Optimal combination of illusory and luminance-defined 3-D surfaces: A role for ambiguity

The shape of the illusory surface in stereoscopic Kanizsa figures is determined by the interpolation of depth from the luminance edges of adjacent inducing elements. Despite ambiguity in the position of illusory boundaries, observers reliably perceive a coherent three-dimensional (3-D) surface. However, this ambiguity may contribute additional uncertainty to the depth percept beyond what is expected from measurement noise alone. We evaluated the intrinsic ambiguity of illusory boundaries by using a cue-combination paradigm to measure the reliability of depth percepts elicited by stereoscopic illusory surfaces. We assessed the accuracy and precision of depth percepts using 3-D Kanizsa figures relative to luminance-defined surfaces. The location of the surface peak was defined by illusory boundaries, luminance-defined edges, or both. Accuracy and precision were assessed using a depth-discrimination paradigm. A maximum likelihood linear cue combination model was used to evaluate the relative contribution of illusory and luminance-defined signals to the perceived depth of the combined surface. Our analysis showed that the standard deviation of depth estimates was consistent with an optimal cue combination model, but the points of subjective equality indicated that observers consistently underweighted the contribution of illusory boundaries. This systematic underweighting may reflect a combination rule that attributes additional intrinsic ambiguity to the location of the illusory boundary. Although previous studies show that illusory and luminance-defined contours share many perceptual similarities, our model suggests that ambiguity plays a larger role in the perceptual representation of illusory contours than of luminance-defined contours.