Spatial, temporal and spectral pre-processing for colour vision

Fourier transforms of the spectral radiance of natural objects were investigated. The average spectral power spectrum S$_{c}$(f$_{c}$) is well described by S$_{c}$(f$_{c}$) = exp (-$\beta $f$_{c}$), with f$_{c}$ the spectral frequency (cycles $\mu $m$^{-1}$), and $\beta $ = 0.419$\pm $0.097 $\mu $m. Average spectral contrast {c$_{c}$ = [$\sum_{f_{c}\neq 0}$ S$_{c}$(f$_{c}$)/S$_{c}$(0)]$^{\frac{1}{2}}$} was 0.224$\pm $0.127. Optimal filters for colour pre-processing were derived using a recently developed theory of early vision (van Hateren (J. comp. Physiol. A 171, 157 (1992))). The theory assumes that the surrounding world is first sampled spatially, temporally and spectrally by an array of pre-filters, and subsequently filtered by an array of neural filters that maximize the information delivered to an array of noisy information channels. These optimal filters show lateral inhibition and spectral opponency for high signal-to-noise ratios (SNRS) and low temporal frequencies (f$_{t}$). Decreasing SNR or increasing f$_{t}$ eventually produce filters that are spatially and spectrally low-pass, resulting in a visual system lacking lateral inhibition and spectral opponency. The optimal filters for high SNR lead to responses in the spectral channels approximately independent of the spectrum of the illumination, which is a first step towards colour constancy. Finally, the optimal spectral pre-filter has a half-width of about 100 nm; this is close to that of the common rhodopsins.