Although the saturation of neurons in LGN might be explained by the need to optimize responses to the input contrasts and the need to match that to natural scene statistics (Tadmor & Tolhurst,
2000), this does not account for the shape of the functions found in later visual areas (Clatworthy et al.,
2003). In particular, the above finding that 20–25% of primate V1 neurons are nonmonotonic in their contrast response functions would suggest that contrast gain controls are only part of the story for nonlinear contrast responses. This raises the question of what other purpose (or purposes) they might serve.
An additional potential use for the saturating functions is in detecting the conjunction of certain features. Peirce and Taylor (
2006) recently described the existence of mechanisms responding selectively to the presence of a plaid, the conjunction of a pair of overlapping gratings. The mechanism we envisaged for such a detector is similar to that proposed by Olzak and Thomas (
1999) and involves a bank of linear, or quasilinear, filters followed by some output nonlinearity (Olzak and Thomas break the saturating nonlinearity into two separate nonlinearities, although for our more limited purposes, this is unnecessary). The nonlinear outputs of the first-level units are then summed by some conjunction detector.
In keeping with the literature, Olzak and Thomas (
1999) suggest that the nonlinearities are important for gain control and normalization. They are, however, also essential for another aspect of the mechanism they describe, namely, for the summing circuit to discriminate between the case of one input channel being stimulated at maximum contrast and that of two input channels each stimulated at 50% (see
Figure 4). For this method of discriminating a plaid from one of its components, some form of compressive nonlinearity is essential rather than merely optimal. Furthermore, the neurons in the input layer of the model (e.g., V1 cells) are likely to reduce their response when a second stimulus is present, through the effect of cross-orientation inhibition (e.g., Bonds,
1989; Freeman, Durand, Kiper, & Carandini,
2002; Morrone, Burr, & Maffei,
1982), which exacerbates the problem. These factors can be overcome by appropriate compressive nonlinearities on the outputs of the neurons potentially like those typically found in V1.