Texture density adaptation and visual number revisited

Burr and Ross [1] have recently proposed that the visual dimension of number is itself directly adaptable. The aftereffect they describe is one that my colleagues and I previously used to investigate the perception of texture density [2–4]. Burr and Ross [1] argue that the effect is new because it concerns visual number, rather than texture density, but they did not report critical tests to support this claim. Here, I shall briefly describe the striking similarity between our prior work and that of Burr and Ross [1], and discuss how some of our results rule out Burr and Ross’s [1] interpretation that numerosity, and not density, is at play. I shall also provide a new demonstration that confirms that these effects are based on density, using a display that explicitly dissociates density from numerosity. Taken together, this line of arguments suggests that Burr and Ross’s [1] recent study may best be thought of as replicating support within a wellestablished line of work on texture density. There is a complex relationship between texture density, area and perceived numerosity. Some theories of numerosity perception have been based on using ‘filled’ area as the sole basis for numerosity discrimination [5], but a combination of area and density has seemed a reasonable model [3]. Critically, because Burr and Ross [1] did not vary the area of the texture displays to be compared, the numerosity judgments made in their experiments could have been made based on perceived relative texture density. Burr and Ross [1] may state that they had ruled out texture density, but all of the major results in their report replicate prior work by my colleagues in support of a density interpretation, some aspects of which are detailed here. In a 1997 paper, Alex Huk and I [4] reported our study of the extent to which aftereffects of perceived density could be understood in terms of prior theories of texture size adaptation [6]. We found they could not. We adapted people to differentially dense textures composed of elements with different Fourier spectra and then measured the extent to which judgments of relative density between other textures presented in the same region were affected. Although Burr and Ross [1] describe similar tests using differently sized and oriented bars (and report that the effects are maintained), our stimuli were more segregated in the Fourier domain. For example, rather than black and white squares on a gray background [1], we used high-pass or low-pass filtered black and white elements [4] (see Figure 1 for examples of the textures). Unlike Burr and Ross [1], we found that the aftereffect was systematically reduced (though not eliminated) when the Fourier spectra of adaptation and test stimuli overlapped least. Because apparent density (and numerosity) was reduced even when adaptation was to low-pass elements, our results showed that the effects were not spatial frequency shifts [4]. However, the Fourier specificity we found indicated that the effects were likely due to early cortical texture analyzers rather than abstract numeric representations. These results are consistent with the conclusion that perceived density of texture is an adaptable dimension that affects perceived numerosity, as we originally reported [3]. Because neither we nor Burr and Ross [1] have previously reported a direct manipulation of area, I correct that omission here with some data collected with displays like that shown in Figure 2, where the left texture is more numerous, but the right texture is more dense. This was accomplished by spreading the more numerous dots over a larger area. When the adapting displays thus dissociate number and density, it is the region of greater density that produces greater adaptation. This result is easy to observe using the figure, and was obtained experimentally with participants naïve to the hypotheses. Burr and Ross may respond that coding of visual number is spatially selective. In other words, they may suggest that number per some unit of cortical area is the adapted dimension. But local number is the same concept as density. Density differs from the perception of number of a whole collection. Rather than requiring that the visual system jump right to a numeric representation, density aftereffects can be explained by earlier visual processes. It is possible to represent a correlate of density as something like statistical kurtosis in the visual image [7] and this may be evaluated at various spatial scales. The computations required to represent this property of texture are probably