Fig. 3

Psychophysical measurements of cue integration. a Single- and (congruent/incongruent) combined-cue stimuli designed for use with red–cyan anaglyphs. b Presentation sequence used to psychophysically assess cue integration: observers judged whether the first or second stimulus was more slanted. c Behavioural sensitivity (the reciprocal of the just noticeable difference in degrees) for slant defined by disparity, texture, and congruent and incongruent combinations of these cues. We assessed the statistical significance in congruent and incongruent conditions using RM ANOVAs. In both cases we found significant main effects of stimulus type (congruent: F_2,34 = 7.92, P = 0.002; incongruent: F_2,28 = 10.68, P = 0.002). We followed this with paired t-tests to compare individual stimulus conditions; asterisks highlight significant differences P < 0.05 (congruent disparity: t₁₈ = 3.85, P = 0.001; congruent texture: t₁₈ = 2.54, P = 0.02; incongruent disparity: t₁₄ = 3.58, P = 0.003; incongruent texture: t₁₄ = 2.16, P = 0.048). Performance in the single-cue conditions was used to generate predictions of incongruent-cue sensitivity based on the maximum likelihood model, the normalization model²⁵ and our proscriptive integration model. As explained in the Procedure section of the Methods, using different slant angles was necessary for the congruent and incongruent stimulus conditions; in particular, to ensure robust behaviour, sensitivity had to be much higher for one cue than the other. This accounts for the differences in sensitivity observed between single cues in congruent (left three bars) vs. incongruent (right three bars) stimulus conditions. To ensure that reduced sensitivity for incongruent cues (relative to texture) was not due to using a different slant angle, we confirmed that, as expected, sensitivity was also better for congruent cues at higher slant angles. Semi-transparent black dots indicate individual data points and error bars indicate SEM