How Recurrent Dynamics Explain Crowding Aaron Clarke1, Frouke Hermens2 and Michael H. Herzog1

1 Laboratory of Psychophysics, Brain Mind Institute, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

2 Laboratory of Experimental Psychology, University of Leuven (K.U. Leuven), Tiensestraat 102 – box 3711, Leuven B-3000 Belgium

http://lpsy.epfl.ch This work was supported by the ProDoc project "Processes of Perception" of the Swiss National Science Foundation (SNF) Corresponding author: aaron.clarke@epfl.ch

Introduction:

• Crowding is the inability to discriminate objects in clutter.

• Vernier discrimination, for example, deteriorates when the Vernier is flanked by parallel lines.

• Pooling and lateral inhibition models predict that adding more parallel lines worsens performance.

• Temporal dynamics:

Conclusions:• Crowding cannot be explained by lateral inhibition or

spatial pooling models.• Crowding can be explained via a Wilson-Cowan type

model.

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Figure 1. Left: Human data from Malania et al. (2007). Right: Model results for the same conditions.

Model Specifics:

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Figure 2. The input image is first convolved with an array of end-stopped receptive fields and then the outputs interact through non-linear dynamics. Connections between layers are Gaussian-weighted.

Figure 3. Excitatory (left) and inhibitory (right) connection weights within a layer as a function of spatial position.

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Figure 5. Model inputs (left column), and outputs (right 3 columns) at readout time. Comparing the Vernier output subplot outlined in black, with the long-flanker output subplot outlined in blue, it is evident that the area of the long-flanker subplot containing the Vernier is largely spared. In contrast, it is evident that for the equal-length-flanker condition much of the Vernier is inhibited. This explains why model performance is better with long flankers than with equal-length flankers.

References:

• Wilson, H.R. & Cowan, J.D. (1972). Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophysical Journal. 12:1-24.

• Malania, M., Herzog, M.H. and Westheimer, G. (2007). Grouping of contextual elements that affect vernier thresholds. Journal of Vision. 7(2):1, 1-7.

• However, more lines can improve performance.• Here, we use a Wilson-Cowan type model to

show why more lines can improve performance.