Shrinking Bouma's window: How to model crowding in dense displays

In crowding, perception of a target deteriorates in the presence of nearby flankers. Traditionally, it is thought that visual crowding obeys Bouma's law, i.e., all elements within a certain distance interfere with the target, and that adding more elements always leads to stronger crowding. Crowding is predominantly studied using sparse displays (a target surrounded by a few flankers). However, many studies have shown that this approach leads to wrong conclusions about human vision. Van der Burg and colleagues proposed a paradigm to measure crowding in dense displays using genetic algorithms. Displays were selected and combined over several generations to maximize human performance. In contrast to Bouma's law, only the target's nearest neighbours affected performance. Here, we tested various models to explain these results. We used the same genetic algorithm, but instead of selecting displays based on human performance we selected displays based on the model's outputs. We found that all models based on the traditional feedforward pooling framework of vision were unable to reproduce human behaviour. In contrast, all models involving a dedicated grouping stage explained the results successfully. We show how traditional models can be improved by adding a grouping stage. Author summary To understand human vision, psychophysical research usually focuses on simple stimuli. Vision is often described as a cascade of feed-forward computations in which local features detectors pool information along the processing hierarchy to form complex and abstract features. Crowding is can be modelled within this framework by the pooling of information from one processing stage to the next. This naturally explains Bouma's law, a hallmark of crowding according to which only elements within a certain region, often proposed to be half the target eccentricity, interfere with the target. However, pooling models are strongly challenged by recent experimental results, because Bouma's law does not hold for more complex stimuli. Visual elements far beyond Bouma's window can increase or alleviate crowding. In addition, Van der Burg and colleagues showed that only the nearest neighbours interfere with the target in dense displays. Hence, Bouma's window can shrink too. Here, we aimed at modelling the range of crowding in dense displays. From previous studies, we know that visual grouping cannot be explained without grouping and segmentation. We compared the performance of different models of vision to the human data of Van der Burg and colleagues. We found that all models based on the traditional pooling framework of vision failed to reproduce the human data, whereas all models that included grouping and segmentation processes were successful in this respect. We concluded that grouping and segmentation processes naturally and consistently explain the difference between simple and complex displays in vision paradigms.