Aaron Clarke amp Michael H Herzog Laboratory of Psychophysics Brain Mind Institute École Polytechnique Fédérale de Lausanne EPFL Switzerland Introduction Crowding is the inability to discriminate objects in clutter ID: 284914
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Slide1
How Recurrent Dynamics Explain Crowding
Aaron Clarke & Michael
H. Herzog Laboratory of Psychophysics, Brain Mind Institute, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
Introduction:
Crowding is the inability to discriminate objects in clutterVernier discrimination, for example, deteriorates when the Vernier is flanked by parallel linesPooling (Wilkinson et al., 1997) and lateral inhibition (Wilson, 1986) models predict that adding more parallel lines should worsen performance
S
S
Lateral Inhibition:
Spatial Pooling:
Inhibitory
Excitatory
Important points about the human data:
Effects of adding more lines depends critically on line-length
Information for lines of different lengths flows through separate channels and may be combined based on
a length-based
similarity metric
To model this we implement an end-stopped receptive field filter-bank sensitive to lines of different lengths
Connection strength between filters selective for different line-lengths depends on their similarity
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Parallel lines of the same length cause maximal interference
Lateral interactions between parallel receptive fields modulate the cells’ outputs
This may be modeled by weighting connections between cells with parallel receptive fields using a lateral-inhibitory association field
Figure 1. Human data. Performance worsens when equal-length flankers are added, but improves when shorter- or longer-length flankers are added (
Malania
et al., 2007).
2
16
10
20
30
40
50
60
Flanks (#)
Threshold (arcsec)
Human Data
Adding more
lines
can, however,
improve
performance
We propose that performance
worsens when the flankers group with the Vernier, but improves when the flankers segregate from the
Vernier
A recurrent architecture employing a Wilson-Cowan type model can explain these results because it allows local information to propagate globally over time
Global grouping arises from local, dynamical interactions without explicit grouping
rules
Conclusions:
Crowding cannot be explained by lateral inhibition or spatial pooling models
Crowding can be explained by a Wilson-Cowan type model
Global grouping arises through local dynamics without explicit grouping rules
Redundant information is suppressed while
inhomogeneities
are
highlighted
References
:
Malania
, M., Herzog, M.H.
&
Westheimer
, G. (2007). Grouping of contextual elements that affect
Vernier
thresholds.
Journal of Vision
. 7(2):1, 1-7.
Wilkinson, F., Wilson, H.R. &
Ellemberg
, D. (1997). Lateral interactions in peripherally viewed texture arrays.
J. Opt. Soc. Am. A
. 14(9): 2057-2068.
Wilson, H.R. (1986). Responses of Spatial Mechanisms Can Explain Hyperacuity.
Vision Research
. 26(3):453-469.
Wilson, H.R.
&
Cowan, J.D.
(1972). Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons.
Biophysical Journal
. 12:1-24
.
http://lpsy.epfl.ch This
work was supported by the
ProDoc
project
“Crowds in Crowding"
of the Swiss National Science Foundation (
SNF) Corresponding author: aaron.clarke@epfl.ch
Model Specifics:
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I
Excitatory
Inhibitory
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I
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Excitatory Layer
Inhibitory Layer
End-stopped receptive field array
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Input Image
Linking Hypothesis:
0.75
0.8
0.85
0.9
0.95
1
15
20
25
30
35
40
45
Cross-Correlation With
Vernier Template
Vernier Threshold (arc sec)
Data
Fit
•X
•X
2
16
10
20
30
40
50
60
Flanks (#)
Threshold (arcsec)
Model Data
No flanks
Short
Equal
Long
Figure 2. In the end the summed cross-correlations are passed
through a sigmoidal non-linearity
.
Figure 3. The model nicely predicts the pattern of results obtained by
Malania
et al. (2007).
Cross-correlate un-flanked Vernier template with the flanked Vernier images
Sum the cross-correlation outputs over space and filter sizes
The
model suppresses homogeneities
while
highlighting
inhomogeneities
Model
outputs for each image
at each
filter size are cross-correlated
(.x) with
the outputs for the un-flanked Vernier and summed over filter
sizes
The equal-length flankers outputs correlate poorly with the un-flanked Vernier outputs (e.g. compare black outlined image with green outlined image)
The long-length flankers outputs correlate well with the un-flanked Vernier outputs (e.g. compare black outlined image with blue outlined image)
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