The existence of complex (non-Fourier, second-order) channels is suggested by some characteristics of segregation perceived between regions distinguished by visual texture. These complex channels consist of two linear-filtering stages separated by a rectification-type non-linearity. We have investigated (i) the spatial frequency selectivity and orientation selectivity of their first-stage filters; (ii) the relationship between the preferred values of orientation and spatial frequency at the first and second filters; (iii) spatial pooling and its implications for the non-linearity at the middle of the complex channel; and (iv) the dynamics of complex and simple linear channels. An intensive non-linearity is also necessary to explain perceived region segregation. This intensive non-linearity might arise from an early local non-linearity preceding the channels (perhaps retinal light adaptation) or from normalization among the channels themselves (perhaps due to intracortical inhibition). Deciding between these two candidates has been more difficult than we had hoped. It appears that: (i) this intensive non-linearity operates for both simple and complex channels; (ii) the effects on it of changing mean luminance or spatial scale may be accounted for by a sensitivity parameter; (iii) it can be dramatically compressive even at contrasts less than 25% for high mean luminances and large scales; and (iv) at even lower contrasts there is an accelerating non-linearity that acts before the second filter of the complex channels.