Seeing number using texture: How summary statistics account for reductions in perceived numerosity in the visual periphery

Peripheral visual perception is characterized by reduced information about appearance due to constraints on how image structure is represented. Visual crowding is a consequence of excessive integration in the visual periphery. Basic phenomenology of visual crowding and other tasks have been successfully accounted for by a summary-statistic model of pooling, suggesting that texture-like processing is useful for how information is reduced in peripheral vision. I attempt to extend the scope of this model by examining a property of peripheral vision: reduced perceived numerosity in the periphery. I demonstrate that a summary-statistic model of peripheral appearance accounts for reduced numerosity in peripherally viewed arrays of randomly placed dots, but does not account for observed effects of dot clustering within such arrays. The model thus offers a limited account of how numerosity is perceived in the visual periphery. I also demonstrate that the model predicts that numerosity estimation is sensitive to element shape, which represents a novel prediction regarding the phenomenology of peripheral numerosity perception. Finally, I discuss ways to extend the model to a broader range of behavior and the potential for using the model to make further predictions about how number is perceived in untested scenarios in peripheral vision.