A model of colour appearance based on efficient coding of natural images
Fig 2
Dynamic range clipping and gain adjustment by the SBL model.
a) human luminance and chromatic detection thresholds for sinewave gratings [37]. b) Clipping adjusts contrasts so that they cannot fall below the CSF at each spatial frequency (α, SUBTHRESHOLD), or above the saturation threshold (β, SATURATED). Subthreshold contrasts are subtracted, and signals at each spatial frequency are multiplied by a gain value—denoted by arrow length in (c)—so that on average natural images have equal power at each spatial frequency (whitening). The saturation threshold is calculated from the CSF and channel bandwidth, ε (4 in this example) at each spatial frequency. High and low spatial frequency channels therefore have low contrast sensitivity, but encode a large range of image contrasts, whereas intermediate spatial frequencies have high sensitivity and a low dynamic range. To demonstrate the clipping effects, we show an input image with sinewaves of different spatial frequencies and contrasts (d). (e) shows bandpass spatial filters and (f) highlights regions that are clipped or preserved. The overlap between neighbouring octaves (f) means that where contrasts are saturated for one channel, they are unlikely to be saturated for all neighbouring channels so that contrast differences are detectable even in high contrast scenes. Ultimately this shows how a system with a severely limited neural bandwidth of 15 contrast levels and peak sensitivity of ~200:1 can code for contrasts in natural scenes larger than 10,000:1. Note that the fine lines in these illustrative images suffer from moiré effects when viewed on a monitor, and we have artificially blurred the higher spatial frequencies in the input and output images to mitigate this effect. These effects were not present in the modelling, which did not use spatial frequencies that exceeded the kernel’s peak sensitivity.