The other approach to modeling crowding (and texture perception) essentially says that the primitives of crowding are not atoms at all, but rather stuff (Adelson,
2001). This other class of models operates on continuous features, such as the outputs of a cascade of filtering operations and nonlinearities. For example, a number of researchers have attempted to reason about the implications of a simple pooling model that averages continuous feature measurements over a pooling region (Levi & Carney,
2009; Manassi, Herzog, Sayim, & Herzog,
2012; Manassi, Sayim, & Herzog,
2013; Saarela, Sayim, Westheimer, & Herzog,
2009). However, this simple pooling model, conceived of as pooling within at most a handful of feature bands, has been disproven by a number of experiments (Kooi, Toet, Tripathy, & Levi,
1994; Levi & Carney,
2009; Levi, Klein, & Hariharan,
2002; Livne & Sagi,
2007; Malania, Herzog, & Westheimer,
2007; Manassi et al.,
2012; Manassi et al.,
2013; Nandy & Tjan,
2012; Sayim, Westheimer, & Herzog,
2010; van den Berg, Roerdink, & Cornelissen,
2007), and serves more as a straw man than as a real contender to model crowding. In contrast, our Texture Tiling Model (TTM) represents its inputs with a high dimensional set of local image statistics (stuff), known to be good for capturing texture appearance (Balas,
2006; Portilla & Simoncelli,
2000). This model measures correlations of the magnitude of responses of oriented V1-like wavelets across differences in orientation, neighboring positions, scale, and phase correlation across scale, as well as the marginal distribution of luminance and luminance autocorrelation (Rosenholtz, Huang, & Ehinger,
2012; Rosenholtz, Huang, Raj, Balas, & Ilie,
2012). A similar model, measuring the same set of statistics, has been put forward to describe early visual cortex (Freeman & Simoncelli,
2011; Freeman, Ziemba, Heeger, Simoncelli, & Movshon,
2013). We have previously shown that this model can predict the results of a number of crowding experiments (Balas et al.,
2009), among other phenomena (Rosenholtz, Huang, Raj, et al.,
2012).