect input
correlations.
Lack of horizontal connections the
representation of V1 is already set, so they're
not necessary and they slow down learning these
connections are important in completion
processes, illusions, recognizing obstructed
objects. Parameters Hebb 0.005, but between
V1/V2 there is only 0.001 because sharing weights
gives more frequent activations hence change.
Learning a rate of 0.01 gt 0.001 after 150
epochs in order to stabilize learning and speed
up the initial learning. Network construction
BuildNet, check connection properties, r.wt.
8Network exploration
- StepTrain, phase and StepTrain, phase
- The whole training requires many hours one
object can be in 4 sizes and 256 positions in a
16x16 grid, together there are 1024 images of one
object, 18 training objects, 18,432 images. - A trained network after 460 epochs x 150 objects
per epoch, after 30,000 presentations reaches
good results, fewer than 2 presentations/image.
net_updt gt cycle_updt will show learning over
the whole cycle on a trained network, phases
and are the same. How does activity of V2 and
V4 correlate with LGN inputs? Receptive fields
resulting from average activation can be seen
looking at the
correlation of x from LGN, with y from V2 or V4,
for each element of the 8x8 hypercolumn we
represent every ri
9Averaged activation receptive fields
- Activation of 16x16 LGN-on-center for one
hypercolumn V2, - 8x8 elements weight sharing gt others the same.
Elements from the lower left corner of V2,
receiving from ¼ of the whole LGN field. Bright
stripes selective unit for the edges (different
sizes) in a specific location. V2 elements don't
react to single lines only to their combinations.
Diffused parallel stripes reaction to the
same combinations in different locations.
10V2 off-center fields
- LGN-off-center activation for one V2 hypercolumn
weight sharing gt others the same.
These elements react more to the ends of shorter
lines. Elements reacting selectively take part
in the representation of many images, they detect
complex features shared among different objects.
11V2 correlations output objects
- The reaction of V2 units to detecting specific
objects, or V2 correlations averaged output 4x5
20 objects.
12V4 correlations output objects
- The reaction of V4 units to detecting specific
objects, or V4 correlations averaged output
4x5.
Greater selectivity than in V2, because of
greater invariance and reaction to more complex
features.
13Receptive field tests
- Observation of V2 and V4 reactions
- 4 probes used in the tests, each shown in all
positions of the left LGN input quadrant, or 8x8.
- V2 columns react to ¼ of the whole field.
- We calculate response on the V2/V4 level,
quadrants respond to specific test probes eg.
for probe 0, reactions to all 8x8 positions of
this probe are in the lower left quadrant for a
given element, all of its activity for 4 elements
is in the 16x16 square. -
14V2 tests for probes
- Hypercolumn V2 has 8x8 elements, the reactions of
each to 4 probes averaged across all positions
are in the small 16x16 squares.
15V4 tests for probes
- V4 has 10x10 elements, the reactions of each to 4
probes averaged across all positions are in the
small 16x16 squares. - Non-dependence on position can be seen by all the
yellow squares. - Some react to single features of probes, others
to the whole probe, and some to the presence of
elements which are in each probe.
16Statistical tests
- Table 8.1 summarizes the test results of
presenting 20 objects in all positions and the
reaction (for probe gt0.5) of V4 elements to these
presentations. - For one object in 256 possible positions and 4
sizes (1024 images) on level V4 there is on
average 10 different activations. - Detailed results are in objrec.swp_pre.err.
- Two unknown objects 18, 19 give only errors.
- Training with the goal of determining
generalizations presenting a new object one out
of 4 times in 36 out of 256 possible positions,
sizes of 5 or 9 pixels, so 14 of positions and
50 of sizes, 72 images (7). - After 60 training epochs, 150 objects/epoch,
learning constant 0.001, object 18 gave 85
correct answers out of 1024 images object 19
gave 66 correct answers, for small sizes.
17Dorsal pathway
- Recognition is a function of the ventral pathway,
now let's turn to the dorsal pathway. Functions
motion detection, localization, "where and how
to act, but also on what to focus attention and
how to shift attention from one object to
another. - Attention allows us to tie different properties
of an object into one whole, to solve the problem
of cohesion of sensations in spite of distributed
processing distributed activation gt features
related to each other, referring to one object. - Mainly an attention model, an emergent process
resulting from the structure and dynamic of
neural networks, mainly inhibition. - The effects of attention are universal, visible
in different situations.
What to pay attention to? Is this a well posed
question? Dogs bite, but not only Spot, not only
mongrels, not only black ones...
