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Walter Makous; Picture size and critical band. Journal of Vision 2004;4(11):63. doi: https://doi.org/10.1167/4.11.63.
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Here I offer an explanation of the effect of stimulus size on the critical bands for faces and letters.
Humans use a band of frequencies 2 to 3 octaves wide to discriminate different faces and letters, but the location of the band depends on the size of the image. A survey of the literature turned up 10 studies of the critical band for identifying faces. Equation 1 accounts for 74% of the variance in these studies:
fc = c1/S0.70, (1)
where fc is the center frequency of the critical band, and S is the size of the image. For letters, the exponent is 0.67.
Increasing image size moves the spectrum left and the amplitude up in proportion to the increase. The upward shift is,
Af = c2S. (2)
The amplitude spectrum of human faces, Af, follows the equation,
Af = c3/f a, (3)
where f is spatial frequency. For 171 images of faces in the literature, a is 1.42. Combining equations 2 and 3 yields:
fA = c4/S0.71. (4)
Increasing the size of an image has the net effect of reducing the amplitudes in what was the critical band, and so the visual system must go to lower frequencies where the amplitudes are sufficient to allow discrimination. Eq. 4 tells how much lower it must go.
The frequency band used to discriminate faces and letters have very similar amplitude spectra (a is 1.36 between 4.2 and 8.4 c/ch), for exchanging their spectra has little effect on the critical bands used. Hence, the explanation of the effect of size on the critical band for letters may be analogous to that for faces.
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