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How Recurrent Dynamics Explain Crowding How Recurrent Dynamics Explain Crowding

How Recurrent Dynamics Explain Crowding - PowerPoint Presentation

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How Recurrent Dynamics Explain Crowding - PPT Presentation

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

model vernier length outputs vernier model outputs length flanked flankers image lateral wilson lines inhibitory parallel data cross crowding

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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

W

Btw

W

Btw

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:

E

I

E

I

E

I

Excitatory

Inhibitory

E

I

E

I

E

I

E

I

E

I

E

I

Excitatory Layer

Inhibitory Layer

End-stopped receptive field array

•X

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)

W

Btw