18Spatial attention model
- The interaction of spatial representations with
object recognition. - How does the ventral pathway interact with the
dorsal pathway? - Different spatial representations in the parietal
cortex, here is a simple map of spatial
relationships.
Posner task attention is directed to the cue,
which affects reaction times to a simple target,
depending on whether it appears in the same
region or a different region. Activation in a
specified location gt speed of recognition.
19Spatial attention model
- It's possible to mediate the attentional effects
by V1, but then inhibition will prevent switching
attention to another object. - Original Posner model the parietal cortex
"frees attention.
There is direct feedback (V4-V5?) between the
dorsal pathway and the ventral pathway plus a
path through V1. Spatial attention influences
recognition thicker lines stronger effect.
Model OReilly
Forced by the dorsal pathway (PC)
20Lesion studies
- Consequences of damage to early visual areas
- Different visual deficits can result from neural
damage at different levels of the visual
processing hierarchy. - Damage to the retina can result in monocular
blindness - Damage to the LGN can lead to loss of vision in
the contralateral visual field - Damage to a small part of V1 can lead to a
clearly defined scotoma. - Patients with damage to V1 area may still perform
better than chance forced choice discrimination
of objects (blindsight), although they claim they
see nothing. - Although the pathway from retina to LGN to V1
provides most of visual inputs to cortex, several
alternative subcortical pathways project to
extrastriate areas (MT, V3, V4), bypassing V1.
This may explain forced choice results.
21Lesion studies
- Extrastriate lesions damage outside area V1
- Motion blindness caused by a lesion to area MT
the world appears to be a series of still
snapshots. - Crossing street is dangerous since the patient
cannot tell how fast the cars are approaching. - Pouring a cap of coffee becomes a challenge since
she cannot tell how fast the liquid was rising.
22Lesion studies
- Cortical color blindness may be caused by a
lesion to area V4 - The world appears to be drained of color, just
shades of gray. - Patients can perceive the boundaries of colors
but cannot name them.
23Lesion studies
- Damage to ventral object areas
- Visual Agnosia Patients with visual agnosia
have difficulties with recognizing objects
because of impairments in basic perceptual
processing or higher-level recognition processes - Three types of agnosia apperceptive agnosia,
associative agnosia, and prosopagnosia - Agnosiato lack knowledge of
24Lesion studies
- Patients with apperceptive agnosia can detect the
appearance of visually presented items, but they
have difficulty perceiving their shape and cannot
recognize or name them. - Associative agnosia refers to the inability to
recognize objects, despite apparently intact
perception of the object. - Patient can copy a picture of the object but does
not recognize it. - A patient mistook his wife for a hat.
- Associative agnosia results from damage to
ventral temporal cortex.
25Lesion studies
- Patients with optic ataxia can perceive visual
orientation and recognize objects but cannot
perform visually guided actions. - Optic ataxia results from damage to parietal lobe
in dorsal pathway. - Patients with prosopagnosia are still able to
recognize objects well, but have great difficulty
recognizing faces. - All faces look the same
- Patients can recognize animals but not people
- Brodman area no. 37 is responsible for face
recognition - over 90 of cells in area 37 responds to faces
only.
26Lesion studies
- fMRI analysis of the face recognition process.
- Visible is activity in right hemisphere in lower
temporal area - Face recognition is important from evolutionary
perspective.
27Lesion studies
- Patients with achromatopsia are unable to
recognize colors. - This is often a result of damage to area V4 or
thalamus. -
28Lesion studies
- Daltonism refers to dichromacy characterized by a
lowered sensitivity to green light resulting in
an inability to distinguish green and
purplish-red. - It is an inherited defect in perception of red
and green, or in other words, red-green
colorblindness.
29Dorsal pathway lesions
- Lesions in the parietal cortex strongly affect
mechanisms of attention and spatial orientation,
extensive lesions in one hemisphere lead to
hemispatial neglect, the inability to focus
attention to the half of the visual space which
is opposite the lesion.
For small unilateral lesions, we can see a
noticeable slowing of attention switching to the
damaged side. For more severe cases, switching
attention is not possible. Bilateral lesions
lead to Balint's syndrome, difficulties with the
coordination of hand and eye movement,
simultanagnosia differences in attention
switching times in the Posner task are
small. Posner contended that this is a result of
attention binding, the inability to disengage,
but he didn't give the disengagement mechanism
it follows after focusing attention elsewhere a
better model assumes normal competition.
