The contrast sensitivity function of the human eye was first measured by Westheimer (1960) and by Arnulf and Dupuy (1960). Campbell and Green (1965) compared the optical and neural contributions to the contrast sensitivity function. They concluded that for a pupil diameter less than 2.4 mm the attenuation of high spatial frequencies was mainly due to neural factors unless the aberrations were large. It is possible to see the contrast sensitivity
Figure. 3.4: The response functions of the four types of receptive fields in the visual system. These are sensitive to a) a bright bar on a dark background, b) a dark bar on a bright background, c) a bright edge to the left of a dark edge and d) a dark edge to the left of a bright edge. a) and b) constitute the even-symmetric (bar-selective) mechanisms whereas c) and d) are the odd-symmetric (edge-selective) mechanisms. These plots indicate the relative response of a neuron to a point of light as a function of position. Negative regions on these plots indicate an inhibitory effect on the neuron’s response whereas the positive regions indicate an excitatory effect. It can also be thought of as the stimulus intensity pattern that would produce the greatest firing rate of the neuron. Diagrams are plotted using equations derived by Marˇcelja (1980).
function of one’s own eye by looking at Figure 3.5, which exhibits a logarithmic variation in contrast against a logarithmic variation in spatial frequency. In this figure a curve can be seen above which the fringes cannot be discerned (see Chapter 2 for the equation describing this curve).
Blakemore and Campbell (1969) were the first to suggest that the human visual system
Figure. 3.5: Campbell-Robson contrast sensitivity chart demonstrating contrast sensitivity as a function of spatial frequency (Campbell & Robson, 1964, 1968). Spatial frequency increases logarithmically from left to right and contrast increases logarithmically from top to bottom. A curve can be seen above which the fringes cannot be discerned. Note that the appearance of this chart depends on viewing distance as well as the MTF of the printer or monitor in which it is displayed.
might perform a kind of Fourier analysis. There are a number of separate channels in the visual system that are selectively sensitive to a relatively narrow band of spatial frequencies (Blakemore & Campbell, 1969; Campbell & Robson, 1968; Graham & Nachmias, 1971). The detection of a spatial frequency, using a grating for example, is mediated by the activation of overlapping channels. The channel most closely aligned to the grating frequency will be
activated first and with the highest neuron firing rate, giving a peak response. The response of this channel will determine the contrast threshold at which the spatial frequency can be detected. It has been argued that the contrast sensitivity function is in fact an envelope of a number of these channels. The centre-surround receptive field is well suited to detecting spatial frequencies and it is thought that this occurs in cortical simple cells (i.e., the bar and edge detectors). The spatial distribution of responsivity of both the centre and surround can be described by Gaussian functions. The responsivity of a ganglion cell is the difference of these Gaussians, as shown by Figure 3.6. The centre and surround represent two low-pass filters with different cut-off frequencies and the difference of these two filters is a band-pass filter. In the frequency domain the responsivity is also a difference of Gaussians (the Fourier transform of a Gaussian is a Gaussian), which when expressed on a logarithmic scale leads to the classic contrast sensitivity curve shown in Figure 3.7 and demonstrated by Figure 3.5. The surround is typically less responsive than the centre at very low spatial frequencies and so the difference is never actually zero, even at a spatial frequency of zero (Enroth-Cugell & Robson, 1984).
Letter recognition
Solomon and Pelli (1994) tested the role of frequency channels in letter recognition by superimposing letters over noise characterised by a certain band of spatial frequencies. This work revealed that a noise frequency of 3 cycles per letter masked letter identification with the most efficiency, indicating that letter identification is mediated by a channel sensitive to this frequency. Subjects always use the same one- or two- octave-wide spatial frequency band (in cycles per letter not cycles per degree) for letter identification. When the letter is band-pass filtered the channel frequency scales with the centre frequency of the pass-band (Majaj, Pelli, Kurshan, & Palomares, 2002). This may signify a difference between the spa- tial frequency channel that mediates sharp text and text viewed with an aberration, which acts to spatially filter the image.
Figure. 3.6: Spatial weighting function of the centre and surround of a receptive field (Enroth-Cugell & Robson, 1984). The short dashes correspond to the centre and the long dashes correspond to the surround. The surround is inverted so that the solid line represents the sum of the two Gaussian components (rather than the difference of Gaussians). Three gratings with different spatial frequencies are shown in a), b) and c).
Figure. 3.7: Spatial frequency responsivity function of the centre and surround of a receptive field (Enroth-Cugell & Robson, 1984). As in Figure 3.6 the short dashes correspond to the centre and the long dashes correspond to the surround. The solid line represents the spatial frequency responsivity of a typical ganglion cell which is the difference of the two Gaussian components. The spatial frequency of the three gratings from Figure 3.6 are indicated by a), b) and c).