Probability summation for multiple patches of luminance modulation.

When components of a compound pattern stimulate different visual mechanisms, psychophysical performance typically improves by a small amount consistent with probability summation amongst independent detectors. Here we extend previous summation experiments by (i) plotting full psychometric functions; and (ii) using compound stimuli with components that varied in up to three stimulus dimensions: spatial frequency (1, 4, 5 or 11 c/deg), orientation (0 degrees, +/-45 degrees ), and position. Stimulus components were isolated circular sine-phase patches of grating centred on up to four corners of an imaginary square surrounding a fixation-point. Combinations of component patches produced compound stimuli made from up to 16 components that differed in various combinations of the three stimulus dimensions. Other than when the spatial frequency was 11 c/deg, results were well described using: (i) probabilistic summation of individual psychometric functions; (ii) the Quick pooling formula; and (iii) the signal detection analysis for 2IFC developed by Tyler and Chen (2000) [Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation (under review)]. We conclude that in general, nonlinear spatial summation is consistent with probabilistic summation across independent detecting mechanisms that vary in spatial frequency (a range of at least 1-5 c/deg), orientation (a range of 90 degrees ) and position (a range of at least 24 cycles at 4 c/deg). In further experiments, results were found to be consistent with probability summation for pairs of orthogonally oriented step-edge stimuli and a matrix of randomly oriented 11 c/deg sine-wave patches. This casts doubt on the generality of a recent suggestion that local interactions between colinearly oriented detectors within a spatial neighbourhood of around four cycles may contribute to nonlinear spatial summation [Bonneh & Sagi, 1998; Vision Research, 38, 3541-3553].