30Lesion studies
Self-portrait
- Damage to the posterior parietal lobe can lead to
a unilateral neglect, in which a patient
completely ignores or does not respond to objects
in the contralateral hemifield. - Patients with damaged spatial-temporal
recognition forget about half the space even
though they see it - Patients with right parietal damage may ignore
the left half of the visual field, eat half of
the food from the plate, or apply make-up to half
of the face.
31Unilateral Neglect
Horizontal line bisection task Copying drawings
32Lesion studies
- Bilateral lesions to parietal areas can lead to a
much more profound deficit called Balints
syndrome, which is primarily a disruption of
spatial attention. - It can be characterized by three main deficits
- Optic ataxia inability to point into a target
- Ocular apraxia inability to shift the gaze
- Simultanagnosia inability to perceive more than
one object in the visual field - People with Balints syndrome appear blind since
they only focus on one object and cannot shift
attention to anything else.
33Linking brain activity and visual experience
- Imagine you are sitting in a dark room and
looking at a jacket on a chair. - Since you cannot see well, your perception is
driven by your imagination you may perceive a
strange animal, a person, or a statue sitting
there. - When vision is ambiguous, perception falters or
alternates between different things. This is
known as multistable perception. - There are many examples of multistable patterns
or ambiguous figures that scientists use to
investigate these neural correlates of
consciousness.
34Linking brain activity and visual experience
You can cause binocular rivalry here using a pair
of red-green glasses
- Binocular rivalry what you see is what you get
activated - When two very different pattern are shown, one to
each eye, the brain cannot fuse them together
like it would normally do. - What happens is striking awareness of one
pattern last few seconds, then the other pattern
appears
35Linking brain activity and visual experience
- What happens in the brain during binocular
rivalry? - Tong et al. tackled this problem by focusing on
two category-selective areas in the ventral
temporal lobes (FFA and PPA). They used the
red-green filter glasses to present a face to one
eye and house to the other eye. Depending on
which image was perceived, they observed
activities either in FFA (face) or PPA (house).
36Linking brain activity and visual experience
- Strength of activation of FFA and PPA was the
same in the rivalry experiment as in the case of
stimulus alternation. - Another approach is to train monkey to report
which of two patterns is dominant during
binocular rivalry and measure activity of a
single neurons in different parts of the brain. - This experiment supports interactive model of
visual perception where feedback projection
modulates lower levels.
37Linking brain activity and visual experience
- Another way to separate physical stimulation and
perceptual awareness is a visual detection task. - A subject has to detect a particular pattern.
- The researcher makes the pattern harder and
harder to see. - Sometimes there is no pattern at all in the
picture. - Because this task gets difficult, people will
get it wrong sometimes. - What is interesting, that when there is false
positive (people see pattern even when it is not
there), there is strong activity in areas V1, V2,
and V3. - When the faint stimulus is not detected
activities in these areas are much weaker. - So, it does not matter what was presented, but
what does matter is what is happening in the
brain.
38Linking brain activity and visual experience
- Close your left eye, look directly at the cross
with your right eye and move the page up close to
your nose, then move it slowly away from your
face, while keeping your eye fixed on the cross.
At the right distance, which should be around 12
inches (30 cm) away from the page you should
notice the red dot vanish. - Likewise, notice how the black stripes now
fill-in they become joined and the red dot
vanishes. - Brain fills-in perception of the blind spot using
visual information from around the blind spot
constructive perception or perceptual filling-in.
39Linking brain activity and visual experience
Adelson's motion without movement
- Optical illusions are a result of our mind
filling-in patterns based on experience
40Linking brain activity and visual experience
Two color spirals
- Zoom in on the color spiral two colors are the
same shade of green.
41Linking brain activity and visual experience
- These pictures illustrate another type of
filling-in known as neon color spreading (a) and
visual phantoms (b). - Neon color spreading were found in V1 area.
- In a similar way apparent motion that we see in a
movie theater is another type of filling-in by
neural activities in V1 area.
42Linking brain activity and visual experience
- Neural correlates of object recognition
- In binocular rivalry, activity in the fusiform
face area and parahippocampal place area is
closely linked to the observers awareness of
faces and houses. - Other studies deals with visually masked objects
which can just barely be recognized. - Mooney face shown in figure can be recognized at
right orientation, while it is hard to recognized
at different orientations. - If the objects are recognized activity in ventral
temporal region is greater, while activity in V1
region shows no difference..
