Neural model of lightness scaling in the staircase Gelb illusion.

In the staircase Gelb illusion, the range of perceived reflectances of grayscale papers arranged from darkest to lightest in a spotlight is highly compressed relative to the range of actual paper reflectances: close to the cube-root compression predicted from applying Stevens' brightness law to the reflected light. Reordering the papers reveals additional effects of spatial paper arrangement on lightness. Here, I model both the perceptual scaling and spatial arrangement effects with a computational neural model based on the principle of edge integration (Rudd, J Vision, 2013; J Percept Imaging, 2020). Edge contrasts are encoded by ON and OFF cells described by Naka-Rushton input-output functions having different parameters for ON and OFF cells. These neural responses are subsequently log-transformed, then integrated across space, to compute lightness. Edges are thus neurally weighted on the basis of two independent factors: 1) distance of the edge from the paper whose lightness is computed, and 2) the edge contrast polarity (whether the edge is a luminance increment or decrement in the target direction). Polarity-dependent weightings of 0.27 for increments and 1.0 for decrements were derived from physiological ON and OFF cell data from macaque LGN. Distance-dependence was modeled as an exponential decay with space constant 1.78 deg. The model accounts to within <5% error for lightness matches made to staircase Gelb and reordered grayscale surfaces in an actual 3D environment.