Figure 4. Surround divisive normalization is optimal only for statistically homogeneous stimuli.

(a) Left: Neighboring locations in homogeneous images contain redundant information. This produces a bowtie-shaped dependency in the outputs of filters representing the RF and surround. The dependency is illustrated in the conditional histogram (bottom): each column represents the histogram of surround filters’ outputs (position on the ordinate), given a particular output of the RF filters (abscissa). Lighter shades of gray indicate larger occurrence probability. Thin and thick lines represent conditional mean ± conditional standard deviation, respectively. Right: Neighboring locations in heterogeneous regions are independent, as evidenced by the absence of any structure in the conditional histogram (bottom). (b) Surround normalization reduces redundancy between RF and surround. Optimality requires that the normalization is turned off when the stimulus is heterogeneous. Schematic is adapted from ref. 27.