43Manipulations of visual awareness
- To find out causal relations between activities
in various brain regions it is useful to directly
stimulate the selected brain area with electrical
impulses. - One way is to use implants for instance in V1
area - Another way is to use transcranial magnetic
stimulation (TMS) - TMS involves rapidly generating a magnetic field
outside of the head to induce electrical activity
on the cortical surface. - Patients report various experiences including
out of body experience seeing its own body
from above. -
44Manipulations of visual awareness
- Unconscious perception
- We use the term unconscious perception when
subjects report not seeing a stimulus, but their
behavior or brain activity suggests that specific
information about the unperceived stimulus was
indeed processed by the brain. - When two different stimuli are flashed in quick
succession, the visual system can no longer
separate the two stimuli. - Instead, what people perceive is a mix, or a
fused blend of the two images. - They may respond to individual images in various
brain areas without being aware of seeing them
45Manipulations of visual awareness
- For instance, a quick presentation of a red
square followed by a green square can be
perceived as a yellow one. - Presentation of the images of the house or face
in complementary colors to different eyes has the
same effect of not seeing one. - However, the brain still responds to these unseen
patterns fusiform face area (FFA) to face and
parahippocampal place area (PPA) to house.
46Summary
- Vision is our most important sensory modality.
- We discussed the functional properties of neurons
as visual signals travel up from the retina to
the primary visual cortex and onward to higher
areas in the dorsal and ventral visual pathways. - Progressing up the visual pathway, receptive
fields gradually become larger and respond to
more complex stimuli, following the hierarchical
organization of the visual system. - V1 supports conscious vision, provides visual
features like orientation, motion and binocular
disparity. - V4 is important for color perception.
- MT is important for motion perception.
- Damage to dorsal pathway leads to optic ataxia
(neglect). - Damage to ventral temporal cortex leads to
impairments in object or face recognition. - In ventral temporal cortex some regions like LOC
have general role in object recognition, while
others like FFA and PPA are more specialized
47Attention model
- Model attn_simple.proj from page
http//grey.colorado.edu/CompCogNeuro/index.php/CE
CN1_AttnSimple
Stimuli single activations in one of 7 places,
for two objects (cue, target). 3 layers,
invariance increases, each element of the higher
layer combines 3 lower ones, from this V1 is
2x7, Spat1, Obj1 2x5, Spat2, Obj2 is 2x3, output
2x1. Reaction time time needed for the activity
of the target output connected with Obj2 to reach
0.6 Spat2 reacts only to location.
48Exploring the model
- r.wt will show connections.
The control panel has several scaling
parameters spat_obj 2, weight scaling
spatgtobj, obj_spat 0.5 (not shown) v1_spat 2,
stronger than v1_obj, light noise noise_var
0.0005 cue_dur 200 number of cycles during the
time when the cue is presented, which is followed
by the target. 3 situations for Multi_objs a)
two different objects, b) two identical objects,
c) two different objects in the same place.
act, step through all events several times
View Graph_log and Run recognition of
overlapping elements is generally slower view
text_log view batch_text_log, run batch.
49Posner Task
- env_type std_Posner
- view events 0 only target,
- 1 cue on the left, target on the left,
- 2 cue on the left, target on the right.
Activation is not zeroed after presentation of
the first stimulus, only after the whole group.
Display on, clear graph log, step. Batch will
repeat 10x, graph gt How does the network
shorten time on the same side? How does it
lengthen time on the opposite side? Test
spat_obj1 and v1_spat1.5, 1 Change to even_type
Close_Posner and check the effects.
50Simple model of the Posner task
- Object recognition times normalization scales
the results to the average adult time.
Cue Valid Invalid D
Adult 350 msec 390 msec 40 msec
Elderly 540 600 60
Patients 640 760 120
Elderly normalized 0.65 350 390 40
Patients normalized 0.55 350 418 68
51Lesion effects
- Patients with lesions even after normalization
have significantly longer times on the Posner
task, while the elderly after normalization have
differences just like normal adults.
Lesion in a model env_type Std_Posner, Lesion,
lesion_lay Spat1_2 to handicap both levels, the
number of locations half, number of elements
half, or 1 of 2.
number of elements half, or 1. Check (r.wt)
that the weights were zeroed two elements in the
right corner of Spat_1, and one from the upper
right corner of Spat_2 Batch to see the effect.
52Lesions reversed
- If we reverse the task and switch attention from
the side with the lesion to the other side.
Set env_type to Reverse_Posner differences are
significantly smaller (different scale).
