Fig. 1.

Illustration of the stimulus space and predictions for the discrimination performance of mechanisms based on the independent or fused use of depth cues. A: an observer is presented with 2 different slanted stimuli (anaglyph stereograms at the top), which we denote with red and blue. We can conceptualize detectors for these stimuli based on independent depth estimates from disparity and texture. These detectors yield an estimate for each stimulus with a certain probability density function. The outputs of these detectors are conceptualized as bivariate Gaussian probability distributions (3D plot below)—with 1 distribution for the blue stimulus and 1 for the red stimulus. The marginal projections (i.e., performance of the single-cue detectors) are illustrated on the walls of the 3D plot. B: a planar projection of the bivariate Gaussians (color saturation indicates probability density) to illustrate 2 possible computations when using the information from 2 depth cues. The red and blue stimuli could potentially be discriminated using either cue alone, but with some uncertainty (overlapping probability distributions). Two computations for reducing this uncertainty are illustrated: Independence—separation orthogonal to the optimal discriminating boundary (negative diagonal) and Fusion—multiplication of the probability densities associated with each cue. C: the idealized performance of a mechanism based on Fusion (top) or Independence (bottom). Illustrations on right depict neural implementations within single voxels for the extreme cases of these 2 alternative computations. Each sphere represents a neuronal population that encodes depth from either component cue (yellow and blue) or from a combination of cues (green). An intermediate implementation (not depicted here) would contain all of these population types within a voxel. T, texture; D, disparity.