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Albert Ahumada; Cortical under-sampling and crowding. Journal of Vision 2008;8(17):41. doi: 10.1167/8.17.41.
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Crowding effects in the periphery have been the focus of many recent studies (Pelli, Cavanagh, Desimone, Tjan, and Treisman, 2007). Perhaps cortical under-sampling contributes strongly to this effect, and crowding is in part an aliasing effect. Optical aliasing can occur in the periphery because the optics pass higher frequencies than the cone array Nyquist frequency (Smith and Cass, 1987). It is also known while the central fovea has about 2 ganglion cells per cone, that even in the near periphery there are increasingly fewer ganglion cells than cones, and that some have small receptive fields (Henrickson, 2004). It appears that the situation is even worse at the cortical level. Tabernero and Ahumada (1992) found that when the cortical representation under-samples the visual signal, a translation-invariance learning process cannot work, leaving the peripheral representations location specific. As a first look at the possible consequences of cortical under-sampling, a version of the Cortex Transform (Watson, 1987) was used to represent letter images. This transform has the convenient, but perhaps unrealistic, property that the post-sampling reconstruction can be done by filtering the channels with their same filters and then adding them back together. Under-sampling was done with random deletion of the transform coefficients. The reconstructed under-sampled letters appear in a halo of noise. However, when the letters are placed close together so the noise halos overlap the letters, there is no striking masking effect. Perhaps strong peripheral inhibitory processes (Xing and Heeger, 2000) are needed to remove the noise, resulting in crowding effects.
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