Beyond Bouma's window: How to explain global aspects of crowding?
Fig 8
Wilson and Cowan network with end-stopped receptive fields: a. Structure of the network in [39] which we augmented with end-stopped receptive fields. An excitatory and an inhibitory layer of neurons are activated by the stimulus and interact with one another. The output of the excitatory layer is cross-correlated with a vernier template to measure performance. b. Output for the squares category (with psychometric function fitted on the squares category). In accordance with human results, performance is better in the 7 squares than in the 1 square case. c. Output for the irregular category (with psychometric function fitted on the squares category). Performance is marginally better in the 7 irregular1 than in the 1 irregular1 case. d. Output for the stars category (with psychometric function fitted on the squares category). There is no uncrowding for this stimulus. Uncrowding occurs only for specific kinds of stimuli, where element size regularities seem important. Further, performance depends strongly on which data are used for the training set (i.e., for fitting the psychometric function), suggestive of overfitting. e. Model output images. Columns are different stimuli: vernier, 1 square and 7 squares. The first row shows the stimuli, and the three subsequent rows show the model output for the short, medium and long end-stopped receptive fields. The crucial result is that the vernier is better represented in the short and medium populations in the 7 squares than in the 1 square conditions (i.e., uncrowding occurs). As mentioned, uncrowding occurred for very few stimuli categories. In cases that didn’t show uncrowding, the vernier representation deteriorated further when flankers were added (see results on the online repository). Note: the model outputs a cross-correlation quantifying how similar the model output is to the model output in the vernier alone condition (so the higher this cross-correlation, the better the performance). To make comparisons with human thresholds easier, we applied the same linking hypothesis as Hermens et al. [39]: we fitted a psychometric function to link model outputs to behavioural results, as explained in the main text.