Why? The normal side more easily competes with
the damaged side, so the differences decrease
in accord with the patient observations.
Bilateral lesions Std_Posner, Full for
location, half for a number of units, Batch The
effect is clear, but weaker than for unilateral
lesions.
53Full lesion
- Unilateral neglect with extensive damage.
Simulation Multi_obj, half for locations, full
for a number of units, Run
The network has a tendency to focus attention on
the undamaged side, regardless of the
presentation, neglecting half the area.
Patients with unilateral neglect are incapable
of picturing one side of the space only when the
other side has a strong stimulus competing for
attention (phenomenon of extinction). Similar
neglect for Std_Posner.
54Delay effects
- If after the cue we make a delay of about 500 ms,
there appears an "inhibition of return"
phenomenon, times partially reverse, a change in
location causes a faster reaction! This can be
simulated by lengthening the cue presentation
time and allowing for neuron fatigue
(accommodation).
Defaults, No_lesion, enc_type Std_Posner,
accommodate Change from 75 to 200 every 25 ms
55Object-based attentional effects
- Attentional effects connected with the
interaction of location and object recognition
will be similar to attentional effects connected
with the recognition of competing objects
(object-based attention). - Env_type Obj_attn, View Events
- Events 2 objects without cues.
- Cue in the central location,
- two objects in the central area, the
- network should focus on the first.
- Last two cue and 2 objects in the same place
yellow greater activation. - Defaults, Step the first object influences the
selection even if the second object is more
active.
56Summary
- Attention effects appear naturally in the model
as a result of competition between inhibition,
interconnection, the necessity of compromise. - Similar effects can be seen in different cortical
mechanisms. - Some psychological mechanisms (slowing attention)
show themselves to be unnecessary. - Attention effects supply specific information
allowing models to be fine-tuned to comply with
experiment results and allowing the use of these
models for other predictions there is also a lot
of neurophysiological data concerning attention.
- Limits of this model
- lack of effects connected with the thalamus
(Wager, OReilly), - very simple representation of objects (one
feature).
57Complex recognition model
- Model objectrec_multiobj.proj.gz, Chapt. 8.6.1
This model has two extra layers Spat1 connected
with V1 and Spat2 connected with V2. The Spat1
layer has an excitatory self-connection, allowing
it to focus on one object. The Target layer
shows which image was chosen and whether it
matches the output.
58Two objects in different places
- BuildNet, r.wt to check connections, receptive
fields in V1. - LoadNet, r.wt to check after training.
- Spat_1 reacts to 8x8 fields in V1, wrapping the
right onto the left - Spat_2 reacts to 16x16 fields in V2.
- Two objects (perpendicular lines) with the same
activation in different locations.
StepTest, object 12, presented in the lower
left corner. Initial oscillations, but gradual
advantage of one of the two locations and the
object found there influence on the lower
layers, in V1 remains the activation of only one.
View Test_log we can see the errors in
recognition, because the objects are small, and
the simultaneous activation of V1 introduces
confusion lack of a saccade mechanism leading
to the next, and not simultaneous activation.
Reducing fm_sapt1_scale from 1 to 0.01,
simultanagnosia, it's not possible to recognize
two objects, only one!
59Influence of spatial location
- Spatial activation can at the most modulate the
recognition process, otherwise we'll know where,
but not what. - This is ensured by inhibition and competition,
recognition is a combination of spatial
activation and strengthened features in lower
layers.
Switching objects we turn on accommodation of
neurons. Accommodate, InitStep, TestStep After
fatiguing the neurons with the first object,
attention moves to the second, after layer
Spat1. Errors are often made, this is not yet a
good control mechanism. Attention connected
with an object can also be seen in this
model. View, Test_Process_ctrl, environment from
vis_sim_test gt obj_attn_test (at bottom of
ScriptEnv). Apply, Reinit, Step. The network
recognizes object 17 Step network recognizes 12
and 17, stays with 17
60Some answers
- Why does the primary visual cortex react to
oriented edges? Because correlational learning in
a natural environment leads to this type of
detector. - Why does the visual system separate information
into the dorsal pathway and the ventral pathway? - Because signal transformations extract
qualitatively different information,
strengthening some contrasts and weakening
others. - Why does damage to the parietal cortex lead to
disorders of spatial orientation and attention
(neglect)? - Because attention is an emergent property of
systems with competition. - How do we recognize objects in different
locations, orientations, distances, with
different images projected on the retina? - Thanks to transformations, which create
distributed representations based on increasingly
complex and spatially invariant features.